Question 4 1 pts The piston in Fig. 3.16 is hit with a hammer and the gas initially at T and P is compressed by dV, after which it settles down. The net heat that flows in is Q. Which is not true? The entropy change of the universe is positive O The work done is less than -PdV The entropy change of the gas is greater than Q/T The entropy change is more than it would be in a quasistatic process between the initial and final states The change in internal energy of the gas depends only on its initial and final states Question 5 1 pts Particles flow from more positive to less positive chemical potential Ofrom more negative to less legative chemical potential O as a result of an entropy gradient O whenever there is a temperature difference Predicting Heat Capacities In the preceding section we saw how to calculate the temperature as a function of energy (or vice versa) for any system for which we have an explicit formula for the multiplicity. To compare these predictions to experiments, we can differentiate the function U(T) to obtain the heat capacity at constant volume (or simply "energy capacity"): au Cy = (3.14) ат. N. V For an Einstein solid with q> N the heat capacity is a Cv (NkT) = Nk, aT = (3.15) while for a monatomic ideal gas, Cv = a (UNkT) = {Nk. (3.16)