The well-known Sackur-Tetrode equation for the entropy S is a fundamental equation S(U,V,N) = NkBlog V N U N 3 2 + 3 2 NkBS0 Use the thermodynamic definitions for the temperature and pressure introduced in the energy and entropy representations to derive the equations of state 3 2 BUNkT= and BPVNkT=.

Fundamental Equation for An Ideal Gas: The well-known Sackur-Tetrode equation for the entropy S is a fundamental equation S(U,V,N)=NkBlog[NV(NU)23]+23NkBS0 Use the thermodynamic definitions for the temperature and pressure introduced in the energy and entropy representations to derive the equations of state U=23NkBT and PV=NkBT