# PHYS6562 F4 Daily Quaetion

## Ergodicity

The system of classical particles bouncing back and forth is not ergodic since each particles can only occupy certain close volume in phase space, with fixed $$x,y$$ position, $$P_x, P_y$$ momenta and $$\pm p_z$$. Therefore, the given volume in phase space of the ensemble will not evolve with time.

## Heat engine

(a) True.
(b) True, since the work in done on the gas.
(c) False, it’s a refrigerator.
(d) True.
$W = (P_0)(3V_0) + \int_{4V_0}^{V_0} \frac{4P_0V_0}{V} dV = 3P_0V_0 - 4P_0V_0\log4$ (e) True, a part does no work so $$\Delta U = Q$$. $\Delta U = \frac{3}{2} nRT_c - \frac{3}{2} nRT_h = -\frac{3}{2} (3P_0V_0) = -\frac{9}{2}P_0V_0$ where n is the number of particles in mole and $$R = 8.317$$ is the ideal gas constant. (f) True. The whole cycle $$\Delta U = 0$$, the heat input and the net work done onto the gas must equal the heat output. $Q_h + W = Q_c$