$C_V = \left(\frac{\partial U}{\partial T}\right)_V$. $\Delta U = nC_V\Delta T$

At constant pressure: $C_P = \left(\frac{\partial H}{\partial T}\right)_P$. $\Delta H = nC_P\Delta T$

Mayer's Relation (for ideal gas): $C_P - C_V = R$

Ratio of heat capacities: $\gamma = \frac{C_P}{C_V}$

Standard Enthalpy Changes:

Standard Enthalpy of Formation ($\Delta H_f^\circ$): Enthalpy change when 1 mole of a compound is formed from its elements in their standard states. ($\Delta H_f^\circ$ of an element in its standard state is 0).
Standard Enthalpy of Reaction ($\Delta H_r^\circ$): $\Delta H_r^\circ = \sum \nu_P \Delta H_f^\circ(\text{products}) - \sum \nu_R \Delta H_f^\circ(\text{reactants})$
Standard Enthalpy of Combustion ($\Delta H_c^\circ$): Enthalpy change when 1 mole of a substance is completely burnt in oxygen.
Standard Enthalpy of Neutralization ($\Delta H_{neut}^\circ$): For strong acid-strong base, approx. $-57.3 \text{ kJ/mol}$.

Hess's Law of Constant Heat Summation: The total enthalpy change for a reaction is independent of the pathway.

Bond Enthalpy (Bond Energy): Energy required to break one mole of a particular type of bond. ($\Delta H = \sum BE(\text{reactants}) - \sum BE(\text{products})$)

5. Second Law of Thermodynamics

Statement: The entropy of an isolated system always increases in the course of a spontaneous change.
Clausius Statement: Heat cannot flow spontaneously from a colder body to a hotter body.
Kelvin-Planck Statement: It is impossible to construct a device which operates in a cycle and produces no effect other than the extraction of heat from a reservoir and the performance of an equivalent amount of work.
Entropy ($S$): Measure of randomness or disorder. State function.
Change in Entropy: $\Delta S = \frac{q_{rev}}{T}$
For a spontaneous process in an isolated system: $\Delta S_{total} = \Delta S_{sys} + \Delta S_{surr} > 0$
For a reversible process: $\Delta S_{total} = 0$
For an irreversible process: $\Delta S_{total} > 0$
Third Law of Thermodynamics: The entropy of a perfectly crystalline substance at absolute zero (0 K) is taken to be zero.
Standard Entropy of Reaction: $\Delta S_r^\circ = \sum \nu_P S^\circ(\text{products}) - \sum \nu_R S^\circ(\text{reactants})$

6. Gibbs Free Energy ($G$)

Definition: $G = H - TS$
Change in Gibbs Free Energy: $\Delta G = \Delta H - T\Delta S$ (at constant T)
Criterion for Spontaneity (at constant T, P):
- $\Delta G < 0$: Spontaneous process.
- $\Delta G > 0$: Non-spontaneous process (reverse is spontaneous).
- $\Delta G = 0$: System is at equilibrium.

Effect of $\Delta H$ and $\Delta S$ on $\Delta G$:

$\Delta H$	$\Delta S$	$\Delta G = \Delta H - T\Delta S$	Spontaneity
$-$	$+$	Always $-$	Spontaneous at all $T$
$+$	$-$	Always $+$	Non-spontaneous at all $T$
$-$	$-$	$-$ at low $T$, $+$ at h