Zeroth Law defines temperature: thermal equilibrium is transitive (A ↔ B and B ↔ C → A ↔ C).

First Law: Q = $\Delta U$ + W. Energy is conserved. Sign convention: absorbed Q > 0; expansion W > 0; temperature-rising $\Delta U$ > 0.

Second Law (Kelvin-Planck): No cyclic engine converts all heat to work. Some heat $Q_{2}$ must always be rejected to a cold reservoir. η < 1 always.

Second Law (Clausius): Heat does not spontaneously flow from cold to hot. External work is required to operate a refrigerator.

Entropy is a state function measuring disorder. In any spontaneous (irreversible) process, total entropy increases. Entropy is conserved only in ideal reversible processes.

Isothermal process: T = constant. For ideal gas: $\Delta U$ = 0 and Q = W = nRT ln($V_{2}$/$V_{1}$). PV diagram: rectangular hyperbola.

Adiabatic process: Q = 0. Temperature changes: expansion cools, compression heats. W = nCᵥ($T_{1}$ − $T_{2}$). Governing: PV^γ = const. PV diagram: steeper than isothermal.

Isochoric process: V = constant. W = 0. All heat changes internal energy: Q = $\Delta U$ = nCᵥ$\Delta T$. PV diagram: vertical line.

Isobaric process: P = constant. W = P$\Delta V$ = nR$\Delta T$. Q = nCₚ$\Delta T$. $\Delta U$ = nCᵥ$\Delta T$. PV diagram: horizontal line.

Mayer's relation: Cₚ − Cᵥ = R for any ideal gas. Cₚ > Cᵥ because at constant pressure, gas must also do expansion work.

Adiabatic is steeper than isothermal on the PV diagram because the exponent γ > 1 in PV^γ = const vs PV = const.

Work done = area under PV curve. For a clockwise cycle, net W > 0 (heat engine). For anticlockwise, net W < 0 (refrigerator).

Carnot efficiency: η = 1 − $T_{2}$/$T_{1}$. Temperatures must be in kelvin. This is the maximum possible efficiency between $T_{1}$ and $T_{2}$.

Refrigerator COP: COP = $T_{2}$/($T_{1}$ − $T_{2}$). Can be > 1. Heat pumps: COP = $T_{1}$/($T_{1}$ − $T_{2}$) = COP_ref + 1.