Thermodynamics for JEE: First Law, Entropy, and Gibbs Free Energy Guide

ΔH = ΔU + PΔV. ΔH accounts for pressure-volume work. For reactions with no gas moles change, ΔH ≈ ΔU. For reactions with gas production, ΔH > ΔU. ΔH = ΔU + Δn_g·RT.

A reaction is spontaneous when ΔG < 0. ΔG = ΔH - TΔS. If ΔH < 0 and ΔS > 0: always spontaneous. If ΔH > 0 and ΔS < 0: never spontaneous. If both same sign: spontaneous depends on temperature.

Hess's law states that the enthalpy change for a reaction is the same whether it occurs in one step or multiple steps. ΔH_total = ΣΔH of individual steps. This allows calculating ΔH for reactions that are hard to measure directly.

The zeroth law states: if two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other. It establishes the concept of temperature and is the basis for thermometry.

The third law states that the entropy of a perfect crystal approaches zero as temperature approaches absolute zero (0 K). At 0 K, there is only one possible microstate, so S = 0.

Heat is energy transfer due to temperature difference (measured in Joules). Temperature is a measure of average kinetic energy of molecules (measured in Kelvin). Heat flows from higher to lower temperature.

The Carnot cycle is an ideal reversible cycle with 4 steps: isothermal expansion, adiabatic expansion, isothermal compression, adiabatic compression. Efficiency = 1 - T₂/T₁. No real engine can exceed Carnot efficiency.

State functions depend only on initial and final states (U, H, S, G, T, P, V). Path functions depend on how the change occurs (q, W). ΔU is a state function but q and W are path functions. However, ΔU = q + W always holds.

ΔG° = -RT ln K. At equilibrium, ΔG = 0. If K > 1, ΔG° < 0 (products favored). If K < 1, ΔG° > 0 (reactants favored). For spontaneous reactions, ΔG < 0.

Standard enthalpy of formation (ΔHf°) is the heat change when 1 mole of a compound is formed from its constituent elements in standard states. By convention, ΔHf° of elements in standard state = 0.

Bond dissociation energy is the energy required to break one mole of bonds in gaseous molecules. Average bond energies: C-H = 413 kJ/mol, C-C = 348 kJ/mol, N≡N = 946 kJ/mol.

Spontaneity is determined by ΔG = ΔH - TΔS. A reaction is spontaneous if ΔG < 0. Note: spontaneous does not mean fast — it means thermodynamically favorable.

ΔS_universe = ΔS_system + ΔS_surroundings. For all spontaneous processes, ΔS_universe > 0 (second law). At equilibrium, ΔS_universe = 0. This is the fundamental criterion for spontaneity.