(10 points) 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...

4. (10 points) 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 T_0 and pressure P_0, are expanded reversibly and adiabatically until the pressure is P_1 = P_0/3. What is the final temperature as a fraction of the initial temperature T_0?