Because state functions depend on only the current state of the system, when a system undergoes a series of processes that bring it back to the original state, a thermodynamic cycle has been completed and all the state functions have returned to their original value. However, properties that depend on the path may have changed.

(a) Verify that there is no difference in the state function S for a process in which 1.00 mol of nitrogen molecules in a cylinder of volume 3.00 L at 302 K undergoes the following three steps:

(i) Cooling at constant volume until T = 75.6 K; 

(ii) Heating at constant pressure until T = 302 K; 

(iii) Compressing at constant temperature until V = 3.00 L. Calculate ΔU and ΔS for this entire cycle.

(b) What are the values of q and w for the entire cycle?

(c) What are ΔS_surr and ΔS_total for the cycle? If any values are nonzero, explain how this can be so, despite entropy being a state function.

(d) Is the process spontaneous, nonspontaneous, or at equilibrium?