Imagine life in flatland, which exists in two dimensional rather than three dimensional space. (with some modification, this model applies to gas molecules adsorbed on a flat surface.) a two-dimensional ideal classical gas of particles is confined to an area a. the number of states with momentum in the momentum range p to p + dp is 2t. apdp f (p)dp = h2 (a) show that the partition fumction associated with translational motion of one molecule of gas is given by: 2tamkt z1 h2 1 without proof 2a | ехp(-аp") рфр - you may use the result: e [4 marks (b) explain why the partition function for translational motion of n molecules of the gas is given by 12tlamkt = z h2 n! [2 marks] (c) (i find an expression for the helmholtz free energy associated with translational motion for this gas. (ii) show that the entropy of the gas is given by 2tmkt a + in s=nkin [8 marks] (d) (i find the average translational energy of the gas and comment on whether this is the expected value (ii) find the chemical potential of the gas as a function of temperature.