The four laws
| Law | Statement | Key equation |
|---|---|---|
| Zeroth | If A is in thermal equilibrium with B, and B with C, then A with C. | Defines temperature |
| First | Energy is conserved — heat and work can interconvert. | ΔU = Q − W |
| Second | Entropy of an isolated system never decreases. | ΔS ≥ 0; η_max = 1 − T_c/T_h |
| Third | Entropy approaches a constant as T → 0 K. | S(T=0) = 0 for a perfect crystal |
Key quantities
| Internal energy U | Sum of kinetic + potential energies of all particles |
|---|---|
| Enthalpy H | = U + PV — useful at constant pressure |
| Entropy S | Measure of microstates; dS = δQ_rev / T |
| Gibbs free energy G | = H − TS — spontaneous if ΔG < 0 at constant T, P |
| Helmholtz free energy F | = U − TS — useful at constant T, V |
Heat engine efficiency
| Carnot (max) | η = 1 − T_c / T_h |
|---|---|
| Otto (gasoline) | η = 1 − 1/r^(γ−1), r = compression ratio |
| Brayton (gas turbine) | η = 1 − 1/(r_p)^((γ−1)/γ) |
| COP (refrigerator) | Q_c / W = T_c / (T_h − T_c) (Carnot) |
Notes
- The second law is why perpetual-motion machines of the second kind are impossible.
- At absolute zero, all thermal motion stops — but zero-point quantum energy remains.
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