Problem 8: Ar gas adsorbed on a surface can be modeled as an ideal monatomic gas confined in two dimensions, e.g., 2-D ideal monatomic gas. a) Using the relationship between the molecular partition function and the average inter- nal energy, determine the internal energy of this 2-D gas. b) What is the expected internal energy of 2-D ideal monatomic gas from the equipartition theorem? c) What is the heat capacity of this 2-D gas? 4 d) How does the heat capacity of 2-D gas obtained in (c) different from those of 3-D monatomic ideal gas? e) The partition function for 3-D monatomic non-ideal (van der Waals) gas has a form: (V - N)"eaN2/VWT 2mkt 31/2 Q(N,V,T) = 7) 3/2, (1) N! h2 where a and bare van der Waals constants and V is the gas volume. Derive the internal total energy of this van der Waals gas. f) Calculate the heat capacity of 3-D van der Waals gas and compare with those of 3-D ideal gas obtained in (d)