Thermodynamics — Revision Notes

⚡ 30-Second Revision

First Law — $\Delta U = Q + W$ (Energy Conservation) \n- Work (Constant P): $W = -P_{ext}\Delta V$ \n- Work (Reversible Isothermal): $W_{rev} = -nRT \ln(V_2/V_1)$ \n- Enthalpy: $H = U + PV$, $\Delta H = \Delta U + \Delta n_g RT$ \n- Second Law: $\Delta S_{total} > 0$ (Spontaneous) \n- Entropy Change: $\Delta S = Q_{rev}/T$ \n- Gibbs Free Energy: $\Delta G = \Delta H - T\Delta S$ \n- Spontaneity: $\Delta G < 0$ (Spontaneous), $\Delta G = 0$ (Equilibrium), $\Delta G > 0$ (Non-spontaneous) \n- Equilibrium Constant: $\Delta G^\circ = -RT \ln K$ \n- Third Law: $S = 0$ at $0\,\text{K}$ for perfect crystal \n- Sign Conventions: Q (+ve absorbed, -ve released); W (+ve on system, -ve by system)

2-Minute Revision

Thermodynamics is the study of energy transformations, focusing on heat and work. Remember the First Law: $\Delta U = Q + W$, which is energy conservation. Pay close attention to sign conventions for Q (heat absorbed +ve, released -ve) and W (work on system +ve, by system -ve).

Work done against constant pressure is $W = -P_{ext}\Delta V$, while for reversible isothermal expansion, $W = -nRT \ln(V_2/V_1)$. Enthalpy, H, is useful for constant pressure processes, with $\Delta H = \Delta U + \Delta n_g RT$ relating it to internal energy.

The Second Law introduces entropy (S), a measure of disorder; for spontaneity, $\Delta S_{total} > 0$. Gibbs Free Energy, $\Delta G = \Delta H - T\Delta S$, is the practical criterion for spontaneity at constant T and P: $\Delta G < 0$ means spontaneous.

The Third Law states that entropy of a perfect crystal is zero at 0 K. Master these formulas and their applications, especially for predicting spontaneity and calculating energy changes.

5-Minute Revision

Begin your revision by solidifying the core definitions: system, surroundings, boundary, and the types of systems (open, closed, isolated). Differentiate clearly between state functions (P, V, T, U, H, S, G) and path functions (Q, W), as this is a common conceptual trap.

\n\nFirst Law of Thermodynamics: $\Delta U = Q + W$. This is the law of energy conservation. Practice applying the correct sign conventions: heat absorbed by the system is positive ($+Q$), heat released is negative ($-Q$).

Work done on the system (compression) is positive ($+W$), work done by the system (expansion) is negative ($-W$). \n* Example: A gas absorbs $100\,\text{J}$ heat and expands, doing $40\,\text{J}$ work.

$\Delta U = (+100) + (-40) = +60\,\text{J}$. \n\nWork Calculations: \n* For constant external pressure: $W = -P_{ext}\Delta V$. Remember $1\,\text{L atm} = 101.3\,\text{J}$. \n* For reversible isothermal expansion/compression: $W_{rev} = -nRT \ln(V_2/V_1)$.

\n\nEnthalpy: $\Delta H = \Delta U + P\Delta V$. For reactions involving gases, $\Delta H = \Delta U + \Delta n_g RT$, where $\Delta n_g$ is the change in moles of gaseous products minus reactants.

This is crucial for converting between constant volume and constant pressure heat changes. \n\nSecond Law of Thermodynamics: Introduces entropy (S), a measure of disorder. For a spontaneous process, the total entropy of the universe must increase ($\Delta S_{total} > 0$).

\n\nGibbs Free Energy: $\Delta G = \Delta H - T\Delta S$. This is the most important criterion for spontaneity at constant T and P. \n* If $\Delta G < 0$: Spontaneous. \n* If $\Delta G > 0$: Non-spontaneous (reverse is spontaneous).

\n* If $\Delta G = 0$: Equilibrium. \n\nAnalyze how $\Delta H$ and $\Delta S$ signs affect spontaneity: \n* $\Delta H < 0, \Delta S > 0$: Always spontaneous. \n* $\Delta H > 0, \Delta S < 0$: Never spontaneous.

\n* $\Delta H < 0, \Delta S < 0$: Spontaneous at low T. \n* $\Delta H > 0, \Delta S > 0$: Spontaneous at high T. \n\nThird Law: $S = 0$ for a perfect crystalline substance at $0\,\text{K}$. This provides a baseline for absolute entropy.

\n\nPractice problems involving all these concepts, paying close attention to units and signs. Remember that spontaneity does not imply speed.

Prelims Revision Notes

1
System & Surroundings — System (part under study), Surroundings (rest of universe), Boundary (separates them). \n * Open: Exchanges matter & energy. \n * Closed: Exchanges energy, not matter. \n * Isolated: Exchanges neither. \n\n2. Properties: \n * Extensive: Depends on amount (mass, volume, U, H, S, G). \n * Intensive: Independent of amount (T, P, density, specific heat). \n\n3. Functions: \n * State Functions: Path independent (P, V, T, U, H, S, G). $\Delta$ denotes change. \n * Path Functions: Path dependent (Q, W). \n\n4. First Law of Thermodynamics: Law of Conservation of Energy. \n * $\Delta U = Q + W$ \n * Sign Conventions: \n * $Q > 0$: Heat absorbed by system. \n * $Q < 0$: Heat released by system. \n * $W > 0$: Work done on system (compression). \n * $W < 0$: Work done by system (expansion). \n\n5. Work Done: \n * Constant Pressure: $W = -P_{ext}\Delta V$. \n * Reversible Isothermal (Ideal Gas): $W_{rev} = -nRT \ln(V_2/V_1) = -nRT \ln(P_1/P_2)$. \n\n6. Enthalpy (H): Heat content at constant pressure. \n * $H = U + PV$ \n * $\Delta H = \Delta U + P\Delta V$ (constant P) \n * $\Delta H = \Delta U + \Delta n_g RT$ (for gaseous reactions, $\Delta n_g = \text{moles of gaseous products} - \text{moles of gaseous reactants}$). \n\n7. Second Law of Thermodynamics: Spontaneity & Entropy. \n * Entropy (S): Measure of disorder/randomness. $S_{gas} > S_{liquid} > S_{solid}$. \n * $\Delta S = Q_{rev}/T$. \n * For spontaneous process: $\Delta S_{total} = \Delta S_{system} + \Delta S_{surroundings} > 0$. \n\n8. Gibbs Free Energy (G): Criterion for spontaneity at constant T, P. \n * $\Delta G = \Delta H - T\Delta S$. \n * $\Delta G < 0$: Spontaneous. \n * $\Delta G > 0$: Non-spontaneous. \n * $\Delta G = 0$: Equilibrium. \n * **Spontaneity based on $\Delta H, \Delta S$**: \n * $\Delta H < 0, \Delta S > 0$: Always spontaneous. \n * $\Delta H > 0, \Delta S < 0$: Never spontaneous. \n * $\Delta H < 0, \Delta S < 0$: Spontaneous at low T. \n * $\Delta H > 0, \Delta S > 0$: Spontaneous at high T. \n\n9. Relationship with Equilibrium Constant: $\Delta G^\circ = -RT \ln K$. \n\n10. Third Law of Thermodynamics: $S = 0$ at $0\,\text{K}$ for a perfect crystalline substance. \n\nKey Points: \n* Spontaneity $\neq$ Speed. \n* Unit consistency (J vs kJ, L atm vs J). \n* Careful with $\Delta n_g$ calculation.

Vyyuha Quick Recall

To remember the spontaneity conditions based on $\Delta H$ and $\Delta S$: \n\n'Happy Students Get To Succeed' \n$\Delta H$ (Happy) and $\Delta S$ (Students) determine $\Delta G$ (Get) at Temperature (To) for Spontaneity (Succeed).

\n\n* H-ve, S+ve: Always spontaneous (Happy, Succeed). \n* H+ve, S-ve: Never spontaneous (Sad, Fail). \n* H-ve, S-ve: Spontaneous at Low T (Happy, but messy, so needs cool head). \n* H+ve, S+ve: Spontaneous at High T (Needs energy, but loves freedom, so needs hot environment).