## Quick Reference

An equation for the entropy of a perfect monatomic gas. The entropy *S* is given by:*S*=*nR*ln(e^{5/2}*V*/*nN*_{A}Λ^{3}), where Λ=*h*/(2π*mkT*)^{½}, where *n* is the amount of the gas, *R* is the gas constant, e is the base of natural logarithms, *V* is the volume of the system, *N*_{A} is the Avogadro constant, *h* is the Planck constant, *m* is the mass of each atom, *k* is the Boltzmann constant, and *T* is the thermodynamic temperature. To calculate the molar entropy of the gas both sides are divided by *n*. The Sackur-Tetrode equation can be used to show that the entropy change Δ*S*, when a perfect gas expands isothermally from *V*_{i} to *V*_{f}, is given by:Δ*S*=*nR*ln(*aV*_{f}) – *nR*ln(*aV*_{i})=*nR*ln(*V*_{f}/*V*_{i}), where *aV* is the quantity inside the logarithm bracket in the Sackur-Tetrode equation.

*S*=*nR*ln(e^{5/2}*V*/*nN*_{A}Λ^{3})

Δ*S*=*nR*ln(*aV*_{f}) – *nR*ln(*aV*_{i})=*nR*ln(*V*_{f}/*V*_{i})

*Subjects:*
Chemistry — Physics.