Laws of Thermodynamics
The zeroth through third laws — with plain-language explanations and key equations.
Reference
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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