{\displaystyle T}∂S{\displaystyle \partial S}N{\displaystyle N}∂T{\displaystyle \partial T}Compressibility β=−{\displaystyle \beta =-}1{\displaystyle 1}∂V{\displaystyle \partial V}V{\displaystyle V}∂p{\displaystyle \partial p}Thermal expansion α={\displaystyle \alpha =}1{\displaystyle 1}∂V{\displaystyle \partial V}V{\displaystyle V}∂T{\displaystyle \partial T}EquationsCarnot's theoremClausius theoremFundamental relationIdeal gas lawMaxwell relationsOnsager reciprocal relationsBridgman's equationsTable of thermodynamic equationsPotentialsFree energyFree entropyInternal energyU(S,V){\displaystyle U(S,V)}EnthalpyH(S,p)=U+pV{\displaystyle H(S,p)=U+pV}Helmholtz free energyA(T,V)=U−TS{\displaystyle A(T,V)=U-TS}Gibbs free energyG(T,p)=H−TS{\displaystyle G(T,p)=H-TS}Hist