Thermodynamics

The power of heating generated by an electrical conductor is proportional to the product of its resistance and the square of the current: $P = I^2 R$.

For a fixed mass of an ideal gas kept at a fixed temperature, pressure and volume are inversely proportional: $P_1 V_1 = P_2 V_2$.

When the pressure on a sample of a dry gas is held constant, the Kelvin temperature and the volume will be in direct proportion: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$.

The pressure of a given mass of gas varies directly with the absolute temperature of the gas, when the volume is kept constant: $\frac{P_1}{T_1} = \frac{P_2}{T_2}$.

Equal volumes of all gases, at the same temperature and pressure, have the same number of molecules: $\frac{V}{n} = k$.

The equation of state of a hypothetical ideal gas, combining Boyle's, Charles's, and Avogadro's laws: $PV = nRT$.

In a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases.

The rate of effusion of a gas is inversely proportional to the square root of the mass of its particles: $\frac{Rate_1}{Rate_2} = \sqrt{\frac{M_2}{M_1}}$.

If two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.

Energy cannot be created or destroyed in an isolated system; the change in internal energy of a system is equal to the heat added to the system minus the work done by the system: $\Delta U = Q - W$.

The total entropy of an isolated system can never decrease over time, and is constant if and only if all processes are reversible.

The entropy of a system approaches a constant value as the temperature approaches absolute zero.

The total energy radiated per unit surface area of a black body across all wavelengths per unit time is directly proportional to the fourth power of the black body's thermodynamic temperature: $j^* = \sigma T^4$.

The spectral radiance of a black-body radiation per unit wavelength peaks at the wavelength $\lambda_{max}$ inversely proportional to the thermodynamic temperature: $\lambda_{max} = \frac{b}{T}$.

The diffusive flux is directly proportional to the concentration gradient: $J = -D \nabla \phi$.

Predicts how diffusion causes the concentration to change with respect to time: $\frac{\partial \phi}{\partial t} = D \frac{\partial^2 \phi}{\partial x^2}$.

The time rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, at right angles to that gradient, through which the heat flows: $\mathbf{q} = -k \nabla T$.

The rate of heat loss of a body is directly proportional to the difference in the temperatures between the body and its surroundings.

Relates the current density of thermionic emission to the temperature of the emitter.

The volume of a gas mixture is equal to the sum of the volumes of the component gases, if each component were present alone at the temperature and pressure of the mixture.

An approximation of the spectral radiance of electromagnetic radiation at all wavelengths from a black body at a given temperature, accurate only at low frequencies.

For an arbitrary body emitting and absorbing thermal radiation in thermodynamic equilibrium, the emissivity is equal to the absorptivity.

Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.

It is impossible to devise a cyclically operating device, the sole effect of which is to absorb energy in the form of heat from a single thermal reservoir and to deliver an equivalent amount of work.

When a system at equilibrium is subjected to a change in concentration, temperature, volume, or pressure, then the system readjusts itself to counteract the effect of the applied change and a new equilibrium is established.

For a system at equilibrium, the number of degrees of freedom $F$, the number of components $C$, and the number of phases $P$ are related by $F = C - P + 2$.