Thermodynamics Key Formulas and Concepts

Comprehensive vocabulary flashcards covering thermodynamic formulas, definitions, laws, and physical constants from the lecture notes.

Linear Thermal Expansion

$$\Delta L = \alpha L_0 \Delta T$$

Volume Thermal Expansion

$$\Delta V = \beta V_0 \Delta T$$

Volume Expansion Coefficient Relation

The relationship between the coefficient of volume expansion $\beta$ and the coefficient of linear expansion $\alpha$, defined as $\beta = 3\alpha$.

Heat Capacity Formulas

by $Q = mc\Delta T$ using mass and specific heat capacity,

or $Q = nC\Delta T$ using moles and molar heat capacity.

Latent Heat

$Q = \pm mL$.

Molar Heat Capacity Relation

$C_p = C_v + R$.

Heat Capacity Ratio ($\gamma$)

$\gamma = \frac{C_p}{C_v}$.

Molar Heat Capacity of a Solid ($C_v$)

$C_v = 3R$.

Thermal Conduction Rate ($H$)

$H = \frac{kA\Delta T}{L}$.

Blackbody Radiation Rate ($H$)

$H = A\sigma T^4$.

Ideal Gas Law

$PV = NkT$ (microscopic form)

or

$PV = nRT$ (macroscopic form).

Gas Constant Relation

$kN_A = R$.

Equipartition Theorem

$\frac{1}{2}m\langle v^2 \rangle = \frac{3}{2}kT$.

Root-Mean-Square Velocity ($v_{\text{rms}}$)

$v_{\text{rms}} = \sqrt{\langle v^2 \rangle_{\text{av}}}$.

Maxwell-Boltzmann Velocity Distribution

$f(v) \propto v^2 e^{-mv^2/(2kT)}$.

Zeroth Law of Thermodynamics

$T_A = T_B = T_C$.

First Law of Thermodynamics

$dU = dQ - dW$.

Cyclic Process Work and Heat

$W = Q = Q_H + Q_C$.

Thermodynamic Work ($W$)

$W = \int p\,dV$.

Entropy (Macroscopic Definition)

$\Delta S = \int \frac{dQ}{T}$.

Entropy (Boltzmann Definition)

$S = k\ln(w)$.

Second Law of Thermodynamics

$\Delta S \ge 0$.

Thermal Engine Efficiency ($e$)

$e = \frac{W}{Q_H}$.

Refrigerator Coefficient of Performance ($K$)

$K = \frac{Q_C}{W}$.

Heat Pump Coefficient of Performance (Heating Mode)

$K=\frac{-Q_{H}}{-W}$ .

Entropy Change of a Carnot Cycle

$\Delta S = \frac{Q_H}{T_H} + \frac{Q_C}{T_C} = 0$.

Specific Heat Capacity of Water

$c_{\text{water}} = 4190\,\text{J}/(\text{kg}\cdot\text{K})$ .

Boltzmann Constant ($k$)

$k = 1.380\,649 \times 10^{-23}\,\text{J}/\text{K}$.

Avogadro's Number ($N_A$)

$N_A = 6.022\,140\,76 \times 10^{23}\,\text{mol}^{-1}$.