An equation for the entropy of a perfect monatomic gas. The entropy S is given by:S=nRln(e5/2V/nNAΛ3), where Λ=h/(2πmkT)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, NA 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 ΔS, when a perfect gas expands isothermally from Vi to Vf, is given by:ΔS=nRln(aVf) – nRln(aVi)=nRln(Vf/Vi), where aV is the quantity inside the logarithm bracket in the Sackur-Tetrode equation.
ΔS=nRln(aVf) – nRln(aVi)=nRln(Vf/Vi)
Subjects: Chemistry — Physics.