The Sackur-Tetrode equation is an expression for the entropy of a
classical ideal gas which uses quantum considerations to arrive
at an exact formula. Classical thermodynamics and statistical mechanics
can only give the entropy of a classical ideal gas to within a constant.
The Sackur-Tetrode equation is written:
![S = k N \log \left[ \left(\frac VN\right) \left(\frac EN \right)^{\frac 32}\right]+ {\frac 32}kN\left( {\frac 53}+ \log\frac{4\pi m}{3h^2}\right)](a/../upload/math/4d4a82fa400fac9ad6c33daf21ced155.png)
where V is the volume of the gas, N is the number of particles in the gas,
E is the internal energy of the gas, k is Boltzmann's constant, m is the
mass of a gas particle, and h is Planck's constant. See Gibbs paradox
for a derivation of the Sackur-Tetrode equation.
The Sackur-Tetrode equation can also be conveniently expressed in terms of the
thermal wavelength Λ. Using the classical ideal gas relationship
E=3kT/2 gives
![\frac{S}{kN} = \ln\left[\frac{V}{N\Lambda^3}\right]+\frac{5}{2}](a/../upload/math/8d796f26923bbd1beeef7d52bddcf024.png)
