I have a rectangular PV diagram of a heat engine. Like this one:
I have to show why this cannot work in reverse as a refrigerator.
U = 0.5fnRT (U = internal energy, f = degrees of freedom, n = number of moles of gas, R = ideal gas constant, T = temperature)
dU = Q + W = TdS - PdV (S = entropy, V = volume, Q = heat, W = work, P = pressure)
PV = nRT
The Attempt at a Solution
According to a website this wouldn't work because the refrigerator would get warmer and warmer until it got warmer than the cold reservoir. However, temperature is a state variable, and when I calculated it, dT = 0 as expected. So, while it may get warmer during the cycle, it will return to its original temperature.
The answer may lie in the entropy, but I am quite sure entropy is a state variable in this case.