1. Fundamental Laws of Thermodynamics
Essential framework for evaluating system energy transformations and state functions:
- First Law ($\Delta U = q + w$): Law of conservation of energy. Internal energy is a state function; work and heat are path functions.
- Second Law ($\Delta S_{\text{univ}} > 0$): For any spontaneous process, total entropy of the universe must continuously increase.
- Third Law: The entropy of a perfectly crystalline pure substance approaches zero at absolute zero ($0\text{ K}$).
$\Delta S_{\text{univ}} = \Delta S_{\text{sys}} + \Delta S_{\text{surr}} > 0$
2. Gibbs Free Energy ($\Delta G$) Criteria
The master criterion for predicting chemical reaction spontaneity at constant temperature and pressure:
$\Delta G = \Delta H - T\Delta S$
High-Yield JEE/NEET Matrix:
- $\Delta H < 0, \Delta S > 0$: Spontaneous at all temperatures.
- $\Delta H > 0, \Delta S < 0$: Non-spontaneous at all temperatures.
- $\Delta H < 0, \Delta S < 0$: Spontaneous at low temperatures ($T < \Delta H/\Delta S$).
- $\Delta H > 0, \Delta S > 0$: Spontaneous at high temperatures ($T > \Delta H/\Delta S$).
3. Enthalpy, Entropy & Equilibrium Link
Connects thermodynamics directly to chemical equilibrium constants and non-expansion work:
- Standard Free Energy: $\Delta G^\circ = -RT \ln K_{eq}$
- Temperature Dependence: van 't Hoff equation links enthalpy change to equilibrium constants at different temperatures.
- Enthalpy ($\Delta H$): Heat absorbed or released at constant pressure ($\Delta H = \Delta U + P\Delta V$).
$\Delta G = \Delta G^\circ + RT \ln Q$