Science & Engineering

Laws of Thermodynamics

The zeroth through third laws — with plain-language explanations and key equations.

The four laws

LawStatementKey equation
ZerothIf A is in thermal equilibrium with B, and B with C, then A with C.Defines temperature
FirstEnergy is conserved — heat and work can interconvert.ΔU = Q − W
SecondEntropy of an isolated system never decreases.ΔS ≥ 0; η_max = 1 − T_c/T_h
ThirdEntropy approaches a constant as T → 0 K.S(T=0) = 0 for a perfect crystal

Key quantities

Internal energy USum of kinetic + potential energies of all particles
Enthalpy H= U + PV — useful at constant pressure
Entropy SMeasure 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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