JEE Chemistry Thermodynamics Notes Set 03

Entropy

1. Entropy S measures the disorder of a system. \(\Delta S=\dfrac{q_{rev}}{T}\).
2. For an ideal gas: \(\Delta S=nC_V\ln\dfrac{T_2}{T_1}+nR\ln\dfrac{V_2}{V_1}=nC_P\ln\dfrac{T_2}{T_1}-nR\ln\dfrac{P_2}{P_1}\).
3. For a phase change at its equilibrium temperature \(\Delta S=\Delta H/T\) (fusion, vaporisation).
4. Entropy is a state function. To find \(\Delta S_{sys}\) for an irreversible process, use any reversible path between the same end states.
5. Third law: the entropy of a perfect crystal is zero at absolute zero, so absolute entropies can be tabulated. \(\Delta_rS^\circ=\sum S^\circ(\text{products})-\sum S^\circ(\text{reactants})\).

Second Law

1. For an isolated system or the universe: \(\Delta S_{total}=\Delta S_{sys}+\Delta S_{surr}\ge0\); equality for reversible processes, greater than zero for spontaneous (irreversible) ones.
2. \(\Delta S_{surr}=-q_{sys}/T_{surr}\) (heat actually exchanged).
3. Heat engine: efficiency \(\eta=\dfrac{w}{q_h}=1-\dfrac{q_c}{q_h}\le1-\dfrac{T_c}{T_h}\), with equality for a reversible (Carnot) engine. An engine that does more work than the Carnot limit is impossible.
4. Free expansion of an ideal gas: \(q=0\), \(w=0\), \(\Delta S_{sys}=nR\ln(V_2/V_1)>0\), \(\Delta S_{surr}=0\).

Gibbs Energy

1. \(G=H-TS\) and, at constant T and P, \(\Delta G=\Delta H-T\Delta S\). A process is spontaneous if \(\Delta G<0\), at equilibrium if \(\Delta G=0\), and non-spontaneous if \(\Delta G>0\).
2. \(-\Delta G\) is the maximum useful (non-expansion) work obtainable at constant T and P.
3. For an ideal gas at constant temperature \(\Delta G=nRT\ln\dfrac{P_2}{P_1}\).
4. \(\Delta G^\circ\) depends on temperature only; \(\Delta G^\circ=-RT\ln K\).
5. Equilibrium temperature of a reaction (\(\Delta G=0\)): \(T=\Delta H/\Delta S\).

Remember

1. On a G-T graph the slope is \(-\Delta S\) and the intercept is \(\Delta H\).
2. Reversible phase change at the normal boiling point: \(\Delta G=0\).
3. Entropy of a gas rises as pressure falls or volume rises.
4. Dissociation or decomposition that forms gas has positive \(\Delta S\).