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Eureka, Missouri

Eureka is a city mainly in St. Louis County, with a small portion in Jefferson County, Missouri, adjacent to Wildwood and Pacific. It is in the extreme southwest of the Greater St. Louis metro area. As of the 2020 census, the city had a population of 11,646. Since 1971, Eureka has been known as the home of the amusement park Six Flags St. Louis.

History
The area's first known inhabitants were Shawnee Native Americans on the banks of the Meramec River; archaeological artifacts can still be found today as evidence of their past occupation of the area.

The village of Eureka was platted in 1858 along the route of the Pacific Railroad. By 1890, the village consisted of about 100 homes. As railroad workers cleared the way for the track, they saw level land with little to clear and declared "Eureka!" which is Greek for "I've found it." Thus, Eureka was founded. In 1898, Eureka became home to the St. Louis Children's Industrial Farm, established to give children from St. Louis tenement neighborhoods a chance to experience life in a rural setting. It later became Camp Wyman (now part of Wyman Center) and is one of the oldest camps in the United States. The first high school class in Eureka was held in 1909. Eureka was incorporated as a fourth-class city on April 7, 1954.

Historically, Eureka was wholly within St. Louis County. In September 2019, the city's Board of Aldermen voted to annex two commercial lots—one of them a 72.5-acre tract that houses Kirkwood Materials West, a sand and gravel quarry, and the other a 75-acre field, both at highways 109 and FF—located just across the Meramec River in Jefferson County into the city. On October 1, 2019, the city voted to annex the under construction 549-home Windswept Farms subdivision just to the south into the city. Both annexations were voluntary by the owners.

City of Allenton
The railroad town of Allenton is a former community on U.S. Route 66 located (now) at the junction of Interstate 44 and Business Loop 44 in western St. Louis County. In 1985, it was annexed by the city of Eureka. The town is currently rural, with adjacent farmland and forested Ozark ridges. This community was declared blighted by St. Louis County in 1973.

Geography
According to the United States Census Bureau, the city has a total area of 10.45 sqmi, of which 10.35 sqmi is land, and 0.10 sqmi is water.

Floods
The city of Eureka has suffered multiple floods, the two most catastrophic being in 2015 and 2017. This caused the city and U.S. Army Corps of Engineers to evaluate a dozen strategic options, from the use of levees and walls, buyouts of high-risk properties, and the restoration of flood plain as water storage. Scientific researchers determined the flooding was a man-made calamity caused in part by "inaccurate Federal Emergency Management Agency flood frequencies based on the assumption that today's river will behave as it has in the past greatly underestimating our real flood risk and leading to inappropriate development in floodways and floodplains."

2015
The December 2015 North American storm complex deeply impacted the state of Missouri, with heavy rain and snow causing severe floods. The storm system was responsible for heavy rain that caused severe flooding. Parts of the state were hit with over 10 in of heavy rainfall. In Eureka, more than 100 boat rescues were conducted by the Eureka Fire Department of people and several pets from the second stories of homes near the Meramec River.

2017
A flooding event caused by a strong spring storm system brought multiple rounds of thunderstorms and heavy rain to portions of the Midwest the weekend of April 29–30, 2017. The middle portion of the Mississippi approached historical record flooding. The National Weather Service anticipated a 48.5 ft. crest at Cape Girardeau, Missouri, on May 5, 2017, which was within 6 inches of the January 2, 2016 crest of 48.86 ft. The first floor of a church flooded with about 48 inches of water, the same amount as in December 2015. Floodwater from the Meramec River covered athletic fields at Eureka High School, encroached on the school's buildings, and ruined the gymnasium floor.

2020 census
The 2020 United States census counted 11,646 people, 3,486 households, and 2,575 families in Eureka. The population density was 1,053.9 per square mile (406.9/km$2$). There were 3,740 housing units at an average density of 338.5 per square mile (130.7/km$2$). The racial makeup was 90.73% (10,566) white, 0.82% (96) black or African-American, 0.12% (14) Native American, 1.57% (183) Asian, 0.05% (6) Pacific Islander, 0.76% (89) from other races, and 5.94% (692) from two or more races. Hispanic or Latino of any race was 2.1% (211) of the population.

Of the 3,486 households, 40.5% had children under the age of 18; 64.5% were married couples living together; 16.1% had a female householder with no husband present. Of all households, 20.1% consisted of individuals, and 11.4% had someone living alone who was 65 years of age or older. The average household size was 2.8, and the average family size was 3.4.

26.4% of the population was under the age of 18, 3.9% from 18 to 24, 20.4% from 25 to 44, 24.1% from 45 to 64, and 12.9% who were 65 years of age or older. The median age was 39.8 years. For every 100 females, the population had 109.5 males. For every 100 females ages 18 and older, there were 98.5 males.

The 2016-2020 5-year American Community Survey estimates show that the median household income was $112,750 (with a margin of error of +/- $13,390) and the median family income was $121,977 (+/- $8,559). Males had a median income of $74,452 (+/- $8,634) versus $47,137 (+/- $8,637) for females. The median income for those above 16 years old was $59,316 (+/- $9,813). Approximately, 0.0% of families and 0.6% of the population were below the poverty line, including 0.0% of those under the age of 18 and 0.8% of those ages 65 or over.

2010 census
As of the 2010 census, there were 10,189 people, 3,474 households, and 2,758 families residing in the city. The population density was 984.4 PD/sqmi. There were 3,683 housing units at an average density of 355.8 /sqmi. The racial makeup of the city was 94.9% White, 0.8% African American, 0.2% Native American, 1.9% Asian, 0.1% Pacific Islander, 0.3% from other races, and 1.7% from two or more races. Hispanic or Latino of any race were 2.0% of the population.

There were 3,474 households, of which 46.9% had children under the age of 18 living with them, 66.2% were married couples living together, 9.3% had a female householder with no husband present, 3.9% had a male householder with no wife present, and 20.6% were non-families. 17.2% of all households were made up of individuals, and 5.9% had someone living alone who was 65 years of age or older. The average household size was 2.87, and the average family size was 3.27.

The median age in the city was 37.1 years. 30.9% of residents were under the age of 18; 6% were between the ages of 18 and 24; 26.6% were from 25 to 44; 26.7% were from 45 to 64, and 9.6% were 65 years of age or older. The gender makeup of the city was 49.6% male and 50.4% female.

2000 census
As of the 2000 census, there were 7,676 people in the city, organized into 2,487 households and two families. Its population density was 763.7 PD/sqmi. There were 2,622 housing units at an average density of 260.9 /sqmi. The racial makeup of the city was 97.38% White, 0.82% Asian, 0.57% Black or African American, 0.20% Native American, no Pacific Islanders, 0.26% from other races, and 0.77% from two or more races. 1.22% of the population were Hispanic or Latino of any race.

There were 2,487 households, out of which half had children under the age of 18 living with them, 71.6% were married couples living together, 8.2% had a female householder with no husband present, and 17.0% were non-families. 13.8% of all households were made up of individuals, and 4.3% had someone living alone who was 65 years of age or older. The average household size was 2.98, and the average family size was 3.30.

In the city, the population was spread out, with 31.9% under the age of 18, 5.7% from 18 to 24, 34.4% from 25 to 44, 19.5% from 45 to 64, and 8.5% 65 years of age or older. The median age was 34 years. For every 100 females, there were 94.9 males. For every 100 females age 18 and over, there were 89.6 males.

The median income for a household in the city was $74,301, and the median income for a family was $80,625. Males had a median income of $51,799 compared to $33,269 for females. The per capita income for the city was $27,553. 2.2% of the population and 1.3% of families were below the poverty line. Out of the total population, 3.1% of those under the age of 18 and 5.9% of those 65 and older were living below the poverty line.

Education
Rockwood R-Vi School District operates three elementary schools, Lasalle Springs Middle School, and Eureka High School.

The city also contains two private schools: St. Mark's Lutheran Church and School and Most Sacred Heart Church and School.

The city has the Eureka Hills Branch lending library, a branch of the St. Louis County Library. It was moved to a newly built location that opened on June 2, 2021.

News media
Local news coverage for the town and some of its neighbors is provided by the Tri-County Journal, the Eureka and Pacific Current NewsMagazine, and the Washington Missourian.

Notable people

 * Clayton Echard, undrafted rookie for the Seatle Seahawks and star of season 26 of The Bachelor
 * Cam Janssen, National Hockey League player
 * Bob Klinger, Major League Baseball player
 * Rissi Palmer, country singer

title: Eureka, Missouri


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Equation of state

In physics and chemistry, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal energy. Most modern equations of state are formulated in the Helmholtz free energy. Equations of state are useful in describing the properties of pure substances and mixtures in liquids, gases, and solid states as well as the state of matter in the interior of stars.

Overview
At present, there is no single equation of state that accurately predicts the properties of all substances under all conditions. An example of an equation of state correlates densities of gases and liquids to temperatures and pressures, known as the ideal gas law, which is roughly accurate for weakly polar gases at low pressures and moderate temperatures. This equation becomes increasingly inaccurate at higher pressures and lower temperatures, and fails to predict condensation from a gas to a liquid.

The general form of an equation of state may be written as $$f(p, V, T) = 0$$

where $$p$$ is the pressure, $$V$$ the volume, and $$T$$ the temperature of the system. Yet also other variables may be used in that form. It is directly related to Gibbs phase rule, that is, the number of independent variables depends on the number of substances and phases in the system.

An equation used to model this relationship is called an equation of state. In most cases this model will comprise some empirical parameters that are usually adjusted to measurement data. Equations of state can also describe solids, including the transition of solids from one crystalline state to another. Equations of state are also used for the modeling of the state of matter in the interior of stars, including neutron stars, dense matter (quark–gluon plasmas) and radiation fields. A related concept is the perfect fluid equation of state used in cosmology.

Equations of state are applied in many fields such as process engineering and petroleum industry as well as pharmaceutical industry.

Any consistent set of units may be used, although SI units are preferred. Absolute temperature refers to the use of the Kelvin (K), with zero being absolute zero.

 * $$n$$, number of moles of a substance
 * $$V_m$$, $$\frac{V}{n}$$, molar volume, the volume of 1 mole of gas or liquid
 * $$R$$, ideal gas constant ≈ 8.3144621J/mol·K
 * $$p_c$$, pressure at the critical point
 * $$V_c$$, molar volume at the critical point
 * $$T_c$$, absolute temperature at the critical point

Historical background
Boyle's law was one of the earliest formulation of an equation of state. In 1662, the Irish physicist and chemist Robert Boyle performed a series of experiments employing a J-shaped glass tube, which was sealed on one end. Mercury was added to the tube, trapping a fixed quantity of air in the short, sealed end of the tube. Then the volume of gas was measured as additional mercury was added to the tube. The pressure of the gas could be determined by the difference between the mercury level in the short end of the tube and that in the long, open end. Through these experiments, Boyle noted that the gas volume varied inversely with the pressure. In mathematical form, this can be stated as:$$ pV = \mathrm{constant}.$$The above relationship has also been attributed to Edme Mariotte and is sometimes referred to as Mariotte's law. However, Mariotte's work was not published until 1676.

In 1787 the French physicist Jacques Charles found that oxygen, nitrogen, hydrogen, carbon dioxide, and air expand to roughly the same extent over the same 80-kelvin interval. This is known today as Charles's law. Later, in 1802, Joseph Louis Gay-Lussac published results of similar experiments, indicating a linear relationship between volume and temperature:$$\frac{V_1}{T_1} = \frac{V_2}{T_2}.$$Dalton's law (1801) of partial pressure states that the pressure of a mixture of gases is equal to the sum of the pressures of all of the constituent gases alone.

Mathematically, this can be represented for $$n$$ species as:$$p_\text{total} = p_1 + p_2 + \cdots + p_n = \sum_{i=1}^n p_i.$$In 1834, Émile Clapeyron combined Boyle's law and Charles' law into the first statement of the ideal gas law. Initially, the law was formulated as pVm = R(TC + 267) (with temperature expressed in degrees Celsius), where R is the gas constant. However, later work revealed that the number should actually be closer to 273.2, and then the Celsius scale was defined with $$0~^{\circ}\mathrm{C} = 273.15~\mathrm{K}$$, giving:$$pV_m = R \left(T_C + 273.15\ {}^\circ\text{C}\right).$$In 1873, J. D. van der Waals introduced the first equation of state derived by the assumption of a finite volume occupied by the constituent molecules. His new formula revolutionized the study of equations of state, and was the starting point of cubic equations of state, which most famously continued via the Redlich–Kwong equation of state and the Soave modification of Redlich-Kwong.

The van der Waals equation of state can be written as

 * $$\left(P+a\frac1{V_m^2}\right)(V_m-b)=R T$$

where $$a$$ is a parameter describing the attractive energy between particles and $$b$$ is a parameter describing the volume of the particles.

Classical ideal gas law
The classical ideal gas law may be written $$pV = nRT.$$

In the form shown above, the equation of state is thus $$f(p, V, T) = pV - nRT = 0.$$

If the calorically perfect gas approximation is used, then the ideal gas law may also be expressed as follows $$p = \rho(\gamma - 1)e$$ where $$\rho$$ is the number density of the gas (number of atoms/molecules per unit volume), $$\gamma = C_p/C_v$$ is the (constant) adiabatic index (ratio of specific heats), $$e = C_v T$$ is the internal energy per unit mass (the "specific internal energy"), $$C_v$$ is the specific heat capacity at constant volume, and $$C_p$$ is the specific heat capacity at constant pressure.

Quantum ideal gas law
Since for atomic and molecular gases, the classical ideal gas law is well suited in most cases, let us describe the equation of state for elementary particles with mass $$m$$ and spin $$s$$ that takes into account quantum effects. In the following, the upper sign will always correspond to Fermi–Dirac statistics and the lower sign to Bose–Einstein statistics. The equation of state of such gases with $$N$$ particles occupying a volume $$V$$ with temperature $$T$$ and pressure $$p$$ is given by

$$p= \frac{(2s+1)\sqrt{2m^3k_\text{B}^5T^5}}{3\pi^2\hbar^3}\int_0^\infty\frac{z^{3/2}\,\mathrm{d}z}{e^{z-\mu/(k_\text{B} T)}\pm 1}$$ where $$k_\text{B}$$ is the Boltzmann constant and $$\mu(T,N/V)$$ the chemical potential is given by the following implicit function $$\frac{N}{V}=\frac{(2s+1)(m k_\text{B}T)^{3/2}}{\sqrt 2\pi^2\hbar^3}\int_0^\infty\frac{z^{1/2}\,\mathrm{d}z}{e^{z-\mu / (k_\text{B} T)}\pm 1}.$$

In the limiting case where $$e^{\mu / (k_\text{B} T)}\ll 1$$, this equation of state will reduce to that of the classical ideal gas. It can be shown that the above equation of state in the limit $$e^{\mu/(k_\text{B} T)}\ll 1$$ reduces to

$$pV = N k_\text{B} T\left[1\pm\frac{\pi^{3/2}}{2(2s+1)} \frac{N\hbar^3}{V(m k_\text{B} T)^{3/2}}+\cdots\right]$$

With a fixed number density $$N/V$$, decreasing the temperature causes in Fermi gas, an increase in the value for pressure from its classical value implying an effective repulsion between particles (this is an apparent repulsion due to quantum exchange effects not because of actual interactions between particles since in ideal gas, interactional forces are neglected) and in Bose gas, a decrease in pressure from its classical value implying an effective attraction. The quantum nature of this equation is in it dependence on s and ħ.

Cubic equations of state
Cubic equations of state are called such because they can be rewritten as a cubic function of $$V_m$$. Cubic equations of state originated from the van der Waals equation of state. Hence, all cubic equations of state can be considered 'modified van der Waals equation of state'. There is a very large number of such cubic equations of state. For process engineering, cubic equations of state are today still highly relevant, e.g. the Peng Robinson equation of state or the Soave Redlich Kwong equation of state.

Virial equation of state
$$\frac{pV_m}{RT} = A + \frac{B}{V_m} + \frac{C}{V_m^2} + \frac{D}{V_m^3} + \cdots$$

Although usually not the most convenient equation of state, the virial equation is important because it can be derived directly from statistical mechanics. This equation is also called the Kamerlingh Onnes equation. If appropriate assumptions are made about the mathematical form of intermolecular forces, theoretical expressions can be developed for each of the coefficients. A is the first virial coefficient, which has a constant value of 1 and makes the statement that when volume is large, all fluids behave like ideal gases. The second virial coefficient B corresponds to interactions between pairs of molecules, C to triplets, and so on. Accuracy can be increased indefinitely by considering higher order terms. The coefficients B, C, D, etc. are functions of temperature only.

The BWR equation of state
$$ p = \rho RT + \left(B_0 RT - A_0 - \frac{C_0}{T^2} + \frac{D_0}{T^3} - \frac{E_0}{T^4}\right) \rho^2 + \left(bRT - a - \frac{d}{T}\right) \rho^3 + \alpha\left(a + \frac{d}{T}\right) \rho^6 + \frac{c\rho^3}{T^2}\left(1 + \gamma\rho^2\right)\exp\left(-\gamma\rho^2\right) $$

where
 * $$p$$ is pressure
 * $$\rho$$ is molar density

Values of the various parameters can be found in reference materials. The BWR equation of state has also frequently been used for the modelling of the Lennard-Jones fluid. There are several extensions and modifications of the classical BWR equation of state available.

The Benedict–Webb–Rubin–Starling equation of state is a modified BWR equation of state and can be written as $$p=\rho RT + \left(B_0 RT-A_0 - \frac{C_0}{T^2} + \frac{D_0}{T^3} - \frac{E_0}{T^4}\right) \rho^2 + \left(bRT-a-\frac{d}{T} + \frac{c}{T^2}\right) \rho^3 + \alpha\left(a+\frac{d}{T}\right) \rho^6 $$

Note that in this virial equation, the fourth and fifth virial terms are zero. The second virial coefficient is monotonically decreasing as temperature is lowered. The third virial coefficient is monotonically increasing as temperature is lowered.

The Lee–Kesler equation of state is based on the corresponding states principle, and is a modification of the BWR equation of state.

$$ p = \frac{RT}{V} \left( 1 + \frac{B}{V_r} + \frac{C}{V_r^2} + \frac{D}{V_r^5} + \frac{c_4}{T_r^3 V_r^2} \left( \beta + \frac{\gamma}{V_r^2} \right) \exp \left( \frac{-\gamma}{V_r^2} \right) \right) $$

Physically based equations of state
There is a large number of physically based equations of state available today. Most of those are formulated in the Helmholtz free energy as a function of temperature, density (and for mixtures additionally the composition). The Helmholtz energy is formulated as a sum of multiple terms modelling different types of molecular interaction or molecular structures, e.g. the formation of chains or dipolar interactions. Hence, physically based equations of state model the effect of molecular size, attraction and shape as well as hydrogen bonding and polar interactions of fluids. In general, physically based equations of state give more accurate results than traditional cubic equations of state, especially for systems containing liquids or solids. Most physically based equations of state are built on monomer term describing the Lennard-Jones fluid or the Mie fluid.

Perturbation theory-based models
Perturbation theory is frequently used for modelling dispersive interactions in an equation of state. There is a large number of perturbation theory based equations of state available today, e.g. for the classical Lennard-Jones fluid. The two most important theories used for these types of equations of state are the Barker-Henderson perturbation theory and the Weeks–Chandler–Andersen perturbation theory.

Statistical associating fluid theory (SAFT)
An important contribution for physically based equations of state is the statistical associating fluid theory (SAFT) that contributes the Helmholtz energy that describes the association (a.k.a. hydrogen bonding) in fluids, which can also be applied for modelling chain formation (in the limit of infinite association strength). The SAFT equation of state was developed using statistical mechanical methods (in particular the perturbation theory of Wertheim ) to describe the interactions between molecules in a system. The idea of a SAFT equation of state was first proposed by Chapman et al. in 1988 and 1989. Many different versions of the SAFT models have been proposed, but all use the same chain and association terms derived by Chapman et al.

Multiparameter equations of state
Multiparameter equations of state are empirical equations of state that can be used to represent pure fluids with high accuracy. Multiparameter equations of state are empirical correlations of experimental data and are usually formulated in the Helmholtz free energy. The functional form of these models is in most parts not physically motivated. They can be usually applied in both liquid and gaseous states. Empirical multiparameter equations of state represent the Helmholtz energy of the fluid as the sum of ideal gas and residual terms. Both terms are explicit in temperature and density: $$\frac{a(T, \rho)}{RT} = \frac{a^\mathrm{ideal\,gas}(\tau, \delta) + a^\textrm{residual}(\tau, \delta)}{RT}$$ with $$\tau = \frac{T_r}{T}, \delta = \frac{\rho}{\rho_r}$$

The reduced density $$\rho_r$$ and reduced temperature $$T_r$$ are in most cases the critical values for the pure fluid. Because integration of the multiparameter equations of state is not required and thermodynamic properties can be determined using classical thermodynamic relations, there are few restrictions as to the functional form of the ideal or residual terms. Typical multiparameter equations of state use upwards of 50 fluid specific parameters, but are able to represent the fluid's properties with high accuracy. Multiparameter equations of state are available currently for about 50 of the most common industrial fluids including refrigerants. The IAPWS95 reference equation of state for water is also a multiparameter equations of state. Mixture models for multiparameter equations of state exist, as well. Yet, multiparameter equations of state applied to mixtures are known to exhibit artifacts at times.

One example of such an equation of state is the form proposed by Span and Wagner.

$$ a^\mathrm{residual} = \sum_{i=1}^8 \sum_{j=-8}^{12} n_{i,j} \delta^i \tau^{j/8} + \sum_{i=1}^5 \sum_{j=-8}^{24} n_{i,j} \delta^i \tau^{j/8} \exp \left( -\delta \right) + \sum_{i=1}^5 \sum_{j=16}^{56} n_{i,j} \delta^i \tau^{j/8} \exp \left( -\delta^2 \right) + \sum_{i=2}^4 \sum_{j=24}^{38} n_{i,j} \delta^i \tau^{j/2} \exp \left( -\delta^3 \right) $$

This is a somewhat simpler form that is intended to be used more in technical applications. Equations of state that require a higher accuracy use a more complicated form with more terms.

Stiffened equation of state
When considering water under very high pressures, in situations such as underwater nuclear explosions, sonic shock lithotripsy, and sonoluminescence, the stiffened equation of state is often used:

$$p = \rho(\gamma - 1)e - \gamma p^0 \,$$

where $$e$$ is the internal energy per unit mass, $$\gamma$$ is an empirically determined constant typically taken to be about 6.1, and $$p^0$$ is another constant, representing the molecular attraction between water molecules. The magnitude of the correction is about 2 gigapascals (20,000 atmospheres).

The equation is stated in this form because the speed of sound in water is given by $$c^2 = \gamma\left(p + p^0\right)/\rho$$.

Thus water behaves as though it is an ideal gas that is already under about 20,000 atmospheres (2 GPa) pressure, and explains why water is commonly assumed to be incompressible: when the external pressure changes from 1 atmosphere to 2 atmospheres (100 kPa to 200 kPa), the water behaves as an ideal gas would when changing from 20,001 to 20,002 atmospheres (2000.1 MPa to 2000.2 MPa).

This equation mispredicts the specific heat capacity of water but few simple alternatives are available for severely nonisentropic processes such as strong shocks.

Morse oscillator equation of state
An equation of state of Morse oscillator has been derived, and it has the following form:

$$p=\Gamma_1\nu+\Gamma_2\nu^2$$

Where $$\Gamma_1$$ is the first order virial parameter and it depends on the temperature, $$\Gamma_2$$ is the second order virial parameter of Morse oscillator and it depends on the parameters of Morse oscillator in addition to the absolute temperature. $$\nu$$ is the fractional volume of the system.

Ultrarelativistic equation of state
An ultrarelativistic fluid has equation of state $$p = \rho_m c_s^2$$ where $$p$$ is the pressure, $$\rho_m$$ is the mass density, and $$c_s$$ is the speed of sound.

Ideal Bose equation of state
The equation of state for an ideal Bose gas is

$$p V_m = RT~\frac{\operatorname{Li}_{\alpha+1}(z)}{\zeta(\alpha)} \left(\frac{T}{T_c}\right)^\alpha $$

where α is an exponent specific to the system (e.g. in the absence of a potential field, α = 3/2), z is exp(μ/kBT) where μ is the chemical potential, Li is the polylogarithm, ζ is the Riemann zeta function, and Tc is the critical temperature at which a Bose–Einstein condensate begins to form.

Jones–Wilkins–Lee equation of state for explosives (JWL equation)
The equation of state from Jones–Wilkins–Lee is used to describe the detonation products of explosives. $$p = A \left( 1 - \frac{\omega}{R_1 V} \right) \exp(-R_1 V) + B \left( 1 - \frac{\omega}{R_2 V} \right) \exp\left(-R_2 V\right) + \frac{\omega e_0}{V}$$

The ratio $$ V = \rho_e / \rho $$ is defined by using $$ \rho_e $$, which is the density of the explosive (solid part) and $$ \rho $$, which is the density of the detonation products. The parameters $$ A $$, $$ B $$, $$ R_1 $$, $$ R_2 $$ and $$ \omega $$ are given by several references. In addition, the initial density (solid part) $$ \rho_0 $$, speed of detonation $$ V_D $$, Chapman–Jouguet pressure $$ P_{CJ} $$ and the chemical energy per unit volume of the explosive $$ e_0 $$ are given in such references. These parameters are obtained by fitting the JWL-EOS to experimental results. Typical parameters for some explosives are listed in the table below.

Others

 * Tait equation for water and other liquids. Several equations are referred to as the Tait equation.
 * Murnaghan equation of state
 * Birch–Murnaghan equation of state
 * Stacey–Brennan–Irvine equation of state
 * Modified Rydberg equation of state
 * Adapted polynomial equation of state
 * Johnson–Holmquist equation of state
 * Mie–Grüneisen equation of state
 * Anton-Schmidt equation of state
 * State-transition equation

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Equation of state


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Talk:Equation of state

'03 thru '05 talk
Hi How can I find Boils tempurates according to Radling - Coene equation

Hello, I was looking for the binary interaction parameters of Hydrogen and Helium for a mixture density calculation for the peng robinson E.O.S. Does any one know it or know where to find this number required for the mixing rule of the Peng? Adam R. Baxter email me at: baxter.56@osu.edu Thanks --- OK, so I take the subscript "c" to refer to the critical properties which I take to be the value of those properties at the critical point (ie, the set of conditions in which solid, liquid, and gas are in equilibrium.)

So, I recognize Tc and Pc as the criticial temperature and pressure, respectively. Fine, so far.

But what is Vc? Volume, I would guess, but T and P are intrinsic properties of the system, whereas volume is extensive, ie, it depends on "how much" material there is. Is Vc defined in relation to one mole of a given substance?

--JoeAnderson (never did well in p-chem)

Vc is the critical volume. Or critical SPECIFIC volume, it is intensive, not extensive.

Actually, the point at which the solid, liquid, and gas are in equilibrium is called the triple point. The critical temperature is that temperature above which unique liquid and gas phases do not exist. As you approach the critical point, the properties of the gas and liquid phase become the same, so above the critical temperature there is only one phase. The critical pressure refers to the vapor pressure at the critical temperature. Vc is the critical molar volume (ie. the volume of one mole) and as such is more like a density (or 1/density) than an actual volume. Note that in all of the listed equations of state, V is defined as the molar volume. This is why PV = RT, instead of PV = nRT.

--Matt Stoker

In order to be more complete, we really should add mixing rules for each equation of state (ie. rules for determining the correct parameters for a mixture). In order to add these we need a summation sign. For example for the Soave Equation, the rules are:

aα = ∑ ∑ yiyj(aα)ij

If anyone knows how to do the summation signs, let me know and I'll updata the page accordingly.

--Matt Stoker

You're forgetting the semicolons on your HTML entity references. Also, I'm sure that "aα" is not what you mean to write here. See Wiki special characters. --LDC

Thanks, Matt! Your discussion above of triple point, critical temperature, critical molar volume, etc. makes it all much more clear, I think. I'd like to see that worked into the main page--if you'd like to do it, that would be fine. I'll wait a while to give you a chance at it, or will go ahead and do it at some later point. --dja

LDC, thanks for the information. As for "aα", it is supposed to be "a" multiplied by the greek letter "alpha". How would you recommend it be specified?

-- Matt Stoker -- Hello, this page had a lot of garbage characters introduced into it somehow (periods became copyright symbols; parentheses became yen). I just pasted in an earlier version of this page from Equations of State (2 caps). I've looked it over and it seems to be ok; please double-check (I'm not a scientist).

--

Hi guys

How do I modify the page to add a new equation of state? I don't understand the editing system well enough to add a new item to the list.

cheers

Robinh 20:41, 10 Dec 2003 (UTC)

--

I think this article should merely refer to the various articles describing the different equations of state: Ideal gas law, Van der Waals equation and so on, instead of repeating them. Bo Jacoby 11:35, 13 October 2005 (UTC)

--

I totally agree, why repeat what is already there. This page should be used to describe when and how the equations are used with respect to each other. Do you have any thoughts to what the specific layout should be for the new page? Thales

In order to add the mixing rules for the equations of state, it will be necessary to add an entire page on it, as several sets of mixing rules are available (see the reference Valderrama for a discussion).

--Ascentury 03:55, 1 May 2007 (UTC)

State functions?
Are equations of state related to State functions? - ElAmericano | talk 21:28, 29 January 2006 (UTC)
 * Yes. Pressure, volume and temperature are state functions, and the equation of state relates them. The equation of state is not sufficient, however. Some other equations must tell the entropy and the energy of the state. Bo Jacoby 09:55, 31 January 2006 (UTC)

Isn't pressure written with a small P?
As in the:
 * === Classical ideal gas law ===
 * $$PV = nRT\,$$

Shouldnt it be:
 * $$pV = nRT\,$$

? — Preceding unsigned comment added by 81.228.244.89 (talk) 15:15, 14 November 2006, (UTC)

 * Agree, the general usage is assign lowercase letter for intensive variables and uppercase for extensive variables. For example:
 * $$V$$ for volume (Units: $$m^3$$ ) and $$v$$ for specific volume (Units: $$m^3/kg$$ ),
 * $$H$$ for enthalpy (Units: $$J$$ ) and $$h$$ for specific enthalpy (Units: $$J/kg$$ or $$J/mol$$ ).
 * $$T$$ for temperature is an exception for present usage (in old texts they refer to temperature by $$\theta$$ instead of $$T$$ ). -- Myth (Talk) 10:59, 6 March 2007 (UTC)

A standard reference: IUPAC pressure notation — DIV (128.250.80.15 (talk) 07:18, 12 September 2008 (UTC))

SAFT equation
Hi do you think that there should be something on this page about the SAFT equation of state, given that its now one of the most modern approaches for this area? — Preceding unsigned comment added by 129.31.67.66 (talk) 10:04, 3 December 2006 (UTC)

Misleading article title
The introduction mentions: "In physics and thermodynamics, an equation of state is a relation between state variables." But the article only deals with state relationship between pressure, temperature and volume. It does not describe any other state equations like:
 * $$H = C_pT$$ or $$dH = TdS -pdV$$

I think the title of the article is misleading. Either the title should be changed to something more appropriate or the text should also cover other equation of states. The former is a better option given the size of the article. -- Myth (Talk) 10:59, 6 March 2007 (UTC)

Ideal gas law and Euler equations
I have deleted the following statement which refers to the ideal gas law in the form$$ P = \rho\left(\gamma-1\right)e$$.
 * "This form is purely in terms of intensive quantities and is useful when simulating the Euler equations because it expresses the relationship between internal energy and other forms of energy (such as kinetic), thus allowing simulations to obey the First Law."

The equation of state ("this form") does not express the relationship between internal energy (e) and kinetic energy (for example) (there is no specific kinetic energy term $$v^2/2$$ in the equation of state?) Making Euler simulations (I assume this refers to computational fluid dynamics, CFD) obey the first law is independent of how you express the gas law. To keep the idea you would have to add something like $$ e = e_{total} - v^2/2$$ where $$e_{total}$$ is the total intrinsic (specific) energy of an element of fluid moving with speed $$v$$. E4mmacro 23:43, 10 April 2007 (UTC)

Virial Equation of State
In the book we are using for Physical Chem class (Thermodynamics, Statistical Thermodynamics, & Kinetics by Thomas Engel and Philip Reid. ISBN 0-8053-3844-6) it states on page 151 that the virial equation is only valid over it's convergence range, which is only under relatively low pressures (Vm > 1 ??). If anyone can confirm this, it should probably be mentioned in the article. I did some calculations using values smaller than 1 and got unreasonable results. Aurimas 20:27, 6 September 2007 (UTC)

 * The virial equation of state can be used at higher densities (and pressures) so long as the series is convergent and enough coefficients are used. You should have low expectations of the series converging unless you're in the gas phase, so it's best to stay out of temperatures / densities where the gas phase isn't stable. Ajschult (talk) 03:18, 11 June 2008 (UTC)

How does the Virial equation relate to Virial stress? 72.74.211.41 02:00, 17 October 2007 (UTC)

The equations $$B = -V_c \,$$ and $$C = \frac{V_c^2}{3}$$ need much more context or should be deleted entirely. The given values for B and C are approximations that are reasonable at the critical temperature. They can be derived by assuming that higher order coefficients (D and above) are 0 and that the critical Compressibility factor is 1/3 (which is reasonable for most fluids). The given values should certainly not be used away from the critical temperature (so the equations as stated are simply wrong). In general, the result doesn't seem sufficiently useful to warrant existing on the page.

 * In the current state, the first subsection of [Equation_of_state#Virial_equations_of_state] ends with an incomplete sentence, please correct that as soon as possible if you know how it should end. --Rubik's Cube (talk) 09:44, 9 July 2008 (UTC)

Beattie-Bridgeman equation of state
The book mentioned in the above section (Thermodynamics, Statistical Thermodynamics, & Kinetics by Thomas Engel and Philip Reid. ISBN 0-8053-3844-6) also lists another "widely used" equation of state - the Beattie-Bridgeman equation of state. It uses 5 experimentally determined parameters:

$$P=\frac{RT}{V_m^2}\left(1-\frac{c}{V_mT^3}\right)(V_m+B)-\frac{A}{V_m^2}$$

where

$$A=A_0\left(1-\frac{a}{V_m}\right)$$  and     $$B=B_0\left(1-\frac{b}{V_m}\right)$$

I am not sure what A0 and B0 stand for. If anyone knows and this formula is not yet on the page (I couldn't find it), please add it. Aurimas 20:44, 10 September 2007 (UTC)

Nomenclature
While the standard symbol for pressure, p, is now used in the text (cf. above), the usage of subscripts still needs to be amended. See IUPAC (Mills & Metanomski, 1999). —DIV (128.250.80.15 (talk) 07:22, 12 September 2008 (UTC))

The abbreviation EOS is never properly introduced and neither is it written bold EOS. -- Arnero (talk) 12:55, 20 December 2009 (UTC)

E = M C^2 as equation of state
Taking into considerations E = M C^2, different type of matters with respect of their density's, differently reflects, i.e. in a different patterns, the Vacuum energy fluctuations (Casimir effect). In my opinion, the synchronized reflections of vacuum energy fluctuations off of a mass constitute the gravitational forces for that mass. In compression to a lesser density mass such as the earth, the matter in the black hole within the event horizon (equation of state), (UC Berkeley, September 24, 2010, high pressure experiments reproduce mineral structure 1,800 miles deep in the earth: where seismic waves have different patterns when run through post-pervoskite's zone of Magnesium silicate perovskite (MgSiO3) above the earth core). In my opinion, The Matter of a lesser density such as the earth matter, would react differently than the matter of the Black Hole to Vacuum waves, vacuum fluctuations, vacuum energy, which (the vacuum energy fluctuation ) when reflected off of these two different matters (equation of state) creates different synchronized reflected vacuum energy waves i.e. different gravitational forces; Where synchronized reflected vacuum energy waves is a gravitational force for a set, a defined system that has a specific equation of state. Also, The matter of the Black Hole (within the event horizon) may not reflects electromagnetic waves, since light have two components vectors: electric and magnetic, as it (the light) does reflects off of a lesser denser mass's such as the earth; therefore no light reflects off of a black hole matter, as observed. (UC Berkeley, September 24, 2010, high pressure experiments reproduce mineral structure 1,800 miles deep in the earth: where seismic waves have different patterns when run through post-pervoskite's zone of Magnesium silicate perovskite (MgSiO3) above the earth core). Or/and, the vacuum, vacuum energy of the atmosphere of a black hole will not support to carry light waves (or, most electromagnitic waves within the "atomspher" of the mass of the black hole. and light speedThat constitute that If we defined the atmosphere of a black hole to be the space between it's event horizon and it's mass surface, and if the rules of equation of state where to apply within the event horizon of a black hole atmosphere's with consideration to light travel; then E = M C^2 as an equation of state, could not probably be applied or used within the atmosphere of a black hole. E = M C^2 is does not apply in the black hole as a Equation of state for the absence of most electromagnetic waves spectrum (Hawking radiation existence?).--e:Y,?:G 19:58, 25 September 2010 (UTC)--e:Y,?:G 19:58, 25 September 2010 (UTC) —Preceding unsigned comment added by E:Y,?:G (talk • contribs)

In the discussion where it says "For Pr<1 and Tr<1, the system is in a state of vapor-liquid equilibrium. The reduced cubic equation of state yields in that case 3 solutions." This is not strictly true. It would be better to say that the system will have a finite range of p over which it has 3 solutions. There are certainly values of Pr and Tr both less than 1 which do not yeild 3 solutions. Luriol (talk) 22:32, 22 November 2010 (UTC)

Factor a in Van der Waals equation of state off by a factor of 0.1?
Hello

So I have a lab exam in Joule-Thomson effect and I have given values for a and b for VdW equation of state for nitrogen and carbon dioxide. When I take the critical temp. and pressure and put the equation on this site, b gives correct value, but a is off by a factor of 0.1.

E.g. For $$CO_2$$, given in the table (the experiments and the Phywe can't be wrong) $$a=3.60 Pa\ m^6\ mol^{-2}$$, and if I put the values from the critical point page, I get: $$a=3.60\times 10^{-1}\ Pa\ m^6\ mol^{-2}$$. Not only for carbon dioxide, but for nitrogen too...

What is even weirder is that b is correct for the same temps and pressure.

So can someone find where this comes from? I calculated from Zemansky and Dittman the coefficients a and b and they are fine. —Preceding unsigned comment added by 89.164.52.165 (talk) 19:06, 16 March 2011 (UTC)

Cosmology obsession
There seems to be an obsession throughout the article with the use of EOS for astrophyisic use ???? why is this ?? I find it unnecesary. — Preceding unsigned comment added by 190.97.61.108 (talk) 19:11, 15 September 2011 (UTC)

predicting...
The overview article sounds like the EOS is a cookbook in alchemistry. The EOS does not ``predict'' anything but is a model (summary, extrapolation, fit) of state variables which otherwise would be only accessible by severe quantum mechanical many-body calculations. R. J. Mathar (talk) —Preceding undated comment added 18:54, 24 February 2012 (UTC).

Merger proposal
I propose to merge State function into Equation of state. I think that the content in the State function article can easily be explained in the context of Equation of state, and the Equation of state article is of a reasonable size that the merging of Foo will not cause any problems as far as article size is concerned. The State functions article appears to be discussing the same topic, but is much less developed. As the distinction between the topics discussed by the articles is not made clear (and likely nonexistent) and neither article points to the other, the separate pages can only serve to confuse readers. Footlessmouse (talk) 12:26, 22 August 2020 (UTC)
 * Hi @FootlessmouseAsking as a Devil's advocate (can't say I know much about this any more): if State function is merged into this (way too dense) article, what'd be your plan for Process function? These functions seem to be discussed together LibreTexts Chemistry - Differentials in Thermodynamics - State and Path Functions Ponor (talk) 16:52, 25 August 2020 (UTC)

 * Hi @Ponor, thanks for your response! I honestly don't know, it's been a really long time since I've dealt with any of these terms. If they represent slightly unique topics, then it would be better if it could be spelled out in the articles somewhere to disambiguate them. I figured someone who knew more about the topic than me would respond and we could figure out what to do. I think I understand now, please correct me if I'm wrong: Equations of state contain both state functions and process functions and the state and process function differ on whether or not they admit curl (path dependence)? If this is the case, I will remove the merger proposal. Footlessmouse (talk) 21:30, 25 August 2020 (UTC)

 * Sorry about that, I didn't realize the textbook was online, yes it appears that is the case, I will remove the merger proposal. Thanks @Ponor. Footlessmouse (talk) 21:31, 25 August 2020 (UTC)

Terrible
This article should contain cubic equations of state not just link to longer article, so the equations at least should be stated here. I have included the basic der Waals equation, for the basic fix. — Preceding unsigned comment added by 78.30.183.44 (talk) 06:06, 2 February 2022 (UTC)

title: Talk:Equation of state


text:
Ecclesiastes

Ecclesiastes  (, Ἐκκλησιαστής) is one of the Ketuvim ("Writings") of the Hebrew Bible and part of the Wisdom literature of the Christian Old Testament. The title commonly used in English is a Latin transliteration of the Greek translation of the Hebrew word קֹהֶלֶת ( or ). An unnamed author introduces "The words of Kohelet, son of David, king in Jerusalem" (1:1) and does not use his own voice again until the final verses (12:9–14), where he gives his own thoughts and summarises the statements of Kohelet; the main body of the text is ascribed to Kohelet himself.

Kohelet proclaims (1:2) "Vanity of vanities! All is futile!"; the Hebrew word, "vapor" or "breath", can figuratively mean "insubstantial", "vain", "futile", or "meaningless". In some versions vanity is translated as "meaningless" to avoid the confusion with the other definition of vanity. Given this, the next verse presents the basic existential question with which the rest of the book is concerned: "What profit hath a man for all his toil, in which he toils under the sun?", expressing that the lives of both wise and foolish people all end in death. In light of this perceived meaninglessness, he suggests that human beings should enjoy the simple pleasures of daily life, such as eating, drinking, and taking enjoyment in one's work, which are gifts from the hand of God. The book concludes with the injunction to "Fear God and keep his commandments; for that is the duty of all of mankind. Since every deed will God bring to judgment, for every hidden act, be it good or evil."

According to rabbinic tradition the book was written by King Solomon (reigned c. 970–931 BCE) in his old age, but the presence of Persian loanwords and Aramaisms point to a date no earlier than about 450 BCE, while the latest possible date for its composition is 180 BCE.

Title
Ecclesiastes is a phonetic transliteration of the Greek word Ἐκκλησιαστής, which in the Septuagint translates the Hebrew name of its stated author, Kohelet (קֹהֶלֶת). The Greek word derives from "assembly," as the Hebrew word derives from  "assembly," but while the Greek word means 'member of an assembly', the meaning of the original Hebrew word it translates is less certain. As Strong's Concordance mentions, it is a female active participle of the verb in its simple  paradigm, a form not used elsewhere in the Bible and which is sometimes understood as active or passive depending on the verb, so that Kohelet would mean '(female) assembler' in the active case (recorded as such by Strong's Concordance), and '(female) assembled, member of an assembly' in the passive case (as per the Septuagint translators). According to the majority understanding today, the word is a more general (, קוֹטֶלֶת) form rather than a literal participle, and the intended meaning of Kohelet in the text is 'someone speaking before an assembly'; hence 'Teacher' or 'Preacher'. This was the position of the Midrash and of Jerome.

Commentators struggle to explain why a man was given an apparently feminine name. According to Isaiah di Trani, "He authored this work in his old age, when he was weak like a woman, and therefore he received a feminine name," an opinion likewise held by Johann Simonis. According to Solomon b. Jeroham (also Lorinus, Zirkel), "This is because, even as a woman births and raises children, Qoheleth revealed and organized wisdom". According to Yefet b. Ali (also adopted by Abraham ibn Ezra and Joseph Ibn Kaspi), "He ascribed this activity to his wisdom, and because Wisdom is female, he used a feminine name". This last opinion is accepted by a wide variety of modern scholars, including C. D. Ginsburg.

Structure
Ecclesiastes is presented as the biography of "Kohelet" or "Qoheleth"; his story is framed by the voice of the narrator, who refers to Kohelet in the third person, praises his wisdom, but reminds the reader that wisdom has its limitations and is not man's main concern. Kohelet reports what he planned, did, experienced and thought, but his journey to knowledge is, in the end, incomplete; the reader is not only to hear Kohelet's wisdom, but to observe his journey towards understanding and acceptance of life's frustrations and uncertainties: the journey itself is important.

The Jerusalem Bible divides the book into two parts, part one comprising Ecclesiastes 1:4-6:12, part two consisting of chapters 7 to 12, each commencing with a separate prologue.

Few of the many attempts to uncover an underlying structure to Ecclesiastes have met with widespread acceptance; among them, the following is one of the more influential: Despite the acceptance by some of this structure, there have been many criticisms, such as that of Fox: "[Addison G. Wright's] proposed structure has no more effect on interpretation than a ghost in the attic. A literary or rhetorical structure should not merely 'be there'; it must something. It should guide readers in recognizing and remembering the author's train of thought."
 * Title (1:1)
 * Initial poem (1:2–11)
 * I: Kohelet's investigation of life (1:12–6:9)
 * II: Kohelet's conclusions (6:10–11:6)
 * Introduction (6:10–12)
 * A: Man cannot discover what is good for him to do (7:1–8:17)
 * B: Man does not know what will come after him (9:1–11:6)
 * Concluding poem (11:7–12:8)
 * Epilogue (12:9–14)

Verse 1:1 is a superscription, the ancient equivalent of a title page: it introduces the book as "the words of Kohelet, son of David, king in Jerusalem."

Most, though not all, modern commentators regard the epilogue (12:9–14) as an addition by a later scribe. Some have identified certain other statements as further additions intended to make the book more religiously orthodox (e.g., the affirmations of God's justice and the need for piety).

It has been proposed that the text is composed of three distinct voices. The first belongs to Qoheleth as the prophet, the "true voice of wisdom", which speaks in the first person, recounting wisdom through his own experience. The second voice belongs to Qoheleth as the king of Jerusalem, who is more didactic and thus speaks primarily in second-person imperative statements. The third voice is that of the epilogist (i.e., the writer of the epilogue), who speaks proverbially in the third person. The epilogist is most identified in the book's first and final verses. Kyle R. Greenwood suggests that following this structure, Ecclesiastes should be read as a dialogue between these voices.

Summary
The ten-verse introduction in verses 1:2–11 are the words of the frame narrator; they set the mood for what is to follow. Kohelet's message is that all is meaningless. This distinction first appeared in the commentaries of Samuel ibn Tibbon (d. 1230) and Aaron ben Joseph of Constantinople (d. 1320).

After the introduction come the words of Kohelet. As king, he has experienced everything and done everything, but concludes that nothing is ultimately reliable, as death levels all. Kohelet states that the only good is to partake of life in the present, for enjoyment is from the hand of God. Everything is ordered in time and people are subject to time in contrast to God's eternal character. The world is filled with injustice, which only God will adjudicate. God and humans do not belong in the same realm, and it is therefore necessary to have a right attitude before God. People should enjoy, but should not be greedy; no one knows what is good for humanity; righteousness and wisdom escape humanity. Kohelet reflects on the limits of human power: all people face death, and death is better than life, but people should enjoy life when they can, for a time may come when no one can. The world is full of risk: he gives advice on living with risk, both political and economic. Kohelet's words finish with imagery of nature languishing and humanity marching to the grave.

The frame narrator returns with an epilogue: the words of the wise are hard, but they are applied as the shepherd applies goads and pricks to his flock. The ending of the book sums up its message: "Fear God and keep his commandments for God will bring every deed to judgment." Some scholars suggest 12:13–14 were an addition by a more orthodox author than the original writer (that the epilogue was added later was first proposed by Samuel ibn Tibbon); others think it is likely the work of the original author.

Title, date and author

The book takes its name from the Greek, a translation of the title by which the central figure refers to himself: "Kohelet", meaning something like "one who convenes or addresses an assembly". According to rabbinic tradition, Ecclesiastes was written by King Solomon in his old age (an alternative tradition that "Hezekiah and his colleagues wrote Isaiah, Proverbs, the Song of Songs and Ecclesiastes" probably means simply that the book was edited under Hezekiah), but critical scholars have long rejected the idea of a pre-exilic origin. According to Christian tradition, the book was probably written by another Solomon (Gregory of Nyssa wrote that it was written by another Solomon; Didymus the Blind wrote that it was probably written by several authors). The presence of Persian loanwords and numerous Aramaisms points to a date no earlier than about 450 BCE, while the latest possible date for its composition is 180 BCE, when the Jewish writer Ben Sira quotes from it. The dispute as to whether Ecclesiastes belongs to the Persian or the Hellenistic periods (i.e., the earlier or later part of this period) revolves around the degree of Hellenization (influence of Greek culture and thought) present in the book. Scholars arguing for a Persian date (c. 450–330 BCE) hold that there is a complete lack of Greek influence; those who argue for a Hellenistic date (c. 330–180 BCE) argue that it shows internal evidence of Greek thought and social setting.

Also unresolved is whether the author and narrator of Kohelet are identical. Ecclesiastes regularly switches between third-person quotations of Kohelet and first-person reflections on Kohelet's words, which would indicate the book was written as a commentary on Kohelet's parables rather than a personally-authored repository of his sayings. Some scholars have argued that the third-person narrative structure is an artificial literary device along the lines of Uncle Remus, although the description of the Kohelet in 12:8–14 seems to favour a historical person whose thoughts are presented by the narrator. It has been argued, however, that the question has no theological importance; one scholar (Roland Murphy) has commented that Kohelet himself would have regarded the time and ingenuity put into interpreting his book as "one more example of the futility of human effort".

Genre and setting
Ecclesiastes has taken its literary form from the Middle Eastern tradition of the fictional autobiography, in which a character, often a king, relates his experiences and draws lessons from them, often self-critical: Kohelet likewise identifies himself as a king, speaks of his search for wisdom, relates his conclusions, and recognises his limitations. The book belongs to the category of wisdom literature, the body of biblical writings which give advice on life, together with reflections on its problems and meanings—other examples include the Book of Job, Proverbs, and some of the Psalms. Ecclesiastes differs from the other biblical Wisdom books in being deeply skeptical of the usefulness of wisdom itself. Ecclesiastes in turn influenced the deuterocanonical works, Wisdom of Solomon and Sirach, both of which contain vocal rejections of the Ecclesiastical philosophy of futility.

Wisdom was a popular genre in the ancient world, where it was cultivated in scribal circles and directed towards young men who would take up careers in high officialdom and royal courts; there is strong evidence that some of these books, or at least sayings and teachings, were translated into Hebrew and influenced the Book of Proverbs, and the author of Ecclesiastes was probably familiar with examples from Egypt and Mesopotamia. He may also have been influenced by Greek philosophy, specifically the schools of Stoicism, which held that all things are fated, and Epicureanism, which held that happiness was best pursued through the quiet cultivation of life's simpler pleasures.

Canonicity
The presence of Ecclesiastes in the Bible is something of a puzzle, as the common themes of the Hebrew canon—a God who reveals and redeems, who elects and cares for a chosen people—are absent from it, which suggests that Kohelet had lost his faith in his old age. Understanding the book was a topic of the earliest recorded discussions (the hypothetical Council of Jamnia in the 1st century CE). One argument advanced at that time was that the name of Solomon carried enough authority to ensure its inclusion; however, other works which appeared with Solomon's name were excluded despite being more orthodox than Ecclesiastes. Another was that the words of the epilogue, in which the reader is told to fear God and keep his commands, made it orthodox; but all later attempts to find anything in the rest of the book that would reflect this orthodoxy have failed. A modern suggestion treats the book as a dialogue in which different statements belong to different voices, with Kohelet himself answering and refuting unorthodox opinions, but there are no explicit markers for this in the book, as there are (for example) in the Book of Job.

Yet another suggestion is that Ecclesiastes is simply the most extreme example of a tradition of skepticism, but none of the proposed examples match Ecclesiastes for a sustained denial of faith and doubt in the goodness of God. Martin A. Shields, in his 2006 book The End of Wisdom: A Reappraisal of the Historical and Canonical Function of Ecclesiastes, summarized that "In short, we do not know why or how this book found its way into such esteemed company".

Themes
Scholars disagree about the themes of Ecclesiastes: whether it is positive and life-affirming, or deeply pessimistic; whether it is coherent or incoherent, insightful or confused, orthodox or heterodox; whether the ultimate message of the book is to copy Kohelet, "the wise man," or to avoid his errors. At times, Kohelet raises deep questions; he "doubted every aspect of religion, from the very ideal of righteousness, to the by now traditional idea of divine justice for individuals". Some passages of Ecclesiastes seem to contradict other portions of the Hebrew Bible, and even itself. The Talmud even suggests that the rabbis considered censoring Ecclesiastes due to its seeming contradictions. One suggestion for resolving the contradictions is to read the book as the record of Kohelet's quest for knowledge: opposing judgments (e.g., "the dead are better off than the living" (4:2) vs. "a living dog is better off than a dead lion" (9:4)) are therefore provisional, and it is only at the conclusion that the verdict is delivered (11–12:7). On this reading, Kohelet's sayings are goads, designed to provoke dialogue and reflection in his readers, rather than to reach premature and self-assured conclusions.

The subjects of Ecclesiastes are the pain and frustration engendered by observing and meditating on the distortions and inequities pervading the world, the uselessness of human ambition, and the limitations of worldly wisdom and righteousness. The phrase "under the sun" appears twenty-nine times in connection with these observations; all this coexists with a firm belief in God, whose power, justice and unpredictability are sovereign. History and nature move in cycles, so that all events are predictable and unchangeable, and life, without the Sun, has no meaning or purpose: the wise man and the man who does not study wisdom will both die and be forgotten: man should be reverent (i.e., fear God), but in this life it is best to simply enjoy God's gifts.

Judaism
In Judaism, Ecclesiastes is read either on Shemini Atzeret (by Yemenites, Italians, some Sephardim, and the mediaeval French Jewish rite) or on the Shabbat of the intermediate days of Sukkot (by Ashkenazim). If there is no intermediate Shabbat of Sukkot, Ashkenazim too read it on Shemini Atzeret (or, in Israel, on the first Shabbat of Sukkot). It is read on Sukkot as a reminder to not get too caught up in the festivities of the holiday and to carry over the happiness of Sukkot to the rest of the year by telling the listeners that, without God, life is meaningless.

The final poem of Kohelet has been interpreted in the Targum, Talmud and Midrash, and by the rabbis Rashi, Rashbam and ibn Ezra, as an allegory of old age.

Catholicism
Ecclesiastes has been cited in the writings of past and current Catholic Church leaders. For example, Doctors of the Church have cited Ecclesiastes. Augustine of Hippo cited Ecclesiastes in Book XX of City of God. Jerome wrote a commentary on Ecclesiastes. Thomas Aquinas cited Ecclesiastes ("The number of fools is infinite.") in his Summa Theologica.

The 20th-century Catholic theologian and cardinal-elect Hans Urs von Balthasar discussed Ecclesiastes in his work on theological aesthetics, The Glory of the Lord. He describes Qoheleth as "a critical transcendentalist avant la lettre", whose God is distant from the world, and whose is a "form of time which is itself empty of meaning". For Balthasar, the role of Ecclesiastes in the Biblical canon is to represent the "final dance on the part of wisdom, [the] conclusion of the ways of man", a logical end-point to the unfolding of human wisdom in the Old Testament that paves the way for the advent of the New.

The book continues to be cited by recent popes, including Pope John Paul II and Pope Francis. Pope John Paul II, in his general audience of October 20, 2004, called the author of Ecclesiastes "an ancient biblical sage" whose description of death "makes frantic clinging to earthly things completely pointless". Pope Francis cited Ecclesiastes in his address on September 9, 2014. Speaking of vain people, he said, "How many Christians live for appearances? Their life seems like a soap bubble."

Influence on Western literature
Ecclesiastes has had a deep influence on Western literature. It contains several phrases that have resonated in British and American culture, such as "eat, drink and be merry", "nothing new under the sun", "a time to be born and a time to die", and "vanity of vanities; all is vanity". American novelist Thomas Wolfe wrote: "[O]f all I have ever seen or learned, that book seems to me the noblest, the wisest, and the most powerful expression of man's life upon this earth—and also the highest flower of poetry, eloquence, and truth. I am not given to dogmatic judgments in the matter of literary creation, but if I had to make one I could say that Ecclesiastes is the greatest single piece of writing I have ever known, and the wisdom expressed in it the most lasting and profound."
 * The opening of William Shakespeare's Sonnet 59 references Ecclesiastes 1:9–10.
 * Line 23 of T. S. Eliot's The Waste Land alludes to Ecclesiastes 12:5.
 * Christina Rossetti's "One Certainty" quotes from Ecclesiastes 1:2–9.
 * Leo Tolstoy's Confession describes how the reading of Ecclesiastes affected his life.
 * Robert Burns' "Address to the Unco Guid" begins with a verse appeal to Ecclesiastes 7:16.
 * The title of Ernest Hemingway's first novel The Sun Also Rises comes from Ecclesiastes 1:5.
 * The title of Edith Wharton's novel The House of Mirth was taken from Ecclesiastes 7:4 ("The heart of the wise is in the house of mourning; but the heart of fools is in the house of mirth.").
 * Ecclesiastes 4: 9–12 is quoted in chapter 28 of John Steinbeck's The Grapes of Wrath (1939).
 * The title of Laura Lippman's novel Every Secret Thing and that of its film adaptation come from Ecclesiastes 12:14 ("For God shall bring every work into judgment, with every secret thing, whether it be good, or whether it be evil.").
 * The main character in George Bernard Shaw's short story The Adventures of the Black Girl in Her Search for God meets Koheleth, "known to many as Ecclesiastes".
 * The title of Henry James's novel The Golden Bowl is taken from Ecclesiastes 12:6.
 * The title and theme of George R. Stewart's post-apocalyptic novel Earth Abides is from Ecclesiastes 1:4.
 * In the dystopian novel Fahrenheit 451, Ray Bradbury's main character, Montag, memorizes much of Ecclesiastes and Revelation in a world where books are forbidden and burned.
 * The passage in chapter 3, with its repetition of "A time to ..." has been used as a title in many other cases, including the novels A Time to Dance by Melvyn Bragg and A Time to Kill by John Grisham, the records ...And a Time to Dance by Los Lobos and A Time to Love by Stevie Wonder, and films A Time to Love and a Time to Die, A Time to Live and A Time to Kill.
 * The opening quote in the movie Platoon by Oliver Stone is taken from Ecclesiastes 11:9.
 * The essay "Politics and the English Language" by George Orwell uses Ecclesiastes 9:11 as an example of clear and vivid writing, and "translates" it into "modern English of the worst sort" to demonstrate common fallings of the latter.
 * The opening pages of Jean Baudrillard's Simulacra and Simulation misquote Ecclesiastes.

Influence on popular music

 * Pete Seeger's 1959 song "Turn! Turn! Turn!", later made famous by the American rock band The Byrds, takes all but one of its lines from chapter 3.
 * Alec Roth's oratorio "A Time to Dance" (2012) takes both its title and the text for its opening movement from chapter 3.
 * Boygenius's song "Satanist" (2023) mentions Ecclesiastes, attributing the writings to King Solomon with the lyric: "Solomon had a point when he wrote "Ecclesiastes", If nothing can be known, then stupidity is holy"
 * Pete Townshend's song "Empty Glass" (1980) from his album of the same name contains the words, "Why was I born today? Life is useless like Ecclesiastes say."
 * Stevie Wonder's instrumental song "Ecclesiastes" appears on side 3 of Stevie Wonder's Journey Through "The Secret Life of Plants"
 * Ace of Base paraphrases Ecclesiastes 3 in their 2009 demo recording "Couldn't Care Less"
 * Architects paraphrases Ecclesiastes 1:7 in the chorus of their song "Doomsday".

title: Ecclesiastes


text:
Ezekiel

Ezekiel, also spelled Ezechiel (יְחֶזְקֵאל ;   ), was an Israelite priest. The Book of Ezekiel, relating his visions and activities, is named after him.

The Abrahamic religions acknowledge Ezekiel as a prophet. During the Babylonian captivity, Ezekiel prophesized the destruction of Judah's capital city Jerusalem, but following the Babylonian siege of Jerusalem, which destroyed Solomon's Temple and brought an end to the Jewish–Babylonian War in 587 BCE, also the restoration of the Jewish people to the Land of Israel in the aftermath.

It is believed that he died around 570 BCE; Ezekiel's Tomb is the most important Jewish religious site in Mesopotamia. The name "Ezekiel" means "God is strong" or "God strengthens" in the Hebrew language. In 539 BCE, three decades after the believed date of his death, the Babylonian captivity ended with the Persian conquest of Babylon and the Jews were subsequently repatriated in an event known as the return to Zion, which began after the Persian king Cyrus the Great issued the Edict of Cyrus.

Biblical account
The author of the Book of Ezekiel presents himself as Ezekiel, the son of Buzi, born into a priestly (kohen) lineage. Apart from identifying himself, the author gives a date for the first divine encounter which he presents: "in the thirtieth year". Ezekiel describes his calling to be a prophet by going into great detail about his encounter with God and four "living creatures" with four wheels that stayed beside the creatures.

According to the Bible, Ezekiel and his wife lived during the Babylonian captivity on the banks of the Kebar Canal in Tel Abib near Nippur with other exiles from the Kingdom of Judah. There is no mention of him having any offspring.

Chronology
Ezekiel's "thirtieth year" is given as the fifth year of the exile of Judah's king Jeconiah by the Neo-Babylonian Empire, counting the years after the exile in 598 BCE, that is from 597 to 593 BCE. The last recorded prophecy of Ezekiel dates to April 571 BCE, sixteen years after the destruction of Jerusalem in 587 BCE. Based on dates given in the Book of Ezekiel, his span of prophecies can be calculated to have occurred over about 22 years, starting in 593 BCE.

The Targum Jonathan on Ezekiel 1:1 and the 2nd-century rabbinic work Seder Olam Rabba (chapter 26) both say that Ezekiel's vision came "in the thirtieth year after Josiah was presented with a Book of the Law discovered in the Temple", the latter taking place about the time of Josiah's reforms in 622 BCE, shortly after the call of Jeremiah to prophetic ministry around 626 BCE. If the "thirtieth year" of Ezekiel 1:1 instead refers to Ezekiel's age, then he was born around 622 BCE and was fifty years old when he had his final vision.

Jewish tradition
According to Jewish tradition, Ezekiel did not write his own book, the Book of Ezekiel, but rather his prophecies were collected and written by the Great Assembly.

Ezekiel, like Jeremiah, is said by Talmud and Midrash to have been a descendant of Joshua by his marriage with the proselyte and former prostitute Rahab. Some statements found in rabbinic literature posit that Ezekiel was the son of Jeremiah, who was (also) called "Buzi" because he was despised by the Jews.

According to Josephus, Ezekiel was already active as a prophet while in the Land of Israel, and he retained this gift when he was exiled with Jehoiachin and the nobles of the country to Babylon. Josephus relates that Nebuchadnezzar of Babylonia's armies exiled three thousand people from Judah, after deposing King Jehoiachin in 598 BCE.

Rava states in the Babylonian Talmud that although Ezekiel describes the appearance of the throne of God (merkabah), this is not because he had seen more than the prophet Isaiah, but rather because the latter was more accustomed to such visions; for the relation of the two prophets is that of a courtier to a peasant, the latter of whom would always describe a royal court more floridly than the former, to whom such things would be familiar. Ezekiel, like all the other prophets, has beheld only a blurred reflection of the divine majesty, just as a poor mirror reflects objects only imperfectly.

According to the midrash Shir HaShirim Rabbah, it was Ezekiel whom the three pious men, Hananiah, Mishael, and Azariah (also called Shadrach, Meshach, and Abednego) asked for advice as to whether they should resist Nebuchadnezzar's command and choose death by fire rather than worship his idol.

At first God revealed to the prophet that they could not hope for a miraculous rescue; whereupon the prophet was greatly grieved, since these three men constituted the "remnant of Judah". But after they had left the house of the prophet, fully determined to sacrifice their lives to God, Ezekiel received this revelation: "When they went out from before Ezekiel, the Holy One blessed be He revealed Himself and said: 'Ezekiel, what do you think, that I will not stand by them? I will certainly stand by them.' That is what is written: "So said the Lord God: Concerning this too, I will acquiesce to the house of Israel" (Ezekiel 36:37). 'But leave them and do not say anything to them. I will leave them to proceed unsuspecting.'"

Christian tradition

Ezekiel is commemorated as a saint in the liturgical calendar of the Eastern Orthodox Church—and those Eastern Catholic Churches which follow the Byzantine Rite—on July 21 (for those churches which use the traditional Julian Calendar, July 21 falls on August 5 of the modern Gregorian Calendar). Ezekiel is commemorated on August 28 on the Calendar of Saints of the Armenian Apostolic Church, and on April 10 in the Roman Martyrology.

Certain Lutheran churches also celebrate his commemoration on July 21.

Saint Bonaventure interpreted Ezekiel's statement about the "closed gate" as a prophecy of the Incarnation: the "gate" signifying the Virgin Mary and the "prince" referring to Jesus. This is one of the readings at Vespers on Great Feasts of the Theotokos in the Eastern Orthodox and Byzantine Catholic Churches. This imagery is also found in the traditional Catholic Christmas hymn "Gaudete" and in a saying by Bonaventure, quoted by Alphonsus Maria de' Liguori: "No one can enter Heaven unless by Mary, as though through a door." The imagery provides the basis for the concept that God gave Mary to humanity as the "Gate of Heaven" (thence the dedication of churches and convents to the Porta Coeli), an idea also laid out in the Salve Regina (Hail Holy Queen) prayer.

John B. Taylor credits the subject with imparting the Biblical understanding of the nature of God.

Islamic tradition
Ezekiel (حزقيال; "Ḥazqiyāl") is recognized as a prophet in Islamic tradition. Although not mentioned by name in the Quran, Muslim scholars, both classical and modern have included Ezekiel in lists of the prophets of Islam.

The Quran mentions a prophet called Dhū al-Kifl (ذو الكفل). Although Dhu al-Kifl's identity is disputed, he is often identified with Ezekiel. Carsten Niebuhr, in his Reisebeschreibung nach Arabian, says he visited Al Kifl in Iraq, midway between Najaf and Hilla and said Kifl was the Arabic form of Ezekiel. He further explained in his book that Ezekiel's Tomb was present in Al Kifl and that the Jews came to it on pilgrimage. The name "Dhu al-Kifl" means "Possessor of the Double" or "Possesor of the Fold" (ذو dhū "possessor of, owner of" and الكفل al-kifl "double, folded"). Some Islamic scholars have likened Ezekiel's mission to the description of Dhu al-Kifl. During the exile, the monarchy and state were annihilated, and political and national life were no longer possible. In the absence of a worldly foundation, it became necessary to build a spiritual one and Ezekiel performed this mission by observing the signs of the time and deducing his doctrines from them. In conformity with the two parts of his book, his personality and his preaching are alike twofold.

Regardless of the identification of Dhu al-Kifl with Ezekiel, Muslims have viewed Ezekiel as a prophet. Ezekiel appears in all collections of Stories of the Prophets. Muslim exegesis further lists Ezekiel's father as Buzi (Budhi) and Ezekiel is given the title ibn al-‘ajūz, denoting "son of the old (man)", as his parents are supposed to have been very old when he was born. A tradition, which resembles that of Hannah and Samuel in the Hebrew Bible, states that Ezekiel's mother prayed to God in old age for the birth of an offspring and was given Ezekiel as a gift from God.

Ezekiel's Tomb, Iraq
Ezekiel's Tomb is located in Al Kifl, Iraq, near Babylon. Historically an important Jewish site, the Al-Nukhailah Mosque for Shia Muslims was constructed over it. Due to the Jewish exodus from Iraq in the 1950s, the presence of the Iraqi Jewish community has diminished, although a disused synagogue remains in place at the location. In 2020, work was reportedly underway to transform the synagogue into a mosque.

Tomb at Ergani, Turkey
A tomb in the Ergani District of Diyarbakır Province in Turkey is also believed to be the resting place of Ezekiel. It is located 5 km from the city centre on a hill, where it is revered and visited by local Muslims, called Makam Dağı.

In popular culture
Ezekiel is portrayed by Darrell Dunham in a 1979 episode of the television series Our Jewish Roots (1978–).

title: Ezekiel


text:
Executable and Linkable Format

In computing, the Executable and Linkable Format (ELF, formerly named Extensible Linking Format), is a common standard file format for executable files, object code, shared libraries, and core dumps. First published in the specification for the application binary interface (ABI) of the Unix operating system version named System V Release 4 (SVR4), and later in the Tool Interface Standard, it was quickly accepted among different vendors of Unix systems. In 1999, it was chosen as the standard binary file format for Unix and Unix-like systems on x86 processors by the 86open project.

By design, the ELF format is flexible, extensible, and cross-platform. For instance, it supports different endiannesses and address sizes so it does not exclude any particular CPU or instruction set architecture. This has allowed it to be adopted by many different operating systems on many different hardware platforms.

File layout
Each ELF file is made up of one ELF header, followed by file data. The data can include:
 * Program header table, describing zero or more memory segments
 * Section header table, describing zero or more sections
 * Data referred to by entries in the program header table or section header table

The segments contain information that is needed for run time execution of the file, while sections contain important data for linking and relocation. Any byte in the entire file can be owned by one section at most, and orphan bytes can occur which are unowned by any section.

File header
The ELF header defines whether to use 32-bit or 64-bit addresses. The header contains three fields that are affected by this setting and offset other fields that follow them. The ELF header is 52 or 64 bytes long for 32-bit and 64-bit binaries respectively.

Program header
The program header table tells the system how to create a process image. It is found at file offset e_phoff, and consists of e_phnum entries, each with size e_phentsize. The layout is slightly different in 32-bit ELF vs 64-bit ELF, because the p_flags are in a different structure location for alignment reasons. Each entry is structured as:

Tools

 * is a Unix binary utility that displays information about one or more ELF files. A free software implementation is provided by GNU Binutils.
 * provides alternative tools to GNU Binutils purely for Linux.
 * is a command for viewing ELF information in an ELF file, available under Solaris and FreeBSD.
 * provides a wide range of information about ELF files and other object formats.  uses the Binary File Descriptor library as a back-end to structure the ELF data.
 * The Unix  utility can display some information about ELF files, including the instruction set architecture for which the code in a relocatable, executable, or shared object file is intended, or on which an ELF core dump was produced.

Unix-like systems
The ELF format has replaced older executable formats in various environments. It has replaced a.out and COFF formats in Unix-like operating systems:
 * Linux
 * Solaris / Illumos
 * IRIX
 * FreeBSD
 * NetBSD
 * OpenBSD
 * Redox
 * DragonFly BSD
 * Syllable
 * HP-UX (except for 32-bit PA-RISC programs which continue to use SOM)
 * QNX Neutrino
 * MINIX

Non-Unix adoption
ELF has also seen some adoption in non-Unix operating systems, such as:
 * OpenVMS, in its Itanium and amd64 versions
 * BeOS Revision 4 and later for x86 based computers (where it replaced the Portable Executable format; the PowerPC version stayed with Preferred Executable Format)
 * Haiku, an open source reimplementation of BeOS
 * RISC OS
 * Stratus VOS, in PA-RISC and x86 versions
 * SkyOS
 * Fuchsia OS
 * Z/TPF
 * HPE NonStop OS
 * Deos

Microsoft Windows also uses the ELF format, but only for its Windows Subsystem for Linux compatibility system.

Game consoles
Some game consoles also use ELF:
 * PlayStation Portable, PlayStation Vita, PlayStation (console), PlayStation 2, PlayStation 3, PlayStation 4, PlayStation 5
 * GP2X
 * Dreamcast
 * GameCube
 * Nintendo 64
 * Wii
 * Wii U

PowerPC
Other (operating) systems running on PowerPC that use ELF:
 * AmigaOS 4, the ELF executable has replaced the prior Extended Hunk Format (EHF) which was used on Amigas equipped with PPC processor expansion cards.
 * MorphOS
 * AROS
 * Café OS (The operating system run by the Wii U)

Mobile phones
Some operating systems for mobile phones and mobile devices use ELF:
 * Symbian OS v9 uses E32Image format that is based on the ELF file format;
 * Sony Ericsson, for example, the W800i, W610, W300, etc.
 * Siemens, the SGOLD and SGOLD2 platforms: from Siemens C65 to S75 and BenQ-Siemens E71/EL71;
 * Motorola, for example, the E398, SLVR L7, v360, v3i (and all phone LTE2 which has the patch applied).
 * Bada, for example, the Samsung Wave S8500.
 * Nokia phones or tablets running the Maemo or the Meego OS, for example, the Nokia N900.
 * Android uses ELF .so (shared object ) libraries for the Java Native Interface. With Android Runtime (ART), the default since Android 5.0 "Lollipop", all applications are compiled into native ELF binaries on installation. It's also possible to use native Linux software from package managers like Termux, or compile them from sources via Clang or GCC, that are available in repositories.

Some phones can run ELF files through the use of a patch that adds assembly code to the main firmware, which is a feature known as ELFPack in the underground modding culture. The ELF file format is also used with the Atmel AVR (8-bit), AVR32 and with Texas Instruments MSP430 microcontroller architectures. Some implementations of Open Firmware can also load ELF files, most notably Apple's implementation used in almost all PowerPC machines the company produced.

Specifications

 * Generic:
 * System V Application Binary Interface Edition 4.1 (1997-03-18)
 * System V ABI Update (October 2009)
 * AMD64:
 * System V ABI, AMD64 Supplement
 * Arm:
 * ELF for the ARM Architecture
 * IA-32:
 * System V ABI, Intel386 Architecture Processor Supplement
 * IA-64:
 * Itanium Software Conventions and Runtime Guide (September 2000)
 * M32R:
 * M32R ELF ABI Supplement Version 1.2 (2004-08-26)
 * MIPS:
 * System V ABI, MIPS RISC Processor Supplement
 * MIPS EABI documentation  (2003-06-11)
 * Motorola 6800:
 * Motorola 8- and 16- bit Embedded ABI
 * PA-RISC:
 * ELF Supplement for PA-RISC Version 1.43 (October 6, 1997)
 * PowerPC:
 * System V ABI, PPC Supplement
 * PowerPC Embedded Application Binary Interface 32-Bit Implementation (1995-10-01)
 * 64-bit PowerPC ELF Application Binary Interface Supplement Version 1.9 (2004)
 * RISC-V:
 * RISC-V ELF Specification
 * SPARC:
 * System V ABI, SPARC Supplement
 * S/390:
 * S/390 32bit ELF ABI Supplement
 * zSeries:
 * zSeries 64bit ELF ABI Supplement
 * Symbian OS 9:
 * E32Image file format on Symbian OS 9

The Linux Standard Base (LSB) supplements some of the above specifications for architectures in which it is specified. For example, that is the case for the System V ABI, AMD64 Supplement.

86open
86open was a project to form consensus on a common binary file format for Unix and Unix-like operating systems on the common PC compatible x86 architecture, to encourage software developers to port to the architecture. The initial idea was to standardize on a small subset of Spec 1170, a predecessor of the Single UNIX Specification, and the GNU C Library (glibc) to enable unmodified binaries to run on the x86 Unix-like operating systems. The project was originally designated "Spec 150".

The format eventually chosen was ELF, specifically the Linux implementation of ELF, after it had turned out to be a de facto standard supported by all involved vendors and operating systems.

The group began email discussions in 1997 and first met together at the Santa Cruz Operation offices on August 22, 1997.

The steering committee was Marc Ewing, Dion Johnson, Evan Leibovitch, Bruce Perens, Andrew Roach, Bryan Wayne Sparks and Linus Torvalds. Other people on the project were Keith Bostic, Chuck Cranor, Michael Davidson, Chris G. Demetriou, Ulrich Drepper, Don Dugger, Steve Ginzburg, Jon "maddog" Hall, Ron Holt, Jordan Hubbard, Dave Jensen, Kean Johnston, Andrew Josey, Robert Lipe, Bela Lubkin, Tim Marsland, Greg Page, Ronald Joe Record, Tim Ruckle, Joel Silverstein, Chia-pi Tien, and Erik Troan. Operating systems and companies represented were BeOS, BSDI, FreeBSD, Intel, Linux, NetBSD, SCO and SunSoft.

The project progressed and in mid-1998, SCO began developing lxrun, an open-source compatibility layer able to run Linux binaries on OpenServer, UnixWare, and Solaris. SCO announced official support of lxrun at LinuxWorld in March 1999. Sun Microsystems began officially supporting lxrun for Solaris in early 1999, and later moved to integrated support of the Linux binary format via Solaris Containers for Linux Applications.

With the BSDs having long supported Linux binaries (through a compatibility layer) and the main x86 Unix vendors having added support for the format, the project decided that Linux ELF was the format chosen by the industry and "declare[d] itself dissolved" on July 25, 1999.

FatELF: universal binaries for Linux
FatELF is an ELF binary-format extension that adds fat binary capabilities. It is aimed for Linux and other Unix-like operating systems. Additionally to the CPU architecture abstraction (byte order, word size, CPU instruction set etc.), there is the potential advantage of software-platform abstraction e.g., binaries which support multiple kernel ABI versions. , FatELF has not been integrated into the mainline Linux kernel.

title: Executable and Linkable Format


text:
Explorers Program

The Explorers program is a NASA exploration program that provides flight opportunities for physics, geophysics, heliophysics, and astrophysics investigations from space. Launched in 1958, Explorer 1 was the first spacecraft of the United States to achieve orbit. Over 90 space missions have been launched since. Starting with Explorer 6, it has been operated by NASA, with regular collaboration with a variety of other institutions, including many international partners.

Launchers for the Explorer program have included Juno I, Juno II, various Thor, Scout, Delta and Pegasus launch vehicles, and Falcon 9.

The program has three classes: Medium-Class Explorers (MIDEX), Small Explorers (SMEX), and University-Class Explorers (UNEX), with select Missions of Opportunity operated with other agencies.

Early Explorer satellites

The Explorer program began as a U.S. Army proposal (Project Orbiter) to place a "civilian" artificial satellite into orbit during the International Geophysical Year (IGY). Although that proposal was rejected in favor of the U.S. Navy's Project Vanguard, which made the first sub-orbital flight Vanguard TV0 in December 1956, the Soviet Union's launch of Sputnik 1 on 4 October 1957 (and the resulting "Sputnik crisis") and the failure of the Vanguard 1 launch attempt resulted in the Army program being funded to match the Soviet space achievements. Explorer 1 was launched on the Juno I on 1 February 1958, becoming the first U.S. satellite, as well as discovering the Van Allen radiation belt.

Four follow-up satellites of the Explorer series were launched by the Juno I launch vehicle in 1958, of which Explorer 3 and Explorer 4 were successful, while Explorer 2 and Explorer 5 failed to reach orbit. The Juno I vehicle was replaced by the Juno II in 1959.

Continuation of the Explorer program

With the establishment of NASA in 1958, the Explorer program was transferred to NASA from the U.S. Army. NASA continued to use the name for an ongoing series of relatively small space missions, typically an artificial satellite with a specific science focus. Explorer 6 in 1959 was the first scientific satellite under the project direction of NASA's Goddard Space Flight Center (GSFC) in Greenbelt, Maryland.

The Interplanetary Monitoring Platform (IMP) was launched in 1963, and involved a network of eleven Explorer satellites designed to collect data on space radiation in support of the Apollo program. The IMP program was a major step forward in spacecraft electronics design, as it was the first space program to use integrated circuit (IC) chips and MOSFETs (MOS transistors). The IMP-A (Explorer 18) in 1963 was the first spacecraft to use IC chips, and the IMP-D (Explorer 33) in 1966 was the first to use MOSFETs.

Over the following two decades, NASA has launched over 50 Explorer missions, some in conjunction to military programs, usually of an exploratory or survey nature or had specific objectives not requiring the capabilities of a major space observatory. Explorer satellites have made many important discoveries on: Earth's magnetosphere and the shape of its gravity field; the solar wind; properties of micrometeoroids raining down on the Earth; ultraviolet, cosmic and X-rays from the Solar System and beyond; ionospheric physics; Solar plasma; solar energetic particles; and atmospheric physics. These missions have also investigated air density, radio astronomy, geodesy, and gamma-ray astronomy.

With drops in NASA's budget, Explorer missions became infrequent in the early 1980s.

SMEX, MIDEX, and Student Explorer programs
In 1988, the Small Explorer (SMEX) class was established with a focus on frequent flight opportunities for highly focused and relatively inexpensive space science missions in the disciplines of astrophysics and space physics. The first three SMEX missions were chosen in April 1989 out of 51 candidates, and launched in 1992, 1996 and 1998 The second set of two missions were announced in September 1994 and launched in 1998 and 1999.

In the mid 1990s, NASA initiated the Medium-class Explorer (MIDEX) to enable more frequent flights. These are larger than SMEX missions and were to be launched aboard a new kind of medium-light class launch vehicle. This new launch vehicle was not developed and instead, these missions were flown on a modified Delta II rocket. The first announcement opportunity for MIDEX was issued in March 1995, and the first launch under this new class was FUSE in 1999.

In May 1994, NASA started the Student Explorer Demonstration Initiative (STEDI) pilot program, to demonstrate that high-quality space science can be carried out with small, low-cost missions. Of the three selected missions, SNOE was launched in 1998 and TERRIERS in 1999, but the latter failed after launch. The STEDI program was terminated in 2001. Later, NASA established the University-Class Explorer (UNEX) program for much cheaper missions, which is regarded as a successor to STEDI.

The Explorer missions were at first managed by the Small Explorer Project Office at NASA's Goddard Space Flight Center (GSFC). In early 1999, that office was closed and with the announcement of opportunity for the third set of SMEX missions NASA converted the SMEX class so that each mission was managed by its principal investigator, with oversight by the GSFC Explorer Project. The Explorer program Office at Goddard Space Flight Center, provides management of the many operational scientific exploration missions that are characterized by relatively moderate costs and small to medium-sized missions that are capable of being built, tested, and launched in a short time interval compared to larger observatories like NASA's Great Observatories.

Excluding the launches, the MIDEX class has a current mission cap cost of US$250 million in 2018, with future MIDEX missions being capped at US$350 million. The cost cap for SMEX missions in 2017 was US$165 million. UNEX missions are capped at US$15 million. A sub-project called Missions of Opportunity (MO) has funded science instruments or hardware components of onboard non-NASA space missions, and have a total NASA cost cap of US$70 million.

Small Explorers (SMEX)
The Small Explorers class was implemented in 1989 specifically to fund space exploration missions that cost no more than US$120 million. The missions are managed by the Explorers Project at the Goddard Space Flight Center (GSFC).

The first set of three SMEX missions were launched between 1992 and 1998. The second set of two missions were launched in 1998 and 1999. These early missions were managed by the Small Explorer Project Office at Goddard Space Flight Center. In early 1999, that office was closed and with the announcement of opportunity for the third set of SMEX missions NASA converted the program so that each mission was managed by its Principal Investigator, with oversight by the GSFC Explorers Project.

NASA funded a competitive study of five candidate heliophysics Small Explorers missions for flight in 2022. The proposals were Mechanisms of Energetic Mass Ejection – eXplorer (MEME-X), Focusing Optics X-ray Solar Imager (FOXSI), Multi-Slit Solar Explorer (MUSE), Tandem Reconnection and Cusp Electrodynamics Reconnaissance Satellites (TRACERS), and Polarimeter to Unify the Corona and Heliosphere (PUNCH). In June 2019 NASA selected TRACERS and PUNCH for flight.

Missions of Opportunity (MO)
Missions of Opportunity (MO) are investigations characterized by being part of a non-NASA space mission of any size and having a total NASA cost of under $55 million. These missions are conducted on a no-exchange-of-funds basis with the organization sponsoring the mission. NASA solicits proposals for Missions of Opportunity on SMEX, MIDEX and UNEX investigations.

Beacon Explorers
Three satellites were planned in this series: Beacon Explorer-A, Beacon Explorer-B, Beacon Explorer-C.

GEOS series
A series of three Geodetic Earth Orbiting Satellite (GEOS) were put in orbit: GEOS 1, GEOS 2, GEOS 3.

Launched spacecraft
Explorer name numbers can be found in the NSSDC master catalog, typically assigned to each spacecraft in a mission. These numbers were not officially assigned until after 1975.

Cancelled missions
Many missions are proposed, but not selected. For example, in 2011, the Explorers Program received 22 full missions solicitations, 20 Missions of Opportunity, and 8 USPI. Sometimes mission are only partially developed but must be stopped for financial, technological, or bureaucratic reasons. Some missions failed upon reaching orbit including WIRE and TERRIERS.

Examples of missions that were not developed or cancelled were:
 * Owl 1 and 2 (cost, 1965)
 * MSS A (Magnetic Storm Satellite, Explorer-A, 1970)
 * CATSAT (STEDI 3) (cost)
 * IMEX (UNEX 2) (cost)
 * FAME (MIDEX 4)
 * SPIDR (SMEX 8) (technical, 2003)
 * GEMS (SMEX 13)

Recent examples of conclusions of launched missions, cancelled due to budgetary constraints:
 * FAST - 2009
 * TRACE - 2010 (Solar observatory, see Solar Dynamics Observatory)
 * Wilkinson MAP - 2010
 * WISE - 2011 (extended in 2013 as NEOWISE mission)
 * RXTE - 2012
 * Galaxy Evolution Explorer - 2013

Launch statistics
Number of launches per decade:

title: Explorers Program