(a) Two iron blocks of same size and at distinct temperatures \(T_{1}\) and \(T_{2}\) are brought in thermal contact with each other. The transfer process is allowed to take place until the thermal equilibrium is attained. Suppose, after the attainment of equilibrium, that the blocks are at final temperature \(T\). Show that the change in entropy of the process is given by

(b) Find the second and third virial coefficients of the van der Waals equation of state.

(c) The total energy of a typical closed system is given by \(E=50+25 T+0.05 T^{2}\) in Joules. The amount of heat absorbed by the system can be expressed as \(Q=\) \(4000+10 T\)
in Joules. Estimate the work done during the processes in which temperature rises from \(400 \mathrm{~K}\) to \(800 \mathrm{~K}\).