Laws of thermodynamics

Remarks

The laws are not proved inside thermodynamics: they are postulates drawn from experience. Statistical mechanics derives them, in a suitable sense, from the microscopic laws of motion. The zeroth law makes thermal equilibrium an equivalence relation and so allows a temperature to be defined. The first law rules out a machine that produces work without using energy. The second law rules out a cyclic engine whose only effect is to turn heat from one reservoir fully into work. For example, it gives the Carnot bound $1 - T_C / T_H$ on the efficiency of an engine between reservoirs at $T_H > T_C$. The third law implies that absolute zero cannot be reached in a finite number of steps.

Going deeper

For a student

Each law introduces or constrains a state function. The zeroth law gives empirical temperature, the first law gives the internal energy $U$, and the second law gives the entropy $S$ and the thermodynamic temperature $T$. Together, the first and second laws give $dU = T \, dS - p \, dV$ for a simple fluid in reversible processes. From this relation come the thermodynamic potentials, the Maxwell relations, and the limits on the efficiency of engines and refrigerators. The third law fixes the additive constant in the entropy and governs behaviour near absolute zero, for example that heat capacities vanish there.