If we increase the average distance between the atoms in the cubic lattice we used to derive the Einstein heat capacity, as from (a) to (b) in the drawing, does the heat capacity increase or decrease? To simplify the scenario, find the effect on the vibrational potential energy for a single atom vibrating along the x axis between two fixed walls and held in place by two bonds each with force constant k and equilibrium separation Re . Let the two walls initially be separated by 2Re , and calculate the potential energy for motion of the atom. then increase the spacing between the two walls by 2R’ and calculate the new potential energy. What is the effect of the change on the heat capacity?
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