Use Mathematica to solve the problems and show the code Problem 3 Consider a system in which atoms of mass m=4 are adsorbed on the surface of a cubic box of side L. Assume that the atoms are unable to le surface and cannot move in the direction perpendicular to the surface. Derive expressions for the free energy, entropy, energy and the heat capacities of the absorbed atoms. Problem 4 Calculate numerically the thermodynamic functions listed in problem 3 , per mole of adsorbed atoms, for a surface density of A/N=10A2 and T=300,600, and 900K. Get the functions in units of calories. Problem 5 Assume the same conditions as in problem 4 but now assume that the atoms can move freely (no force) in a direction perpendicular to the surface distance =6A. Calculate numerically the thermodynamic functions (listed at problem 3) for this system for a surface density of A/N=10A2 and T=300,600, and 900 K. Get the functions in units of calories. Be careful: the adsorbed molecule are trapped in a box that is infinitely large in two directions and very small in one direction