Given a two state system in which the low energy level is 600 cal/mol, the high energy level is 1800 cal/mol, and the temperature of the system is 300 K, calculate the following:
(a) (10%) The partition function of the system.
(b) (10%) The average internal energy of the system.
(c) (10%) The Helmholtz free energy of the system.
(d) (10%) The entropy of the system.