Consider a two-dimensional ideal gas of energy E and confined to area A, with identical molecules that are able to translate but not rotate or vibrate.
(a) How many degrees of freedom does each molecule have?
(b) How many degrees of freedom does a system of N molecules have?
(c) What is the total internal energy of a system of 1 022 such molecules at a temperature of 300 K?
(d) Write down the number of quantum states C2 available to a system of N such particles as a function of A, N, and E. (Combine all the constants into one.)
(e) What is the entropy as a function of A, N, and E?