Key formulae — Thermodynamics

Summary of thermodynamics formulae (ch. 8b, 9–12). Derivations and limits of validity are in the respective chapters.

Ideal gas $PV = nRT$

Internal energy (gas with $f$ degrees of freedom) $E_\text{int} = \tfrac{f}{2}nRT$

First law

$\Delta E_\text{int} = Q - L$

Specific heats $C_p = C_v + R$

Adiabatic transformation $PV^\gamma = \text{cost}$

Carnot efficiency $\eta = 1 - \frac{T_f}{T_c}$

Second law

Entropy: $\Delta S = \displaystyle\int \frac{\dd Q}{T}$; in real processes $\Delta S_\text{tot} \geq 0$.

Links

Topics: Thermodynamics · Kinetic theory of gases · Heat engines · Entropy and the second law

Related exercises: Worked exercise — reversible vs irreversible isothermal expansion · Problem — True or false on engines and fridges · Problem — True or false on reversibility and cycles