Thermodynamics
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Direct answer
Thermodynamics tracks energy changes through state functions. The first law, delta U = q + w (work done on the system positive, the NCERT convention), links heat and work to internal energy, while delta H = delta U + delta_ng R T converts between heat at constant pressure and constant volume. Spontaneity rests on Gibbs energy: delta G = delta H - T delta S, negative for spontaneous change, zero at equilibrium.
What you must remember
- Work: w = -p_ext × delta V for irreversible change; reversible isothermal expansion w = -2.303 nRT log(V2/V1); free expansion into vacuum gives w = 0, so isothermally q = 0 and delta U = 0.
- delta H = delta U + delta_ng R T, counting only gaseous moles; the two are equal when delta_ng = 0.
- C_p - C_v = R for an ideal gas; monatomic C_v = 3/2 R, diatomic about 5/2 R.
- Hess's law: delta H is path-independent, so target equations are built from given ones; delta H_reaction = sum delta H_f(products) - sum delta H_f(reactants).
- Neutralising a strong acid with a strong base releases about -57.3 kJ per mole of water; weak acids release less because ionisation consumes heat.
- Entropy: delta S = q_rev/T; at a phase change delta S = delta H_transition / T; entropy rises gas > liquid > solid.
- delta G = delta H - T delta S: negative spontaneous, zero equilibrium, positive non-spontaneous; delta G° = -2.303 R T log K. Exothermic with positive entropy change is spontaneous at all temperatures; endothermic with negative entropy change at none.
- Third law: the entropy of a perfect crystal at 0 K is zero.
Common confusion
The classic muddle is the sign convention for work — under the NCERT convention work done on the gas is positive, so compression has w > 0, expansion w < 0. Students then misapply delta H = delta U + delta_ng R T by counting all species instead of only gaseous ones. The deepest confusion equates spontaneity with speed: a negative delta G says a reaction can proceed, never that it will proceed quickly — that is kinetics.
Exam-focused takeaway
JEE Main tests the machinery directly: w, q and delta U for standard processes, delta H to delta U conversion, delta G from delta H and delta S, and delta G° from K. JEE Advanced prefers composites — reversible versus irreversible work for the same expansion, the temperature window where spontaneity flips sign, Hess cycles and entropy changes at phase transitions. Write the convention at the top of your rough sheet; it prevents most sign errors.
Frequently asked questions
What is the difference between delta H and delta U?
delta H is heat at constant pressure, delta U at constant volume; they connect through delta H = delta U + delta_ng R T for gases.
Why is reversible expansion work maximum in magnitude?
The external pressure always equals the internal pressure, so the gas pushes against the largest possible opposing force.
When is a reaction spontaneous at all temperatures?
When delta H is negative and delta S is positive — both terms then favour a negative delta G.
What does the third law state?
The entropy of a perfect crystal is zero at absolute zero — the reference point for absolute entropies.
Why is neutralisation enthalpy of a weak acid below 57.3 kJ per mole?
Part of the heat is consumed ionising the weak acid, so less is released.
Is an exothermic reaction always spontaneous?
No — if delta S is strongly negative, the -T delta S term can outweigh the enthalpy gain at high temperature.