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Materials Science and Engineering/Equations/Thermodynamics

Laws of Thermodynamics
First Law of Thermodynamics:

 * $$dU=\delta Q-\delta W\,$$

Second Law of Thermodynamics:

 * $$\int \frac{\delta Q}{T} \ge 0$$

Fundamental Equations
The Fundamental Equation:

 * $$dU \le TdS-pdV+\sum_{i=1}^p\mu_idN_i$$

The equation may be seen as a particular case of the chain rule:

 * $$dU=

\left(\frac{\partial U}{\partial S}\right)_{V,\{N_i\}}dS+ \left(\frac{\partial U}{\partial V}\right)_{S,\{N_i\}}dV+ \sum_i\left(\frac{\partial U}{\partial N_i}\right)_{S,V,\{N_{j \ne i}\}}dN_i $$

from which the following identifications can be made:

 * $$\left(\frac{\partial U}{\partial S}\right)_{V,\{N_i\}}=T$$
 * $$\left(\frac{\partial U}{\partial V}\right)_{S,\{N_i\}}=-p$$
 * $$\left(\frac{\partial U}{\partial N_i}\right)_{S,V,\{N_{j \ne i}\}}=\mu_i$$

These equations are known as "equations of state" with respect to the internal energy.

Thermodynamic Potentials
Thermodynamic Potentials:

 * {| border="0" cellpadding="4" style="margin: 0 0 1em 1em"

 * Name
 * Formula
 * Natural variables
 * Internal energy
 * $$U\,$$
 * align="center"|$$S,V,\{N_i\}\,$$
 * Helmholtz free energy
 * $$A=U-TS\,$$
 * align="center"|$$T,V,\{N_i\}\,$$
 * Enthalpy
 * $$H=U+pV\,$$
 * align="center"|$$S,p,\{N_i\}\,$$
 * Gibbs free energy
 * $$G=U+pV-TS\,$$
 * align="center"|$$T,p,\{N_i\}\,$$
 * }
 * Gibbs free energy
 * $$G=U+pV-TS\,$$
 * align="center"|$$T,p,\{N_i\}\,$$
 * }
 * }

For the above four potentials, the fundamental equations are expressed as:

 * $$dU\left(S,V,{N_{i}}\right) = TdS - pdV + \sum_{i} \mu_{i} dN_i$$
 * $$dA\left(T,V,N_{i}\right) = -SdT - pdV + \sum_{i} \mu_{i} dN_{i}$$
 * $$dH\left(S,p,N_{i}\right) = TdS + Vdp + \sum_{i} \mu_{i} dN_{i}$$
 * $$dG\left(T,p,N_{i}\right) = -SdT + Vdp + \sum_{i} \mu_{i} dN_{i}$$

Euler Integrals:

Because all of natural variables of the internal energy U are extensive quantities, it follows from Euler's homogeneous function theorem that

 * $$U=TS-pV+\sum_i \mu_i N_i\,$$

Substituting into the expressions for the other main potentials we have the following expressions for the thermodynamic potentials:

 * $$A= -pV+\sum_i \mu_i N_i\,$$

 * $$H=TS  +\sum_i \mu_i N_i\,$$

 * $$G=     \sum_i \mu_i N_i\,$$

Note that the Euler integrals are sometimes also referred to as fundamental equations.

Gibbs Duhem Relationship:

Differentiating the Euler equation for the internal energy and combining with the fundamental equation for internal energy, it follows that:

 * $$0=SdT-Vdp+\sum_iN_id\mu_i\,$$

which is known as the Gibbs-Duhem relationship. The Gibbs-Duhem is a relationship among the intensive parameters of the system. It follows that for a simple system with r components, there will be r+1 independent parameters, or degrees of freedom. For example, a simple system with a single component will have two degrees of freedom, and may be specified by only two parameters, such as pressure and volume for example. The law is named after Josiah Gibbs and Pierre Duhem.

Materials Properties
Compressibility: At constant temperature or constant entropy
 * $$~ \beta_{T \text{ or } S} = -{ 1\over V } \left ( {\partial V\over \partial p} \right )_{T,N \text{ or } S,N}$$

Heat Capacity at Constant Pressure:

$$~ C_p=\left ( {\partial U\over \partial T} \right )_p +p \left ( {\partial V\over \partial T} \right )_p = \left ( {\partial H\over \partial T} \right )_p = T \left ( {\partial S\over \partial T} \right )_p ~$$

Heat Capacity at Constant Volume:

$$~ C_V=\left ( {\partial U\over \partial T} \right )_V = T \left ( {\partial S\over \partial T} \right )_V ~$$

Coefficient of Thermal Expansion:

 * $$\alpha_{p} = \frac{1}{V}\left(\frac{\partial V}{\partial T}\right)_p$$

Maxwell Relations:

Maxwell relations are equalities involving the second derivatives of thermodynamic potentials with respect to their natural variables. They follow directly from the fact that the order of differentiation does not matter when taking the second derivative. The four most common Maxwell relations are:

= -\left ( {\partial p\over \partial S} \right )_{V,N} ~$$ = \left ( {\partial V\over \partial S} \right )_{p,N} ~$$ = -\left ( {\partial p\over \partial S} \right )_{T,N} ~$$ = \left ( {\partial V\over \partial S} \right )_{T,N} ~$$
 * $$~ \left ( {\partial T\over \partial V} \right )_{S,N}
 * $$~ \left ( {\partial T\over \partial V} \right )_{S,N}
 * width="80"|
 * $$~ \left ( {\partial T\over \partial p} \right )_{S,n}
 * $$~ \left ( {\partial T\over \partial V} \right )_{p,N}
 * $$~ \left ( {\partial T\over \partial V} \right )_{p,N}
 * width="80"|
 * $$~ \left ( {\partial T\over \partial p} \right )_{V,N}
 * }

Processes
Incremental Processes:

$$~ dU = T\,dS-p\,dV + \mu\,dN ~$$

$$~ dA = -S\,dT-p\,dV + \mu\,dN ~$$

$$~ dG = -S\,dT+V\,dp + \mu\,dN = \mu\,dN +N\,d\mu ~$$

$$~ dH = T\,dS+V\,dp + \mu\,dN ~$$

Equation Table for an Ideal Gas ($$PV^m=constant$$):


text:
Materials Science and Engineering/Derivations/Quantum Mechanics

Schrodinger Equation
Schrödinger's equation follows very naturally from earlier developments:

In 1905, by considering the photoelectric effect, Albert Einstein had published his
 * $$E = h f\;$$

formula for the relation between the energy E and frequency f of the quanta of radiation (photons), where h is Planck's constant.

In 1924 Louis de Broglie presented his de Broglie hypothesis which states that all particles (not just photons) have an associated wavefunction $$\Psi\;$$ with properties:
 * $$p=h / \lambda\;$$, where $$\lambda\,$$ is the wavelength of the wave and p the momentum of the particle.

De Broglie showed that this was consistent with Einstein's formula and special relativity so that
 * $$E = h f\;$$

still holds, but now this is hypothesized to hold for all particles, not just photons anymore.

Expressed in terms of angular frequency $$\omega = 2\pi f\;$$ and wavenumber $$k = 2\pi / \lambda\;$$, with $$\hbar = h / 2 \pi\;$$ we get:
 * $$E=\hbar \omega$$

and
 * $$\mathbf{p}=\hbar \mathbf{k}\;$$

where we have expressed p and k as vectors.

Schrödinger's great insight, late in 1925, was to express the phase of a plane wave as a complex phase factor:
 * $$\psi \approx e^{i(\mathbf{k}\cdot\mathbf{x}- \omega t)}$$

and to realize that since
 * $$ \frac{\partial}{\partial t} \psi = -i\omega \psi $$

then
 * $$ E \psi = \hbar \omega \psi = i\hbar\frac{\partial}{\partial t} \psi $$

and similarly since:
 * $$ \frac{\partial}{\partial x} \psi = i k_x \psi $$

then
 * $$ p_x \psi = \hbar k_x \psi = -i\hbar\frac{\partial}{\partial x} \psi $$

and hence:
 * $$ p_x^2 \psi = -\hbar^2\frac{\partial^2}{\partial x^2} \psi $$

so that, again for a plane wave, he got:
 * $$ p^2 \psi = (p_x^2 + p_y^2 + p_z^2) \psi = -\hbar^2\left(\frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + \frac{\partial^2}{\partial z^2}\right) \psi = -\hbar^2\nabla^2 \psi $$

And by inserting these expressions into the Newtonian formula for a particle with total energy E, mass m, moving in a potential V:
 * $$E=\frac{p^2}{2m}+V$$ (simply the sum of the kinetic energy and potential energy; the plane wave model assumed V = 0)

he got his famed equation for a single particle in the 3-dimensional case in the presence of a potential:
 * $$i\hbar\frac{\partial}{\partial t}\Psi=-\frac{\hbar^2}{2m}\nabla^2\Psi + V\Psi$$

Solution of the Time-Dependent Schrodinger Equation
On inserting a solution of the time-independent Schrödinger equation into the full Schrödinger equation, we get

 * $$\mathrm{i} \hbar \frac{\partial}{\partial t} \left| \psi_n \left(t\right) \right\rangle = E_n \left|\psi_n\left(t\right)\right\rang. $$

It is relatively easy to solve this equation. One finds that the energy eigenstates (i.e., solutions of the time-independent Schrödinger equation) change as a function of time only trivially, namely, only by a complex phase (waves)|phase:

 * $$ \left| \psi \left(t\right) \right\rangle = \mathrm{e}^{-\mathrm{i} Et / \hbar} \left|\psi\left(0\right)\right\rang. $$

It immediately follows that the probability amplitude,
 * $$\psi(t)^*\psi(t) = \mathrm{e}^{\mathrm{i} Et / \hbar}\mathrm{e}^{-\mathrm{i} Et / \hbar}

\psi(0)^*\psi(0) = |\psi(0)|^2, $$ is time-independent. Because of a similar cancellation of phase factors in bra and ket, all average (expectation) values of time-independent observables (physical quantities) computed from $$\psi(t)\,$$ are  time-independent.

Energy eigenstates are convenient to work with because they form a complete set of states. That is, the eigenvectors $$ \left\{\left|n\right\rang\right\} $$ form a basis (linear algebra)|basis for the state space. We introduced here the short-hand notation $$|\,n\,\rang = \psi_n$$. Then any state vector that is a solution of the time-dependent Schrödinger equation (with a time-independent $$H$$) $$ \left|\psi\left(t\right)\right\rang $$ can be written as a linear superposition of energy eigenstates:

 * $$\left|\psi\left(t\right)\right\rang = \sum_n c_n(t) \left|n\right\rang \quad,\quad H \left|n\right\rang = E_n \left|n\right\rang \quad,\quad \sum_n \left|c_n\left(t\right)\right|^2 = 1.$$

(The last equation enforces the requirement that $$ \left|\psi\left(t\right)\right\rang $$, like all state vectors, may be normalized to a unit vector.) Applying the Hamiltonian operator to each side of the first equation, the time-dependent Schrödinger equation in the left-hand side and using the fact that the energy basis vectors are by definition linearly independent, we readily obtain

 * $$\mathrm{i}\hbar \frac{\partial c_n}{\partial t} = E_n c_n\left(t\right).$$

Therefore, if we know the decomposition of $$ \left|\psi\left(t\right)\right\rang $$ into the energy basis at time $$t = 0$$, its value at any subsequent time is given simply by

 * $$\left|\psi\left(t\right)\right\rang = \sum_n \mathrm{e}^{-\mathrm{i}E_nt/\hbar} c_n\left(0\right) \left|n\right\rang. $$

Note that when some values $$c_n(0)\,$$ are not equal to zero for differing energy values $$E_n\,$$, the left-hand side is not an eigenvector of the energy operator $$H$$. The left-hand is an eigenvector when the only $$c_n(0)\,$$-values not equal to zero belong the same energy, so that $$\mathrm{e}^{-\mathrm{i}E_nt/\hbar}$$ can be factored out. In many real-world application this is the case and the state vector $$\psi(t)\,$$ (containing time only in its phase factor) is then a solution of the time-independent Schrödinger equation.


text:
Materials Science and Engineering/Equations/Quantum Mechanics

Relation between energy and frequency of a quanta of radiation
$$E=hf\;$$ $$E=\hbar \omega$$

$$\mathbf{p}=\hbar \mathbf{k}\;$$

 * Energy: $$E$$

 * Frequency: $$f$$

 * Angular Frequency: $$\omega = 2\pi f$$

 * Wavenumber: $$k = 2\pi / \lambda$$

 * Plank's Constant: $$h$$

De Broglie Hypothesis
$$p=h/\lambda\;$$

 * Wavelength: $$\lambda$$

 * Momentum: $$p$$

Phase of a Plane Wave Expressed as a Complex Phase Factor
$$\psi \approx e^{i(\mathbf{k}\cdot\mathbf{x}- \omega t)}$$

Time-Dependent Schrodinger Equation
$$i\hbar\frac{\partial}{\partial t}\Psi=-\frac{\hbar^2}{2m}\nabla^2\Psi + V\Psi\;$$

$$\mathrm{i}\hbar \frac{d}{d t} \left| \psi \left(t\right) \right\rangle = H(t)\left|\psi\left(t\right)\right\rangle$$

 * Ket: $$|\psi(t)\rangle$$

 * Reduced Planck's Constant: $$\hbar$$

 * Hamiltonian: $$H(t)$$

 * The Hamiltonian describes the total energy of the system.

 * Partial Derivative: $$\partial / \partial t$$

 * Mass: $$m$$

 * Potential: $$V$$

Derivation
Begin with a step from the time-independent derivation

$$\frac{1}{\Psi} \frac{d^2 \Psi}{dx^2} = \frac{1}{c^2 \zeta} \frac{d^2 \zeta}{dt^2}$$

Set each side equal to a constant, $$- \kappa^2$$

$$-\kappa^2 = \frac{1}{c^2 \zeta} \frac{d^2 \zeta}{dt^2}$$

Multiply by $$c^2$$ to remove constants on the right side of the equation.

$$-\beta^2 = \frac{1}{\zeta} \frac{d^2 \zeta}{dt^2}$$

The solution is similar to what was found previously

$$\zeta (t) = Ne^{\pm i \beta t}$$

The amplitude at a point $$t$$ is equal to the amplitude at a point $$t + \tau$$

$$N e^{\pm i \beta t} = N e^{\pm i \beta (t + \tau)}$$

The following equation must be true:

$$\beta \tau = 2 \pi \;$$

Rewrite $$\beta$$ in terms of the frequency

$$\beta = 2 \pi v \;$$

Enter the equation into the expression of $$\zeta$$

$$\zeta (t) = Ne^{\pm 2 \pi i v t}$$

$$\zeta (t) = N e^{-i E t / \hbar}$$

The time-dependent Schrodinger equation is a product of two 'sub-functions'

$$\Psi (x,t) = \psi (x) \zeta (t)\;$$

$$\Psi (x,t) = \psi e^{-iEt/\hbar}$$

To extract $$E$$, differentiate with respect to time:

$$\frac{\partial \Psi}{\partial t} = \frac{-iE}{\hbar} \psi e^{-iEt/\hbar}$$

$$\frac{\partial \Psi}{\partial t} = \frac{E}{i \hbar} \psi e^{-iEt/\hbar}$$

Rearrange:

$$i \hbar \frac{\partial \Psi}{\partial t} = E \Psi$$ $$\hat H \Psi = E \Psi$$

Time-Independent Schrodinger Equation
$$H\Psi = E\Psi\;$$

 * $$ -\frac{\hbar^2}{2 m} \frac{d^2 \psi (x)}{dx^2} + U(x) \psi (x) = E \psi (x)$$

 * $$ \left[-\frac{\hbar^2}{2 m} \nabla^2 + U(\mathbf{r}) \right] \psi (\mathbf{r}) = E \psi (\mathbf{r})$$

$$ -\frac{\hbar^2}{2 m} \nabla^2 \psi + (U - E) \psi = 0$$

$$ H \left|\psi_n\right\rang = E_n \left|\psi_n \right\rang. $$

 * Del Operator: $$ \nabla $$

Derivation
The Schrodinger Equation is based on two formulas:

 * The classical wave function derived from the Newton's Second Law
 * The de Broglie wave expression

Formula of a classical wave:

$$\frac{d^2z}{dx^2} = \frac{1}{c^2} \frac{d^2 z}{dt^2}$$

Separate the function into two variables:

$$z(x,t) = \Psi (x) \zeta (t)\;$$

Insert the function into the wave equation:

$$\zeta \frac{d^2 \Psi}{dx^2} = \frac{\Psi}{c^2} \frac{d^2 \zeta}{dt^2}$$

Rearrange to separate $$\Psi$$ and $$\zeta$$

$$\frac{1}{\Psi} \frac{d^2 \Psi}{dx^2} = \frac{1}{c^2 \zeta}\frac{d^2 \zeta}{dt^2}$$

Set each side equal to an arbitrary constant, $$-\kappa^2$$

$$\frac{1}{\Psi} \frac{d^2 \Psi}{dx^2} = - \kappa^2$$

$$\frac{d^2 \Psi}{dx^2} = - \kappa^2 \Psi$$

Solve this equation

$$\Psi (x) = Ne^{\pm i \kappa x}$$

The amplitude at one point needs to be equal to the amplitude at another point:

$$N e^{\pm i \kappa x} = N e^{\pm i \kappa (x + \lambda)}$$

The following condition must be true:

$$\kappa \lambda = 2 \pi\;$$

Incorporate the de Broglie wave expression

$$\frac{h}{mv} = \lambda$$

$$\kappa = \frac{2 \pi m v}{h}$$

Use the symbol $$\hbar$$

$$\hbar = \frac{h}{2\pi}$$

$$\frac{d^2 \Psi}{dx^2} = - \frac{m^2 v^2}{\hbar^2} \Psi$$

$$\frac{- \hbar^2}{m^2 v^2} \frac{d^2 \Psi}{dx^2} = \Psi$$

Use the expression of kinetic energy, $$E_{kinetic} = \frac{1}{2} mv^2$$

$$\frac{-\hbar^2}{2m} \frac{d^2 \Psi}{dx^2} = E \Psi$$

Modify the equation by adding a potential energy term and the Laplacian operator

$$\frac{-\hbar^2}{2m} \nabla^2 \Psi + V \Psi = E \Psi$$ $$\hat H \Psi = E \Psi$$

Non-Relativistic Schrodinger Wave Equation
In non-relativistic quantum mechanics, the Hamiltonian of a particle can be expressed as the sum of two operators, one corresponding to kinetic energy and the other to potential energy. The Hamiltonian of a particle with no electric charge and no spin in this case is:

$$ H \psi\left(\mathbf{r}, t\right) = \left(T + V\right) \psi\left(\mathbf{r}, t\right) $$

$$ H \psi\left(\mathbf{r}, t\right) = \left[ - \frac{\hbar^2}{2m} \nabla^2 + V\left(\mathbf{r}\right) \right] \psi\left(\mathbf{r}, t\right) $$

$$ H \psi\left(\mathbf{r}, t\right) = \mathrm{i} \hbar \frac{\partial \psi}{\partial t} \left(\mathbf{r}, t\right) $$

 * kinetic energy operator: $$ T = \frac{p^2}{2m}$$
 * mass of the particle: $$m\;$$
 * momentum operator: $$ \mathbf{p} = -\mathrm{i}\hbar\nabla $$
 * potential energy operator: $$ V = V\left(\mathbf{r}\right)$$
 * real scalar function of the position operator $$\mathbf{r}$$: $$V$$
 * Gradient operator: $$\nabla$$
 * Laplace operator: $$\nabla^2$$


text:
Materials Science and Engineering/Glossary of Terms/Thermodynamics

Thermodynamics
Adiabatic Walls: Adiabatic walls don’t allow any exchange of heat with the surroundings.

Adiabatic Transformation: Up to a constant, $$E(X)$$ can be obtained from the amount of work $$\Delta W$$ needed for an adiabatic transformation from an initial state $$X_i$$ to a final state $$X_f$$, using $$\Delta W=E(X_f)-E(X_i)$$.

Calorie: A calorie is a unit of measurement for energy. * The small calorie or gram calorie approximates the energy needed to increase the temperature of 1 gram of water by 1 degree°C. This is about 4.184 joules.
 * The large calorie or kilogram calorie approximates the energy needed to increase the temperature of 1 kg of water by 1 °C. This is about 4.184 kJ, and exactly 1000 small calories.

In some scientific contexts such as physics and chemistry, the name "calorie" refers strictly to the gram calorie, and this unit has the symbol cal (a symbol also used by many for the large calorie).

Celsius Scale: Celsius is, or relates to, the Celsius temperature scale (previously known as the centigrade scale). Until 1954, 0 °C on the Celsius scale was defined as the melting point of ice and 100 °C was defined as the boiling point of water under a pressure of one standard atmosphere; this close equivalency is taught in schools today. However, the unit “degree Celsius” and the Celsius scale are currently, by international agreement, defined by two different points: absolute zero, and the triple point of specially prepared water. This definition also precisely relates the Celsius scale to the Kelvin scale, which is the SI base unit of temperature (symbol: K). Absolute zero—the temperature at which no energy remains in a substance—is defined as being precisely 0 K and −273.15 °C. The triple point of water is defined as being precisely 273.16 K and 0.01 °C.

Classical Thermodynamics: Classical thermodynamics is a branch of physics developed in the nineteenth century, by Sadi Carnot (1824), Emile Clapeyron (1834), Rudolf Clausius (1850), Willard Gibbs (1876), Hermann von Helmholtz (1882), and others that studied heat and work and their relation to the collision and interaction of particles in large, near-equilibrium systems.

The term classical thermodynamics is used in distinction to statistical thermodynamics, which came to be pioneered from the 1860s onwards. Statistical thermodynamics analyses thermodynamic properties by relating them to molecular-level models of microscopic behaviour in the thermodynamic system. In contrast, classical thermodynamics analyses what can be deduced solely from the macroscopic properties of the system and the laws of thermodynamics, regardless of microscopic interpretation.

Closed System: A closed system is an idealization similar to a point particle in mechanics in that it is assumed to be completely isolated by adiabatic walls that don’t allow any exchange of heat with the surroundings.

Continuum: The continuum concept ignores the fact that matter is made of atoms, is not continuous, and that it commonly has some sort of heterogeneous microstructure. It assumes that the substance of the body is distributed uniformly throughout, and completely fills the space it occupies, allowing the approximation of physical quantities, such as energy and momentum, at the infinitesimal limit. Differential equations can thus be employed in solving problems in continuum mechanics. Some of these differential equations are specific to the materials being investigated and are called constitutive equations, while others capture fundamental physical laws, such as conservation of mass or conservation of momentum and energy.

Critical Point: In physical chemistry, thermodynamics, chemistry and condensed matter physics, a critical point, also called a critical state, specifies the conditions (temperature, pressure) at which the liquid state of the matter ceases to exist.

Diathermal Walls: Diathermic walls allow heat exchange for an open system.

Density: In physics, density is mass (m) per unit volume (V) — the ratio of the amount of matter in an object compared to its volume. A small, heavy object, such as a rock or a lump of lead, is denser than a larger object of the same mass, such as a piece of cork or foam.

In the common case of a homogeneous substance, density is expressed as:

 * $$\rho = \frac {m}{V}$$

where, in SI Units:
 * ρ (rho) is the density of the substance, measured in kg·m–3
 * m is the mass of the substance, measured in kg
 * V is the volume of the substance, measured in m3

Empirical Temperature: Despite its apparent simplicity, the zeroth law has the consequence of implying the existence of an important state function, the empirical temperature Θ, such that systems in equilibrium are at the same temperature.

Enthalpy: In thermodynamics and molecular chemistry, the enthalpy or heat content (denoted as H or ΔH, or rarely as χ) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the "useful" work obtainable from a closed thermodynamic system under constant pressure.

Enthalpy change of an ideal gas: $$\Delta h = \int C_p (T) dT$$

Equation of State: In physics and thermodynamics, an equation of state is a relation between state variables.[1] More specifically, an equation of state is a thermodynamic equation describing the state of matter under a given set of physical conditions. It is a constitutive equation which provides a mathematical relationship between two or more state functions associated with the matter, such as its temperature, pressure, volume, or internal energy. Equations of state are useful in describing the properties of fluids, mixtures of fluids, solids, and even the interior of stars.

Equilibrium: A system under study is said to be in equilibrium when its properties do not change appreciably with time over the intervals of interest (observation times). The dependence on the observation time makes the concept of equilibrium subjective. For example, window glass is in equilibrium as a solid over many decades, but flows like a fluid over time scales of millennia. At the other extreme, it is perfectly legitimate to consider the equilibrium between matter and radiation in the early universe during the first minutes of the big bang.

Extensive Quantity: Quantity proportional to the system size

First Law: The amount of work required to change the state of an otherwise adiabatically isolated system depends only on the initial and final states, and not on the means by which the work is performed, or on the intermediate stages through which the system passes.

Force Constant: The (infinitesimal) ratio of displacement to force and are generalizations of the spring constant.

Gas Constant: The gas constant (also known as the universal or ideal gas constant, usually denoted by symbol R) is a physical constant used in equations of state to relate various groups of state functions to one another. It is another name for the Boltzmann constant, but when used in the ideal gas law it is usually expressed in the more convenient units of energy per kelvin per mole rather than simply energy per kelvin per particle.

Heat Capacity: The change in temperature upon addition of heat to the system. Since heat is not a function of state, the path by which it is supplied must also be specified.

Ideal Gas: The ideal gas occupies an important place in thermodynamics. Empirical observations indicate that the product of pressure and volume is constant along the isotherms of any gas that is sufficiently dilute. The ideal gas refers to this dilute limit of real gases, and the ideal gas temperature is proportional to the product.

Ideal Gas Specific Heat Relation: $$C_p = C_v + R$$

Internal Energy Change of an Ideal Gas: $$\Delta u = \int C_v (T) dT$$

Incompressible Substances:

Independent Properties:

Intensive Quantity: Quantity independent of size

Isobaric Process: An isobaric process is a thermodynamic process in which the pressure stays constant: Δp = 0. The heat transferred to the system does work but also changes the internal energy of the system. An isobaric process is shown on a P-V diagram as a straight horizontal line, connecting the initial and final thermostatic states. If the process moves towards the right, then it is an expansion. If the process moves towards the left, then it is a compression.

Isochoric Process: An isochoric process, also called an isometric process or an isovolumetric process, is a process during which volume remains constant. The name is derived from the Greek "iso" meaning "equal", and "chor" meaning "place".

If an ideal gas is used in an isochoric process, and the quantity of gas stays constant, then the increase in energy is proportional to an increase in temperature and pressure. Take for example a gas heated in a rigid container: the pressure and temperature of the gas will increase, but the volume will remain the same.

A real life example of an isochoric process is burning of a petrol-air mixture in an internal combustion engine, of any petrol/gasoline car.

Isolated System: In the natural sciences an isolated system, as contrasted with a open system, is a physical system that does not interact with its surroundings. It obeys a number of conservation laws: its total energy and mass stay constant. They cannot enter or exit, but can only move around inside.

Isothermal Process: An isothermal process is a thermodynamic process in which the temperature of the system stays constant: ΔT = 0. This typically occurs when a system is in contact with an outside thermal reservoir (heat bath), and processes occur slowly enough to allow the system to continually adjust to the temperature of the reservoir through heat exchange. An alternative special case in which a system exchanges no heat with its surroundings (Q = 0) is called an adiabatic process. During an isothermal process, all heat accepted by the system from its surroundings must have its energy entirely converted to work which it performs on the surroundings. That is, all the energy which comes into the system comes back out; the internal energy and thus the temperature of the system remain constant.

Joule: The joule is the SI unit of energy. It was named after James Prescott Joule for his work on the relationship between heat, electricity and mechanical work. One joule is the work done, or energy expended, by a force of one newton moving an object one meter along the direction of the force. This quantity is also denoted as a Newton-meter with the symbol N·m.

Kelvin Scale: The Kelvin scale is a thermodynamic (absolute) temperature scale where absolute zero — the coldest possible temperature — is zero kelvins (0 K).

Kinetic Energy: The kinetic energy of an object is the extra energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its current velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. Negative work of the same magnitude would be required to return the body to a state of rest from that velocity.

Latent Energy or Latent Heat: The latent internal energy of a system is the internal energy a system has due to phase change. Latent internal energy is the energy required for 1kg of a substance to change phase.

Macroscopic System:

Mechanical Equilibrium: A system is in mechanical equilibrium if its position in configuration space is a point at which the gradient of the potential energy is zero.

Melting Line:

Microscopic:

Newton: The newton is the amount of force that is required to accelerate a kilogram of mass at a rate of one meter per second squared. Algebraically:

 * $${\rm 1~N = 1~\frac{kg\cdot m}{s^2}}.$$

Non-Adiabatic Transformation: In a generic (non–adiabatic) transformation, the amount of work does not equal to the change in the internal energy. The difference $$\Delta Q=\Delta E-\Delta W$$is defined as the heat intake of the system from its surroundings.

Open System: Diathermic walls allow heat exchange for an open system.

Pascal: The pascal (symbol: Pa) is the SI derived unit of pressure or stress (also: Young's modulus and tensile strength). It is a measure of perpendicular force per unit area i.e. equivalent to one newton per square meter or one Joule per cubic meter.

Path of a Process:

Phase Diagram: In physical chemistry, mineralogy, and materials science, a phase diagram is a type of graph used to show the equilibrium conditions between the thermodynamically-distinct phases.

Phase Equilibrium: Gibbs' phase rule, stated by Josiah Willard Gibbs in the 1870s, is the fundamental rule on which phase diagrams are based.

 * F = 2 − π + C

where π is the number of phases present in equilibrium (Types of solid, liquid, gas phases etc). F is the number of degrees of freedom or independent variables taken from temperature, pressure and composition of the phases present. C is the number of chemical components required to describe the system

Piezoelectric Effect: Piezoelectricity is the ability of some materials (notably crystals and certain ceramics) to generate an electric potential[1] in response to applied mechanical stress. This may take the form of a separation of electric charge across the crystal lattice. If the material is not short-circuited, the applied charge induces a voltage across the material. The word is derived from the Greek piezein, which means to squeeze or press.

The piezoelectric effect is reversible in that materials exhibiting the direct piezoelectric effect (the production of electricity when stress is applied) also exhibit the converse piezoelectric effect (the production of stress and/or strain when an electric field is applied). For example, lead zirconate titanate crystals will exhibit a maximum shape change of about 0.1% of the original dimension. The effect finds useful applications such as the production and detection of sound, generation of high voltages, electronic frequency generation, microbalances, and ultra fine focusing of optical assemblies.

Potential Energy: Potential energy can be thought of as energy stored within a physical system. This energy can be released or converted into other forms of energy, including kinetic energy. It is called potential energy because it has the potential to change the states of objects in the system when the energy is released. A formal definition is that potential energy is the energy of position, that is, the energy an object is considered to have due to its position in space.

Pressure: The force per unit area applied on a surface in a direction perpendicular to that surface. Mathematically:

p = \frac{F}{A}\ \mbox{or}\ p = \frac{dF}{dA} $$

where:
 * $$p$$ is the pressure,
 * $$F$$ is the normal force
 * $$A$$ is the area.

Principle of Corresponding States:

Process: In science, a process is every sequence of changes of a real object/body which is observable using scientific method. Therefore, all sciences analyse and model processes.

Property: A property of an object is some intrinsic or extrinsic quality of that object

Quasi-static Transformation: A quasi-static transformation is one that is performed sufficiently slowly so that the system is always in equilibrium. Thus at any stage of the process, the thermodynamic coordinates of the system existandcan in principle be computed.For such transformations, the work done on the system (equal in magnitude but opposite in sign to the work done by the system) can be related to changes in these coordinates. Typically one can divide the state functions $${X}$$ into a set of generalized displacements $${x}$$, and their conjugate generalized forces $${J}$$, such that for an infinitesimal quasi-static transformation $$dW=\sum_{i} J_i dx_i$$.

Reduced Pressure: In thermodynamics, the reduced pressure of a fluid is defined as its actual pressure divided by its critical pressure.

 * $$P_r = {P \over P_c}$$

Reference State: For a given material or substance, the standard state is the reference state for the material's thermodynamic state properties such as enthalpy, entropy, Gibbs free energy, and for many other material standards. The standard enthalpy of formation for an element in its standard state is 0.

Saturated Liquid: a liquid at its boiling point

Saturated Vapor:

Saturation Pressure:

Saturation Temperature:

Secondary Dimensions:

Simple Compressible System:

Solid Phase: A solid object is in the states of matter characterized by resistance to deformation and changes of volume. At the microscopic scale, a solid has these properties :

 * The atoms or molecules that comprise the solid are packed closely together.
 * These constituent elements have fixed positions in space relative to each other. This accounts for the solid's rigidity. In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms in a crystal. A crystal structure is composed of a unit cell, a set of atoms arranged in a particular way; which is periodically repeated in three dimensions on a lattice. The spacing between unit cells in various directions is called its lattice parameters. The symmetry properties of the crystal are embodied in its space group. A crystal's structure and symmetry play a role in determining many of its properties, such as cleavage, electronic band structure, and optical properties.* If sufficient force is applied, either of these properties can be disrupted, causing permanent deformation.
 * Because any solid has some thermal energy, its atoms vibrate. However, this movement is very small, and cannot be observed or felt under ordinary conditions.

Specific Gravity: Specific Gravity (SG) is a special case of relative density defined as the ratio of the density of a given substance, to the density of water (H2O). Substances with a specific gravity greater than 1 are heavier than water, and those with a specific gravity of less than 1 are lighter than water.

$$\mbox{SG} = \frac{\rho_\mathrm{substance}}{\rho_{\mathrm{H}_2\mathrm{O}}}$$

Specific Heat: Specific heat capacity, also known simply as specific heat, is the measure of the heat energy required to increase the temperature of a unit quantity of a substance by a certain temperature interval.

Specific Properties: Specific properties of a substance are derived from other intrinsic and extrinsic properties (or intensive and extensive properties) of that substance. For example, the density of steel (a specific and intrinsic property) can be derived from measurements of the mass of a steel bar (an extrinsic property) divided by the volume of the bar (another extrinsic property). Similarly, the specific gravity of a liquid is derived from the density of the liquid divided by the density of water (two intrinsic properties).

Specific Volume: Specific volume (v) is the volume occupied by a unit of mass of a material. It is equal to the inverse of density. Specific volume may be expressed in $$ \frac{m^3}{kg} $$

 * $$ v = \frac{V}{m} = \frac{1}{\rho} $$

Specific Weight: The specific weight (also known as the unit weight) is the weight per unit volume of a material, or:

 * $$\gamma = \rho \, g$$

where
 * $$\gamma$$ is the specific weight of the material (Weight per unit volume, typically N·m−3 units)
 * $$\rho$$ is the density of the material (Mass per unit volume, typically kg·m−3)
 * $$g$$ is acceleration due to gravity (rate of change of velocity, given in m·s−2)

State: In thermodynamics/statistical mechanics, a thermodynamic state, or more precisely, a macrostate, is the specification of a particular combination of physical properties (e.g. temperature, volume, pressure, etc). For example, an equation of state describes the relationship between macrostates of the system. In the same context as above, a microstate is a detailed description of a collection of atoms or other particles. There may be many microstates corresponding to the same macrostate.

State Functions: In thermodynamics, a state function, or state quantity, is a property of a system that depends only on the current state of the system, not on the way in which the system got to that state. A state function describes the equilibrium state of a system. For example, internal energy, enthalpy and entropy are state quantities because they describe quantitatively an equilibrium state of thermodynamic systems. At the same time, mechanical work and heat are process quantities because they describe quantitatively the transition between equilibrium states of thermodynamic systems.

Statistical Thermodynamics: In thermodynamics, statistical thermodynamics is the study of the microscopic behaviors of thermodynamic systems using probability theory. Statistical thermodynamics, generally, provides a molecular level interpretation of thermodynamic quantities such as work, heat, free energy, and entropy. Statistical thermodynamics was born in 1870 with the work of Austrian physicist Ludwig Boltzmann, much of which was collectively published in Boltzmann's 1896 Lectures on Gas Theory.

Sublimation: Sublimation of an element or compound is a transition from the solid to gas phase with no intermediate liquid stage. Sublimation is a phase transition that occurs at temperatures and pressures below the triple point.

Thermal Equilibrium: Two systems are in thermal equilibrium when their temperatures are the same.

Thermal Responses: Change in the thermodynamic coordinates with temperature.

Thermodynamics: A phenomenological description of equilibrium properties of macroscopic systems

Thermodynamic Coordinates: Some common examples of such coordinates are pressure and volume (of a fluid), surface tension and area (of a film), tension and length (of a wire), electric field and polarization (of a dielectric)

Thermodynamic System: In thermodynamics, a thermodynamic system, originally called a working substance, is defined as that part of the universe that is under consideration. A real or imaginary boundary separates the system from the rest of the universe, which is referred to as the environment or surroundings (sometimes called a reservoir.) A useful classification of thermodynamic systems is based on the nature of the boundary and the quantities flowing through it, such as matter, energy, work, heat, and entropy. A system can be anything, for example a piston, a solution in a test tube, a living organism, a planet, etc.

Thermodynamic Temperature Scale: Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics. Thermodynamic temperature is an “absolute” scale because it is the measure of the fundamental property underlying temperature: its null or zero point, absolute zero, is the temperature at which the particle constituents of matter have minimal motion and can be no colder.

Total Energy: In classical physics, the total energy of an object is the sum of its potential energy and its kinetic energy. Note that since all other forms of energy can be derived from these two types, the total energy is effectively the theoretical maximum amount of energy that could be taken from the object.

In modern physics, the total energy of an object is the sum of its rest energy, its total kinetic energy, and its potential energy.

Triple Line:

Triple Point: In physics and chemistry, the triple point of a substance is the temperature and pressure at which three phases (gas, liquid, and solid) of that substance may coexist in thermodynamic equilibrium.

Van der Waals Equation of State: The van der Waals equation is an equation of state for a fluid composed of particles that have a non-zero size and a pairwise attractive inter-particle force (such as the van der Waals force.) It was derived by Johannes Diderik van der Waals in 1873, based on a modification of the ideal gas law. The equation approximates the behavior of real fluids, taking into account the nonzero size of molecules and the attraction between them.

 * $$\left(p + \frac{a'}{v^2}\right)\left(v-b'\right) = kT$$

where
 * p is the pressure of the fluid
 * v is the volume of the container holding the particles divided by the total number of particles
 * k is Boltzmann's constant
 * T is the absolute temperature
 * a' is a measure for the attraction between the particles
 * b' is the average volume excluded from v by a particle

Work: In thermodynamics, work is the quantity of energy transferred from one system to another without an accompanying transfer of entropy. It is a generalization of the concept of mechanical work in mechanics. In the SI system of measurement, work is measured in joules (symbol: J). The rate at which work is performed is power.

Zeroth Law: If two systems, A and B, are separately in equilibrium with a third system C, then they are also in equilibrium with one another.


text:
User:S2891

Hi. Going to enter tertiary studies soon filling my time before enrolling with studying various fields.

title: User:S2891


text:
User talk:S2891

Welcome
Hello S2891, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
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title: User talk:S2891


text:
User talk:Erinschuman

Welcome
Hello Erinschuman, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
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title: User talk:Erinschuman


text:
User talk:Auntant

Welcome
Hello Auntant, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
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title: User talk:Auntant


text:
User:Auntant

This is AuntAnt's Wikipage.

title: User:Auntant


text:
Wikipedia arbitration committee/Elections

2007 election

 * Source of the data.
 * Those selected for service: Wikipedia Signpost coverage.


text:
Talk:Wikipedia arbitration committee/Elections

I think it would be useful to expand the table to include the stated positions of the candidates on some of the issues that were raised in questions for the candidates. --JWSchmidt 05:48, 26 December 2007 (UTC)


text: Bloom Clock/Keys/Southeastern Pennsylvania/June/Green Flowers


text:
Bloom Clock/Keys/Southeastern Pennsylvania/July/Green Flowers

The plants pictured below have been recorded as blooming during the month of July in Southeastern Pennsylvania.

Note: Because many species have variation in flower color, some of the photographs on this page show flowers of a different color than blue. In most cases, the "typical" (most common) color is shown here.

last updated 14:39, 26 December 2007 (UTC) with 4 plants


text: Bloom Clock/Keys/Southeastern Pennsylvania/June/Brown Flowers


text: Bloom Clock/Keys/Southeastern Pennsylvania/June/Black Flowers


text:
User talk:Suyash asthana~enwikiversity

Welcome
Hello Suyash asthana, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
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Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Suyash asthana. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Suyash asthana~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 00:04, 18 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:23, 19 April 2015 (UTC)

title: User talk:Suyash asthana~enwikiversity


text:
User talk:Mayank~enwikiversity

Welcome
Hello Mayank, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
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And don't forget to explore Wikiversity with the links to your left. Be bold, and see you around Wikiversity! --mikeu 17:10, 26 December 2007 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Mayank. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Mayank~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:43, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:15, 19 April 2015 (UTC)

title: User talk:Mayank~enwikiversity


text:
User talk:Honeye safary

Welcome
Hello Honeye safary, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
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title: User talk:Honeye safary


text:
User talk:Xyz~enwikiversity

Welcome
Hello Xyz, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
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And don't forget to explore Wikiversity with the links to your left. Be bold, and see you around Wikiversity! --mikeu 17:12, 26 December 2007 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Xyz. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Xyz~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 00:12, 18 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:25, 19 April 2015 (UTC)

title: User talk:Xyz~enwikiversity


text:
User talk:Baranidaranm

Welcome
Hello Baranidaranm, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
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title: User talk:Baranidaranm


text:
User talk:Promulgation

Welcome
Hello Promulgation, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
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title: User talk:Promulgation


text:
File:Pruthvirajg SBTDS Sound 1.ogg

Used with the WikiU Film School Lesson on how to do Animatic Dialog Recording.

title: File:Pruthvirajg SBTDS Sound 1.ogg


text:
File:Pruthvirajg SBTDS Sound 2.ogg

Used with the WikiU Film School Lesson on how to do Animatic Dialog Recording.

title: File:Pruthvirajg SBTDS Sound 2.ogg


text:
File:Pruthvirajg SBTDS Sound 3.ogg

Used with the WikiU Film School Lesson on how to do Animatic Dialog Recording.

title: File:Pruthvirajg SBTDS Sound 3.ogg


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File:Pruthvirajg SBTDS Sound 5.ogg

Used with the WikiU Film School Lesson on how to do Animatic Dialog Recording.

title: File:Pruthvirajg SBTDS Sound 5.ogg


text:
File:Pruthvirajg SBTDS Sound 4.ogg

Used with the WikiU Film School Lesson on how to do Animatic Dialog Recording.

title: File:Pruthvirajg SBTDS Sound 4.ogg


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File:Pruthvirajg SBTDS Sound 6.ogg

Used with the WikiU Film School Lesson on how to do Animatic Dialog Recording.

title: File:Pruthvirajg SBTDS Sound 6.ogg


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File:Pruthvirajg SBTDS Sound 7.ogg

Used with the WikiU Film School Lesson on how to do Animatic Dialog Recording.

title: File:Pruthvirajg SBTDS Sound 7.ogg


text:
File:Pruthvirajg SBTDS Sound 9.ogg

Used with the WikiU Film School Lesson on how to do Animatic Dialog Recording.

title: File:Pruthvirajg SBTDS Sound 9.ogg


text:
File:Pruthvirajg SBTDS Sound 8.ogg

Used with the WikiU Film School Lesson on how to do Animatic Dialog Recording.

title: File:Pruthvirajg SBTDS Sound 8.ogg


text:
File:Pruthvirajg SBTDS Sound 11.ogg

Used with the WikiU Film School Lesson on how to do Animatic Dialog Recording.

title: File:Pruthvirajg SBTDS Sound 11.ogg


text:
File:Pruthvirajg SBTDS Sound 10.ogg

Used with the WikiU Film School Lesson on how to do Animatic Dialog Recording.

title: File:Pruthvirajg SBTDS Sound 10.ogg


text:
User:Sunderland06

I am User:Sunderland06, which of course means that i am from sunderland and i made account on wikipedia in 2006.

I am also registered on English Wikipedia, and my user name is also User:Sunderland06

I am also registered on Italian Wikipedia, and my user name is also Utente:Sunderland06 although i do not contribute there much.

title: User:Sunderland06


text:
User talk:Speilberg0

Welcome
Hello Speilberg0, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
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And don't forget to explore Wikiversity with the links to your left. Be bold, and see you around Wikiversity! --mikeu 23:52, 26 December 2007 (UTC)

title: User talk:Speilberg0


text:
User talk:Sunderland06

Welcome
Hello Sunderland06, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
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And don't forget to explore Wikiversity with the links to your left. Be bold, and see you around Wikiversity! --JWSchmidt 23:57, 26 December 2007 (UTC)

title: User talk:Sunderland06


text:
Materials Science and Engineering/Equations/Kinetics

Time-Dependent Field
$$\frac{dc}{dt} = \nabla c \cdot \overrightarrow{v} + \frac{\partial c}{\partial t}$$

 * $$\overrightarrow{v}(\overrightarrow{r})$$: Velocity
 * $$c(\overrightarrow{r},t)$$: Time-Dependent Field

Accumulation
Rate of accumulation is the negative of the divergence of the flux of the quantity plus the rate of production

$$\frac{\partial c_i}{\partial t} = - \nabla \cdot \overrightarrow{J_i} + \dot{\rho_i}$$

 * $$\dot{\rho_i}(\overrightarrow{r})$$: Rate of production of the density of $$i$$ in $$\Delta V$$
 * $$\nabla \cdot \overrightarrow{J_i}$$: The divergence of $$\overrightarrow{J_i}$$

$$\dot{M_i} = \int_{\Delta V} - \nabla \cdot \overrightarrow{J_i} + \dot{\rho_i}\,dx$$

 * $$\dot{M_i}$$: Rate at which $$i$$ flows through area $$\Delta \overrightarrow{A}$$

Divergence Theorem
$$\int_{\Beta (\Delta V)} \overrightarrow{J} \cdot \dot{n} \,dA = \int_{\Delta V} \nabla \cdot \overrightarrow{J} \,dV$$

 * $$\Beta (\Delta V)$$: Oriented surface around a volume

General Set of Linear Equations
$$\begin{alignat}{7} M_{11} x_1 &&\; + \;&& M_{12} x_2 &&\; + \cdots + \;&& M_{1n} x_n &&\; = \;&&& y_1     \\ M_{21} x_1 &&\; + \;&& M_{22} x_2 &&\; + \cdots + \;&& M_{2n} x_n &&\; = \;&&& y_2     \\ \vdots\;\;\; &&    && \vdots\;\;\; &&              && \vdots\;\;\; &&     &&& \;\vdots \\ M_{m1} x_1 &&\; + \;&& M_{m2} x_2 &&\; + \cdots + \;&& M_{mn} x_n &&\; = \;&&& y_m     \\ \end{alignat}$$

The vector equation is equivalent to a matrix equation of the form $$M\mathbf{x}=\mathbf{y}$$ where M is an m×n matrix, x is a column vector with n entries, and y is a column vector with m entries.

M= \begin{bmatrix} M_{11} & M_{12} & \cdots & M_{1n} \\ M_{21} & M_{22} & \cdots & M_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ M_{m1} & M_{m2} & \cdots & M_{mn} \end{bmatrix},\quad \mathbf{x}= \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_n \end{bmatrix},\quad \mathbf{y}= \begin{bmatrix} y_1 \\ y_2 \\ \vdots \\ y_m \end{bmatrix} $$

Eigenvalue Equation
$$\underline{M} \overrightarrow{e} = \lambda \overrightarrow{e}$$

 * $$\underline{M}$$: $$n x n$$ square matrix or tensor
 * $$\overrightarrow{e}$$: eigenvector (special vector)
 * $$\lambda$$: eigenvalue (special scalar multiplier)

Transformation of Rank-Two Tensor
$$\left [ \mbox{diagonalized matrix} \right ] = \left [ \mbox{eigenvector column matrix} \right ]^{-1} \left [ \mbox{square matrix} \right ] \left [ \mbox{eigenvector column matrix} \right ]$$

Differential Change in Entropy
$$T dS = du - \sum_j \Psi_j d \zeta_j\;$$

 * $$\sum_j \Psi_j d \zeta_j = -Pdv + \phi dq + \gamma dA + \mu_1 dc_1+\cdots\;$$

Entropy Production
$$T \dot{\sigma} = - \frac{\overrightarrow{J_Q}}{T} \cdot \nabla T - \sum_j \overrightarrow{J_i} \cdot \nabla \Psi_j $$

 * $$\dot{\sigma}$$: Rate of entropy-density creation
 * $$\overrightarrow{J_Q}$$: Flux of heat
 * $$\overrightarrow{J_i}$$: Conjugate force
 * $$\nabla \Psi_j$$: Conjugate flux

Fourier's
$$\overrightarrow{J_Q} = -K \nabla T$$

Modified Fick's
$$\overrightarrow{J_i} = -M_i c_i \nabla \mu_i$$

Ohm's
$$\overrightarrow{J_q} = - \rho \nabla \phi$$

Basic Postulate of Irreversible Thermodynamics
The local generation of entropy, $$\dot{\sigma}$$ is nonnegative

$$\dot{\sigma} = \frac{\partial s}{\partial t} + \nabla \cdot \overrightarrow{J_Q} \ge 0$$

Coupling Between Forces and Fluxes
$$\begin{alignat}{7} \frac{\partial J_Q}{\partial F_Q} F_Q &&\; + \;&& \frac{\partial J_Q}{\partial F_q} F_q &&\; + \cdots + \;&& \frac{\partial J_Q}{\partial F_{N_c}} F_{N_c} &&\; = \;&&& J_Q (F_Q, F_q, F_1, F_2, ..., F_{N_c})      \\ \frac{\partial J_q}{\partial F_Q} F_Q &&\; + \;&& \frac{\partial J_q}{\partial F_q} F_q &&\; + \cdots + \;&& \frac{\partial J_q}{\partial F_{N_c}} F_{N_c} &&\; = \;&&& J_q (F_Q, F_q, F_1, F_2, ..., F_{N_c})      \\ \vdots\;\;\; &&    && \vdots\;\;\; &&              && \vdots\;\;\; &&     &&& \;\vdots \\ \frac{\partial J_{N_c}}{\partial F_Q} F_Q &&\; + \;&& \frac{\partial J_{N_c}}{\partial F_q} F_q &&\; + \cdots + \;&& \frac{\partial J_{N_c}}{\partial F_{N_c}} F_{N_c} &&\; = \;&&& J_{N_c} (F_Q, F_q, F_1, F_2, ..., F_{N_c})      \\ \end{alignat}$$

Abbreviated form:

$$J_{\alpha} = \sum_{\beta} L_{\alpha \beta} F_{\beta}\;$$

 * $$L_{\alpha \beta} = \frac{\partial J_{\alpha}}{\partial F_{\beta}}$$

Force-Flux Relations with Constrained Extensive Quantities
$$TdS = du + dw - \sum_{i=1}^{N_c - 1} \left ( \mu_i - \mu_{N_c} \right ) dc_i$$

 * $$\overrightarrow{F_i} = - \nabla \left ( \mu_i - \mu_{N_c} \right )$$

Diffusion Potential
$$\overrightarrow{F_1} = - \nabla \Phi_1$$

Onsager Symmetry Principle
$$L_{\alpha \beta} = L_{\beta \alpha}\;$$

$$ \frac{\partial J_{\alpha}}{\partial F_{\beta}}=\frac{\partial J_{\beta}}{\partial F_{\alpha}}$$

Diffusion in Absence of Chemical Effects

 * Components diffuse in chemically homogeneous material
 * Diffusion measured with radioactive tracer
 * Fick's law flux equation derived when self-diffusion occurs by the vacancy-exchange mechanism.
 * The crystal is network-constrained
 * There are three components:
 * Inert atoms
 * Radioactive atoms
 * Vacancies
 * C-frame: single reference frame
 * Vacancies assumed to be in equilibrium throughout
 * Raoultian behavior

$$J_{^*1}^C = -kT \left [ \frac{L_{11}}{c_1} - \frac{L_{1^*1}}{c_{^*1}} \right ] \frac{\partial c_{^*1}}{\partial x}$$

$$J_{^*1}^C = -^*D \frac{\partial c_{^*1}}{\partial x}$$

Diffusion of i in Chemically Homogeneous Binary Solution
$$J_{^*1}^C = -kT \left [ \frac{L_{11}}{c_1} - \frac{L_{1^*1}}{c_{^*1}} \right ] \frac{\partial c_{^*1}}{\partial x}$$ $$J_{^*1}^C = -^*D_1 \frac{\partial c_{^*1}}{\partial x}$$

Diffusion of Substitutional Particles in Concentration Gradient

 * Constraint associated with vacancy mechanism: $$\overrightarrow{J_1^c}+ \overrightarrow{J_2^c}+\overrightarrow{J_v^c}=0$$
 * Difference in fluxes of the two substitutional species requires net flux of vacancies.
 * Gibbs-Duhem relation: $$c_1 \frac{\partial \mu_1}{\partial x} + c_2 \frac{\partial \mu_2}{\partial x} + c_v \frac{\partial \mu_v}{\partial x}$$
 * Chemical potential gradients related to concentration gradients: $$\mu_i = \mu_i^{\circ} + kT \ln ( \gamma_i < \Omega > c_i )$$

Flux is proportional to the concentration gradient

$$J_1^c = -k T \left[ \frac{L_{11}}{c_1} - \frac{L_{12}}{c_2} \right ] \left [ 1+\frac{\partial \ln \gamma_1}{\partial \ln c_1} + \frac{\partial \ln < \Omega >}{\partial \ln c_1} \right ] \frac{\partial c_1}{\partial x}$$ $$J_1^c = -D_1 \frac{\partial c_1}{\partial x}$$

Assumptions that simplify $$D_1\;$$

 * Concentration-independent average site volume $$< \Omega >\;$$
 * The coupling (off-diagonal) terms, $$L_{12}/c_2\;$$ and $$L_{1^*1}/c_{^*1}\;$$, are small compared with the direct term $$L_{11}/c_2\;$$

$$D_1 \approx \left [ 1 + \frac{\partial \ln \gamma_1}{\partial \ln c_1} \right ] {}^*D_1$$

Diffusion in a Volume-Fixed (V-Frame)

 * Velocity of a local C-frame with respect to the V-frame: velocity of any inert marker with respect to the V-frame
 * Flux of 1 in the V-frame:

$$J_1^v = - [c_1 \Omega_1 D_2 + c_2 + \Omega_2 D_1 ] \frac{\partial c_1}{\partial x}$$

 * The interdiffusivity, $$c_1 \Omega_1 D_2 + c_2 + \Omega_2 D_1\;$$, can be simplified through $$\Omega_1 = \Omega_2 = < \Omega > \;$$
 * The L-frame and the V-frame are the same

Diffusion of Interstitial Particles in Concentration Gradient

 * $$\overrightarrow{J_1^c} = L_{11} \overrightarrow{F_1}$$
 * $$\overrightarrow{J_1^c} = -L_{11} \nabla \Phi_1$$
 * $$\overrightarrow{J_1^c} = -L_{11} \nabla \mu_1$$
 * $$\mu_1 = \mu_1^{\circ} + kT \ln (K_1 c_1)$$
 * $$\nabla \mu_1 = \frac{kT}{c_1} \nabla c_1$$

$$\overrightarrow{J_1^c} = -L_{11} \frac{kT}{c_1} \nabla c_1$$

 * Evaluate $$L_{11}$$ by substitution of interstitial mobility, $$M_1$$
 * $$\overrightarrow{v_1^c} = -M_1 \nabla \mu_1$$
 * $$\overrightarrow{v_1^c} = \frac{-M_1 k T}{c_1} \nabla c_1$$
 * $$\overrightarrow{J_1^c} = \overrightarrow{v_1^c} c_1$$

$$\overrightarrow{J_1^c} = -M_{1} kT \nabla c_1$$

Diffusion of Charged Ions in Ionic Conductors
$$\overrightarrow{J_1} = -D_1 \nabla c_1 - \frac{D_1 c_1 q_1}{kT} \nabla (\phi)$$
 * $$\overrightarrow{J_1} = L_{11} \overrightarrow{F_1}$$
 * $$\overrightarrow{J_1} = -L_{11} \nabla \Phi_1$$
 * $$\overrightarrow{J_1} = -L_{11} \nabla (\mu_1 + q_1 \phi)$$

 * $$\overrightarrow{E} = - \nabla \phi \;$$: Electric field
 * Absence of concentration gradient:
 * $$\overrightarrow{J_q} = q_1 \overrightarrow{J_1}$$
 * $$\overrightarrow{J_q} = - \frac{D_1 c_1 q_1^2}{kT} \nabla (\phi)$$

 * Electrical conductivity:
 * $$\rho = \frac{D_1 c_1 q_1^2}{kT}$$

Electromigration in Metals

 * Two fluxes when electric field is applied to a dilute solution of interstitial atoms in metal
 * $$J_q\;$$: Flux of conjuction electrons
 * $$J_1\;$$: Flux of interstitials
 * $$F_q = E\;$$
 * $$F_q = - \nabla \phi$$

$$\overrightarrow{J_1} = -L_{11} \nabla \mu_1 + L_{1q} \overrightarrow{E}$$ $$\overrightarrow{J_1} = -D_1 \left ( \nabla c_1 - \frac{c_1 \beta}{k T} \overrightarrow{E} \right )$$

Mass Diffusion in Thermal Gradient

 * Interstitial flux with thermal gradient where both heat flow and mass diffusion of interstitial component occurs:

$$\overrightarrow{J_1} = -L_{11} \nabla \mu_1 - \frac{L_{1q}}{T} \nabla T$$ $$\overrightarrow{J_1} = -D_1 \nabla c_1 - \frac{D_1 c_1 Q_1^{\mbox{trans}}}{k T^2} \nabla T$$

Mass Diffusion Driven by Capillarity

 * The system consists of two network-constrained components:
 * Host atoms
 * Vacancies
 * No mass flow within the crystal (the crystal C-frame is also the V-frame)
 * Constant temperature and no electric field
 * $$\overrightarrow{J_A} = L_{AA} \overrightarrow{F_A}$$
 * $$\overrightarrow{J_A} = - L_{AA} \nabla \Phi_A$$
 * $$\overrightarrow{J_A} = - L_{AA} \nabla ( \mu_A - \mu_v )$$
 * $$\overrightarrow{J_V} = - \overrightarrow{J_A}$$

Diffusion Equation in the General Form
$$\frac{\partial c}{\partial t} = \dot n - \nabla \cdot \overrightarrow{J}$$

 * $$\dot n$$: source or sink term
 * $$\overrightarrow{J}$$: any flux in a V-frame

Fick's Second Law
$$\frac{\partial c}{\partial t} = \nabla \cdot \overrightarrow{J}$$ $$\frac{\partial c}{\partial t} = \nabla \cdot (D \nabla c)$$

Linearization of Diffusion Equation
$$\frac{\partial c}{\partial t} = D_o \nabla^2 c$$

Heat Equation
$$\frac{\partial h}{\partial t} = - \nabla \cdot \overrightarrow{J_Q}$$ $$c_P \frac{\partial T}{\partial t} = - \nabla \cdot ( -K \nabla T) $$ $$\frac{\partial T}{\partial t} = \nabla \cdot \left ( \frac{K}{c_P} \nabla T \right )$$ $$\nabla \cdot ( \kappa \nabla T)$$

 * $$h\;$$: enthalpy density
 * $$c_P\;$$: heat capacity
 * $$K / c_p = \kappa\;$$: thermal diffusivity

Constant Diffusivity
$$\frac{\partial c}{\partial t} = D \nabla^2 c$$

One-Dimensional Diffusion Along x from an Initial Step Function
$$c(x,t) = \bar {c} + \frac{\Delta c}{2} \mbox{erf} \left ( \frac{x}{\sqrt{4 D t}} \right )$$

Localized Source
$$c(x,t) = \frac{c_o \Delta x}{\sqrt{4 \pi D t}} e^{-x^2 / (4Dt)}$$ $$c(x,t) = \frac{n_d}{\sqrt{4 \pi D t}} e^{-x^2 / (4Dt)}$$

 * Source strength, $$n_d = \int_{-\infty}^{\infty} c(x) dx$$

Diffusivity as a Function of Concentration
$$\frac{\partial c}{\partial t} = \nabla \cdot [D(c) \nabla c]$$

 * Interdiffusivity: $$D(c_1) = - \frac{1}{2 \tau} \frac{d x}{d c_1} \int_{c_1^R}^{c_1} x(c') dc'$$

Diffusivity as a Function of Time
$$\frac{\partial c}{\partial t} = \nabla \cdot [D(t) \nabla c]$$ $$\frac{\partial c}{\partial t} = D(t) \nabla^2 c]$$

 * Change of variable: $$\tau_D = \int_0^t D(t')dt'$$
 * Transformed equation: $$\frac{\partial c}{\partial \tau_D} = \nabla^2 c$$
 * Solution:

 * $$c(x, \tau_D) = \bar{c} + \frac{\Delta c}{2} \mbox{erf} \left ( \frac{x}{\sqrt{4 \tau_D}} \right )$$
 * $$c(x, t) = \bar{c} + \frac{\Delta c}{2} \mbox{erf} \left ( \frac{x}{\sqrt{4 \int_0^t D(t') dt'}} \right )$$

Diffusivity as a Function of Direction
$$\overrightarrow{J} = - \mathbf{D} \nabla c$$

 * The diagonal elements of $$\hat{\mathbf{D}}$$ are the eigenvalues of $$\mathbf{D}$$, and the coordinate system of $$\hat{\mathbf{D}}$$ defines the principal axes.

 * $$\frac{\partial c}{\partial t} = - \nabla \cdot \overrightarrow{J}$$
 * $$\frac{\partial c}{\partial t} = \nabla \cdot \hat{\mathbf{D}} \nabla c$$

 * Relation of $$\mathbf{D}$$ and $$\hat{\mathbf{D}}$$:

$$\hat{\mathbf{D}} = \underline{R} \mathbf D \underline{R}^{-1}$$

Harmonic Functions
$$\nabla^2 c = 0$$

One Dimension
$$J = -D \frac{dc}{dx}$$ $$J = D \frac{c^0 - c^L}{L}$$

Cylindrical Shell

 * Laplacian Operator: $$\nabla^2 c = \frac{1}{r} \frac{\partial}{\partial r} \left ( r \frac{\partial c}{\partial r} \right ) + \frac{1}{r^2} \frac{\partial^2 c}{\partial \theta^2} + \frac{\partial^2 c}{\partial x^2}$$
 * Integrate Twice and Apply the Boundary Conditions:

$$c(r) = c^{\mbox{in}} - \frac{c^{\mbox{in}} - c^{\mbox{out}}}{\ln(r^{\mbox{out}}/r^{\mbox{in}} )} \ln \left ( \frac{r}{r^{\mbox{in}}} \right )$$

Spherical Shell

 * Laplacian operator in spherical coordinates

$$\nabla^2 c = \frac{1}{r^2} \left [ \frac{\partial}{\partial r} \left ( r^2 \frac{\partial c}{\partial r} \right ) + \frac{1}{\sin{\theta}} \frac{\partial}{\partial \theta} \left ( \sin \theta \frac{\partial c}{\partial \theta} \right ) + \frac{1}{\sin^2 \theta} \frac{\partial^2 c}{\partial \phi^2} \right ]$$

Variable Diffusivity

 * Steady-state conditions
 * $$D$$ varies with position

$$\partial \cdot (D \nabla c) = 0$$

 * Solution is obtained by integration:

$$c(x) = c(x_1) + a_1 \int_{x_1}^{x} \frac{d \zeta}{D( \zeta )}$$

Infinite Media with Instantaneous Localized Source
$$c(x,y,z,t) = \frac{n_{d_x}}{\sqrt{4 \pi D t}} e^{-x^2 /(4Dt)} \times \frac{n_{d_y}}{\sqrt{4 \pi D t}} e^{-y^2 /(4Dt)} \times \frac{n_{d_z}}{\sqrt{4 \pi D t}} e^{-z^2 /(4Dt)}$$

Solutions with the Error Function

 * Uniform distribution of point, line, or plana source placed along $$x > 0$$
 * Contribution at a general position $$x$$ from the source:

 * $$c_{\zeta}(x,t) = \frac{c_o d \zeta}{\sqrt{4 \pi D t}} e^{- ( \zeta - x)^2 / (4 D t)}$$

 * Integral over all sources:

 * $$c(x,t) = \frac{c_o}{\sqrt{4 \pi D t}} \int_0^{\infty} e^{-(\zeta - x)^2 / (4 D t)} d \zeta$$

$$c(x,t) = \frac{c_o}{2} + \frac{c_o}{2} \mbox{erf} \left ( \frac{x}{2 \sqrt{D t}} \right )$$

Method of Separation of Variables

 * System : Three Dimensions, $$(x,y,z)$$
 * Equation : $$\frac{dc}{dt} = D \nabla^2 c$$
 * Solution : $$c(r, \theta, z, t) = R(r) \Theta(\theta) Z(z) T(t)\;$$

Method of Laplace Transforms

 * Laplace transform of a function $$f(x,t)\;$$

$$L\{f(x,t)\} = \hat{f} (x,p)$$ $$L\{f(x,t)\} = \int_0^{\infty} e^{-pt} f(x,t) dt$$

Model of One-Particle with Step Potential-Energy Wells
$$\Tau' = \sqrt{\frac{kT}{2 \pi m}} \frac{1}{L^{\mbox{well}}} e^{-(E^A - E^{\mbox{well}})/(kT)}$$ $$\Tau' = \sqrt{\frac{kT}{2 \pi m}} \frac{1}{L^{\mbox{well}}} e^{-(E^m)/(kT)} $$

Model of One-Particle with Step Potential-Energy Wells
$$\Tau' = \frac{1}{2 \pi} \sqrt{\frac{\beta}{m}} e^{-(E^A - E^{\mbox{well}})/(kT)}$$ $$\Tau' = \nu e^{-E^m/(kT)}$$

Many-Body Model
$$\Tau' = \nu e^{-G^m/(kT)}$$

Diffusion as Series of Discrete Jumps
$$ = N_{\tau} + 2 < ( \sum_{j=1}^{N_{\tau} - 1} \sum_{i=1}^{N_{\tau - j}} | \overrightarrow{r_i} || \overrightarrow{r}_{i+j}| \cos \theta_{i, i+j} >$$

Diffusivity and Mean-Square Particle Displacement
$$ = 6D \tau\;$$

Relation of Macroscopic Diffusivity and Microscopic Jump Parameters
$$D = \frac{\Tau }{2}$$

Diffusion and Correlated Jumps

 * Correlation factor:

$$\mathbf f = 1 + \frac{2}{N_{\tau}} < ( \sum_{j=1}^{N_{\tau} - 1} \sum_{i=1}^{N_{\tau - j}} | \overrightarrow{r_i} || \overrightarrow{r}_{i+j}| \cos \theta_{i, i+j} >$$

 * Macroscopic Diffusivity and Microscopic Parameters:

$$D = \frac{ N_{\tau}}{6 \tau} \mathbf f$$ $$D = \frac{\Tau \tau}{6 \tau} \mathbf f$$ $$D = \frac{\Tau }{6} \mathbf f$$

Correlation Factor
$$\mathbf f = \frac{1+<\cos \theta>}{1-<\cos \theta>}$$ $$\mathbf f \approx \frac{z-1}{z+1}$$

Isotope Effect
$$\frac{^*D(mass 1)}{^*D(mass 2)} = \frac{\Tau_1}{\Tau_2} = \frac{\Tau'_1}{\Tau'_2} = \frac{\nu_1}{\nu_2} = \frac{m_1}{m_2}$$


text:
User:Whiteknight/graph.js

//This function produces simple graphs from a series of data points. //Used currently for the hit counter. See User:Whiteknight/Graph. //current limit of one graph per page. Will correct that eventually.

function WKGraphCanvas { var tab = document.getElementById("WKGraphTable"); if(tab == null) return; tab.style.display = "block"; tab.style.margin = "0.5em auto"; var div = document.getElementById("WKCanvasGraph"); var mtr = document.getElementById("WKGraphMax"); if(div == null) return; var pts = div.innerHTML; if(pts == "") pts = "0"; div.innerHTML = ""; pts = pts.split(","); var max = 1; for(var i = 0; i < pts.length; i++) { pts[i] = parseInt(pts[i]); if(pts[i] > max) max = pts[i]; } mtr.innerHTML = max; for(i = 0; i < pts.length; i++) { pts[i] = Math.floor((pts[i] / max) * 100); } if(pts.length == 1) { var step = 1; } else { var step = Math.floor(500 / (pts.length - 1)); } var can = document.createElement("canvas"); can.setAttribute("width", "510"); can.setAttribute("height", "115"); var ctx = can.getContext("2d");

ctx.beginPath; ctx.moveTo(5, 110 - pts[0]); for(var i = 1; i < pts.length; i++) { ctx.lineTo(i * step + 5, 110 - pts[i]); } ctx.strokeStyle = "#FF0000"; ctx.stroke; ctx.strokeStyle = "#0000FF"; for(i = 0; i < pts.length; i++) { ctx.strokeRect(i * step, 110 - pts[i] - 5, 10, 10); }

div.appendChild(can); }

/*@cc_on @if(@_jscript) //no graph for you @else*/ $(WKGraphCanvas); /*@end @*/

title: User:Whiteknight/graph.js


text: User:Whiteknight/Count Ticker/2007/December


text: User:Whiteknight/WJHits

title: User:Whiteknight/WJHits


text:
User:Elwooddrums~enwikiversity

I am Ryan Elwood, freelance drummer in the Denver area. I also teach private drum lessons.

title: User:Elwooddrums~enwikiversity


text:
User talk:Elwooddrums~enwikiversity

Welcome
Hello Elwooddrums, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
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And don't forget to explore Wikiversity with the links to your left. Be bold, and see you around Wikiversity! --JWSchmidt 02:31, 27 December 2007 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Elwooddrums. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Elwooddrums~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:35, 17 March 2015 (UTC)

Renamed
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title: User talk:Elwooddrums~enwikiversity


text:
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title: Template:Archive top


text: Template:Archive bottom

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text:
User:Wakedream

I'm Wakedream, and I'm here--unless I'm dreaming.

Like many professional writers, I spend a lot of time looking for things to do other than work on what I'm supposed to be writing. Unlike many professional writers, those other things often involve writing. Perhaps this is why I'm not rich.

title: User:Wakedream


text:
User talk:Wakedream

Welcome
Hello Wakedream, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
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And don't forget to explore Wikiversity with the links to your left. Be bold, and see you around Wikiversity! --HappyCamper 13:58, 27 December 2007 (UTC)

title: User talk:Wakedream


text:
User:Namd3r~enwikiversity

Interests:
 * Computer Science
 * Mathematics
 * Music
 * Film Making

title: User:Namd3r~enwikiversity


text:
User talk:Namd3r~enwikiversity

Welcome
Hello Namd3r, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
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 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold, and see you around Wikiversity! --JWSchmidt 19:33, 27 December 2007 (UTC)

Thanks for your addition over at the Russian Revolution! The G 18:35, 3 January 2008 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Namd3r. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Namd3r~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:39, 17 March 2015 (UTC)

Renamed
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title: User talk:Namd3r~enwikiversity


text:
Lunar Boom Town/Tourist Frisbee Courses in Lunar Farm Tunnels

Business Model:

Hotel employees arrange frisbee courses and act as caddies for large fees.

Advantages:
 * No large capital outlays required to entertain tourists while improving Lunar Terran trade deficit. * Helps creates upwardly mobile entrepreneurial track starting at low dollar bottom.

Disadvantages:
 * Minor production impacts in farm outputs.
 * Must shuffle personal work schedule to accommodate tourists.

http://en.wikipedia.org/wiki/Disc_golf

Design issues:

 * Lower lunar gravity results in higher longer trajectories.
 * Lower air pressure results in lower lift.
 * Farm productivity must not be impacted or damages must be assessed and forwarded to farm owners.
 * Spacesuits must be worn in some high risk tunnels


text:
Trigonometry/Graphs

The graphs of trigonometric functions are periodic, that is, their graphs repeat in cycles, like the sine function.

Many trigonometric functions have graphs that are symmetric with respect to one of the axes or to the origin.

Videos: Graphing the Sine Function Graphing Trig Functions

Quiz: Topic:Trigonometry_Lesson 4:Graphs of Trigonometric Functions_quiz

title: Trigonometry/Graphs


text:
Materials Science and Engineering/List of Topics/Thermodynamics/Zeroth Law of Thermodynamics

The zeroth law of thermodynamics is a generalized statement about bodies in contact at thermal equilibrium and is the basis for the concept of temperature. The most common enunciation of the zeroth law of thermodynamics is:

"If two thermodynamic systems are in thermal equilibrium with a third, they are also in thermal equilibrium with each other."

In other words, the zeroth law says that if considered a mathematical binary relation, thermal equilibrium is transitive.

Temperature and the zeroth law
It is often claimed, for instance by Max Planck in his influential textbook on thermodynamics, that this law proves that we can define a temperature function, or more informally, that we can 'construct a thermometer'. Whether this is true is a subject in the philosophy of thermal and statistical physics.

In the space of thermodynamic parameters, zones of constant temperature will form a surface, which provides a natural order of nearby surfaces. It is then simple to construct a global temperature function that provides a continuous ordering of states. Note that the dimensionality of a surface of constant temperature is one less than the number of thermodynamic parameters (thus, for an ideal gas described with 3 thermodynamic parameter P, V and n, they are 2D surfaces). The temperature so defined may indeed not look like the Celsius temperature scale, but it is a temperature function.

For example, if two systems of ideal gas are in equilibrium, then $$P1V1/N1 = P2V2/N2$$ where $$P_i$$ is the pressure in the ith system, $$V_i$$ is the volume, and $$N_i$$ is the 'amount' (in moles, or simply number of atoms) of gas.

The surface $$PV / N = \mbox{const}$$ defines surfaces of equal temperature, and the obvious (but not only) way to label them is to define T so that $$PV / N = RT$$ where R is some constant. These systems can now be used as a thermometer to calibrate other systems.


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Materials Science and Engineering/List of Topics/Thermodynamics/Equations of State

In physics and thermodynamics, an equation of state is a relation between state variables.[1] More specifically, an equation of state is a thermodynamic equation describing the state of matter under a given set of physical conditions. It is a constitutive equation which provides a mathematical relationship between two or more state functions associated with the matter, such as its temperature, pressure, volume, or internal energy. Equations of state are useful in describing the properties of fluids, mixtures of fluids, solids, and even the interior of stars.

Overview
The most prominent use of an equation of state is to predict the state of gases and liquids. One of the simplest equations of state for this purpose is the ideal gas law, which is roughly accurate for gases at low pressures and high temperatures. However, this equation becomes increasingly inaccurate at higher pressures and lower temperatures, and fails to predict condensation from a gas to a liquid. Therefore, a number of much more accurate equations of state have been developed for gases and liquids. At present, there is no single equation of state that accurately predicts the properties of all substances under all conditions.

In addition to predicting the behavior of gases and liquids, there are also equations of state for predicting the volume of solids, including the transition of solids from one crystalline state to another. There are equations that model the interior of stars, including neutron stars. A related concept is the perfect fluid equation of state used in cosmology.


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Lunar Boom Town/Aluminum Production

Potential Markets

 * Lunar Rocket Fuel
 * AL-LOX Monopropellant Tests

 * Conducting wires
 * Aluminium is one of the most abundant materials on the moon, much more abundant than copper.

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Talk:Technical writing/Job interview

–68.9.117.230 14:48, 12 June 2009 (UTC)Don't delete this page please.

I'm going to add content in the near future. TWFred 10:14, 28 December 2007 (UTC)

Formatting
Hi Kristine,

Great work so far. Thank you.

Do you think we should get into resume formatting details? I've tried to avoid to much prescription on fonts and positioning and such, and instead focus on general themes that are not specific to any one tool. It's up to you, and I'm not itching to change what you wrote, but I wonder if it's not a trap we can fall into...giving too many picky details at the expense of the main theme which is the importance of content...

212.71.168.45 16:23, 16 February 2008 (UTC)

 * If it's important, include it, IMO. The Jade Knight 08:56, 3 September 2008 (UTC)

"Learning any documentation tool takes only a day or two."

Yikes. If it takes me more than "a day or two" to learn Dreamweaver, Photoshop, Framemaker, or XML, am I to conclude from this assertion that I'm in the wrong place when I aspire to work as a tech writer? Or are the applications that I list here not to be confused with "documentation tools"? What's up with that?

title: Talk:Technical writing/Job interview


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Filmmaking Basics/3D Storyboard/FrameForge:Teachers corrections

Under construction today

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Student's storyboards

 * Pruthvirajg
 * Here are the storyboards that he submitted.

Instructor's storyboards

 * Corrections
 * Here are suggested corrections by the instructor.

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The next page

 * Look at the completed storyboards.

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Lesson:3D Storyboard

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Lesson:3D Storyboard


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Materials Science and Engineering/List of Topics/Thermodynamics/First Law of Thermodynamics

The first law of thermodynamics states:

The increase in the internal energy of a system is equal to the amount of energy added by heating the system, minus the amount lost as a result of the work done by the system on its surroundings.

Description
The first law of thermodynamics basically states that a thermodynamic system can store or hold energy and that this internal energy is conserved. Heat is a process by which energy is added to a system from a high-temperature source, or lost to a low-temperature sink. In addition, energy may be lost by the system when it does mechanical work on its surroundings, or conversely, it may gain energy as a result of work done on it by its surroundings. The first law states that this energy is conserved: The change in the internal energy is equal to the amount added by heating minus the amount lost by doing work on the environment. The first law can be stated mathematically as:

 * $$dU=\delta Q-\delta w\,$$

where $$dU$$ is a small increase in the internal energy of the system, $$\delta Q$$ is a small amount of heat added to the system, and $$\delta W$$ is a small amount of work done by the system.

The δ's before the heat and work terms are used to indicate that they describe an increment of energy which is to be interpreted somewhat differently than the dU increment of internal energy. Work and heat are processes which add or subtract energy, while the internal energy U is a particular form of energy associated with the system. Thus the term "heat energy" for $$\delta Q$$ means "that amount of energy added as the result of heating" rather than referring to a particular form of energy. Likewise, the term "work energy" for $$\delta w$$ means "that amount of energy lost as the result of work". The most significant result of this distinction is the fact that one can clearly state the amount of internal energy possessed by a thermodynamic system, but one cannot tell how much energy has flowed into or out of the system as a result of its being heated or cooled, nor as the result of work being performed on or by the system.

The first explicit statement of the first law of thermodynamics was given by Rudolf Clausius in 1850: "There is a state function E, called ‘energy’, whose differential equals the work exchanged with the surroundings during an adiabatic process."

Note that the above formulation is favored by engineers and physicists. Chemists prefer a second form, in which the work term $$\delta w $$ is defined as the work done on the system, and therefore insert a plus sign in the above equation before the work term. This article will use the first definition exclusively.

Mathematical formulation
The mathematical statement of the first law is given by:

 * $$dU=\delta Q-\delta w\,$$

where $$dU$$ is the infinitesimal increase in the internal energy of the system, $$\delta Q$$ is the infinitesimal amount of heat added to the system, and $$\delta w$$ is the infinitesimal amount of work done by the system. The infinitesimal heat and work are denoted by δ rather than d because, in mathematical terms, they are not exact differentials. In other words, they do not describe the state of any system. The integral of an inexact differential depends upon the particular "path" taken through the space of thermodynamic parameters while the integral of an exact differential depends only upon the initial and final states. If the initial and final states are the same, then the integral of an inexact differential may or may not be zero, but the integral of an exact differential will always be zero. The path taken by a thermodynamic system through state space is known as a thermodynamic process.

An expression of the first law can be written in terms of exact differentials by realizing that the work that a system does is equal to its pressure times the infinitesimal change in its volume. In other words $$\delta w=PdV$$ where $$P$$ is pressure and $$V$$ is volume. For a reversible process, the total amount of heat added to a system can be expressed as $$\delta Q=TdS$$ where $$T$$ is temperature and $$S$$ is entropy. For a reversible process, the first law may now be restated:

 * $$dU=TdS-PdV\,$$

In the case where the number of particles in the system is not necessarily constant and may be of different types, the first law is written:

 * $$dU=\delta Q-\delta W + \sum_i \mu_i dN_i\,$$

where $$dN_i$$ is the (small) number of type-i particles added to the system, and $$\mu_i$$ is the amount of energy added to the system when one type-i particle is added, where the energy of that particle is such that the volume and entropy of the system remains unchanged. $$\mu_i$$ is known as the chemical potential of the type-i particles in the system. The statement of the first law for reversible processes, using exact differentials is now:

 * $$dU=TdS-PdV + \sum_i \mu_i dN_i\,$$

A useful idea from mechanics is that the energy gained by a particle is equal to the force applied to the particle multiplied by the displacement of the particle while that force is applied. Now consider the first law without the heating term: $$dU=PdV$$. The pressure P can be viewed as a force (and in fact has units of force per unit area) while dV  is the displacement (with units of distance times area). We may say, with respect to this work term, that a pressure difference forces a transfer of volume, and that the product of the two (work) is the amount of energy transferred as a result of the process.

It is useful to view the TdS term in the same light: With respect to this heat term, a temperature difference forces a transfer of entropy, and the product of the two (heat) is the amount of energy transferred as a result of the process. Here, the temperature is known as a "generalized" force (rather than an actual mechanical force) and the entropy is a generalized displacement.

Similarly, a difference in chemical potential between groups of particles in the system forces a trasfer of particles, and the corresponding product is the amount of energy transferred as a result of the process. For example, consider a system consisting of two phases: liquid water and water vapor. There is a generalized "force" of evaporation which drives water molecules out of the liquid. There is a generalized "force" of condensation which drives vapor molecules out of the vapor. Only when these two "forces" (or chemical potentials) are equal will there be equilibrium, and the net transfer will be zero.

The two thermodynamic parameters which form a generalized force-displacement pair are termed "conjugate variables". The two most familiar pairs are, of course, pressure-volume, and temperature-entropy.

Types of thermodynamic processes
Paths through the space of thermodynamic variables are often specified by holding certain thermodynamic variables constant. It is useful to group these processes into pairs, in which each variable held constant is one member of a conjugate pair.

The pressure-volume conjugate pair is concerned with the transfer of mechanical or dynamic energy as the result of work.

 * An isobaric process occurs at constant pressure. An example would be to have a movable piston in a cylinder, so that the pressure inside the cylinder is always at atmospheric pressure, although it is isolated from the atmosphere. In other words, the system is dynamically connected, by a movable boundary, to a constant-pressure reservoir.

 * An isochoric process is one in which the volume is held constant, meaning that the work done by the system will be zero. It follows that, for the simple system of two dimensions, any heat energy transferred to the system externally will be absorbed as internal energy. An isochoric process is also known as an isometric process. An example would be to place a closed tin can containing only air into a fire. To a first approximation, the can will not expand, and the only change will be that the gas gains internal energy, as evidenced by its increase in temperature and pressure. Mathematically, $$\delta Q=dU$$. We may say that the system is dynamically insulated, by a rigid boundary, from the environment.

The temperature-entropy conjugate pair is concerned with the transfer of thermal energy as the result of heating.

 * An isothermal process occurs at a constant temperature. An example would be to have a system immersed in a large constant-temperature bath. Any work energy performed by the system will be lost to the bath, but its temperature will remain constant. In other words, the system is thermally connected, by a thermally conductive boundary to a constant-temperature reservoir.

 * An isentropic process occurs at a constant entropy. For a reversible process this is identical to an adiabatic process (see below). If a system has an entropy which has not yet reached its maximum equilibrium value, a process of cooling may be required to maintain that value of entropy.

 * An adiabatic process is a process in which there is no energy added or subtracted from the system by heating or cooling. For a reversible process, this is identical to an isentropic process. We may say that the system is thermally insulated from its environment and that its boundary is a thermal insulator. If a system has an entropy which has not yet reached its maximum equilibrium value, the entropy will increase even though the system is thermally insulated.

The above have all implicitly assumed that the boundaries are also impermeable to particles. We may assume boundaries that are both rigid and thermally insulating, but are permeable to one or more types of particle. Similar considerations then hold for the (chemical potential)-(particle number) conjugate pairs.