Thermodynamics Crash Course

Cheatsheet Content

1. First Law of Thermodynamics **Internal Energy Change:** $\Delta U = q + w$ 2. Work (w) **Pressure-Volume Work (General):** $w = -p_{ex} \Delta V$ **Isothermal Reversible Expansion (Ideal Gas):** $w_{rev} = -nRT \ln \frac{V_f}{V_i} = -2.303 nRT \log \frac{V_f}{V_i}$ **Work at Constant Volume:** $w = 0$ (since $\Delta V = 0$) **Free Expansion:** $w = 0$ (since $p_{ex} = 0$) 3. Enthalpy (H) **Definition:** $H = U + pV$ **Enthalpy Change at Constant Pressure:** $\Delta H = q_p$ **Relationship between $\Delta H$ and $\Delta U$:** For processes at constant pressure: $\Delta H = \Delta U + p\Delta V$ For reactions involving gases: $\Delta H = \Delta U + \Delta n_g RT$ 4. Heat Capacity (C) & Heat Transfer (q) **General Heat Transfer:** $q = C \Delta T$ **Specific Heat Capacity:** $q = c \times m \times \Delta T$ **Molar Heat Capacity:** $q = C_m \times n \times \Delta T$ **Relation for Ideal Gas:** $C_p - C_V = R$ 5. Enthalpy Changes of Reactions ($\Delta_r H$) **From Standard Enthalpies of Formation:** $\Delta_r H^\circ = \sum a_i \Delta_f H^\circ (\text{products}) - \sum b_i \Delta_f H^\circ (\text{reactants})$ **From Bond Enthalpies (Approximation for Gas Phase):** $\Delta_r H^\circ \approx \sum (\text{bond enthalpies of reactants}) - \sum (\text{bond enthalpies of products})$ **Hess's Law:** $\Delta_r H = \sum \Delta H_{\text{steps}}$ **Enthalpy of Solution:** $\Delta_{sol} H^\circ = \Delta_{lattice} H^\circ + \Delta_{hyd} H^\circ$ 6. Entropy (S) & Second Law of Thermodynamics **Entropy Change (Reversible Process):** $\Delta S = \frac{q_{rev}}{T}$ **Entropy Change of Surroundings:** $\Delta S_{surr} = -\frac{\Delta H_{sys}}{T}$ (for constant P process) **Total Entropy Change (Spontaneity Criterion):** $\Delta S_{total} = \Delta S_{sys} + \Delta S_{surr}$ Spontaneous: $\Delta S_{total} > 0$ Equilibrium: $\Delta S_{total} = 0$ 7. Gibbs Energy (G) & Spontaneity **Definition:** $G = H - TS$ **Gibbs-Helmholtz Equation (at constant T, P):** $\Delta G = \Delta H - T\Delta S$ **Criteria for Spontaneity (at constant T, P):** Spontaneous: $\Delta G Non-spontaneous: $\Delta G > 0$ Equilibrium: $\Delta G = 0$ **Standard Gibbs Energy Change and Equilibrium Constant (K):** $\Delta_r G^\circ = -RT \ln K = -2.303 RT \log K$ 8. Important Constants **Gas Constant (R):** $8.314 \text{ J K}^{-1} \text{ mol}^{-1}$ or $0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1}$ **Absolute Zero:** $0 \text{ K} = -273.15^\circ \text{C}$