The fundamental equation of a pure substance is given by E = a V 2 exp(S/R ), where E, V , and S are the molar energy, volume, and entropy,...

The fundamental equation of a pure substance is given by E¯ = a V¯ 2 exp(S/R ¯ ), where E¯, V¯ , and S¯ are the molar energy, volume, and entropy, respectively, and a is a constant. N moles of this substance, initially at temperature T0 and pressure P0, are expanded reversibly and adiabatically until the pressure is P1 = P0/3. What is the final temperature as a fraction of the initial temperature T0?