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Physics LibreTexts

10.11: K- Useful Formulas

( \newcommand{\kernel}{\mathrm{null}\,}\)

Isothermal compressibility:

κT=1VVp)T,N=1ρρp)T=1ρ22pμ2)T

Master thermodynamic equation:

dF=SdTpdVMdH+iμidNi

Gibbs-Helmholtz equation:

E(T,V,N)=(F/T)(1/T))V,N=lnZβ)V,N

Free energy from partition function:

F(T,V,N)=kBTlnZ(T,V,N)

Classical pure point-particle partition function:

Z(T,V,N)=1h3NN!d3Npd3NreH(r,p)/kBT

Z(T,V,N)=1λ3N(T)d3NreU(r)/kBT where λ(T)=h2πmkBT

Quantal ideal gases (+ for fermions, − for bosons):

Ξ(β,μ)=Mr=1[1±eβ(ϵrμ)]±1

nr=1eβ(ϵrμ)±1


10.11: K- Useful Formulas is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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