Energy and Entropy: Winter-2026 Not used: Due Additional material
Analyze TS rectangle
Consider a monatomic ideal gas that undergoes a 4-step cyclic process. On a \(T\)-\(S\) diagram, the four steps of the process trace out a rectangle. The cycle proceeds in the clockwise direction around the rectangular path. The four sides of the rectangle correspond to
(A) Constant temperature, \(T_h\)
(B) Constant entropy, \(S_h\)
(C) Constant temperature, \(T_l\)
(D) Constant entropy, \(S_l\)
Make a \(T\)-\(S\) diagram that represents this cyclic process. Label the axes, the four steps (A through D), the direction of each process, and the key values of \(S\) and \(T\). The horizontal axis corresponds to which variable? Why?
Does a clockwise path in \(T\)-\(S\) space correspond to a heat engine or a heat pump?
Create a table, like the one below, and fill in all the values in terms of \(T_l\), \(T_h\), \(S_l\) and \(S_h\):
Process
\(\Delta U\)
\(Q\)
\(W\)
A
B
C
D
If this cycle corresponds to a heat engine, find the efficiency in terms of \(T_h\) and \(T_l\). Alternatively, if this cycle corresponds to a heat pump, find the coefficient of performance in terms of \(T_h\) and \(T_l\).