\(n\) moles of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes.
\(A\rightarrow B\) | Isothermal expansion at temperature \(T\) so that the volume is doubled from \(V_1\) to \(V_2=2V_1\) and pressure changes from \(P_1\) to \(P_2.\) |
\(B\rightarrow C\) | Isobaric compression at pressure \(P_2\) to initial volume \(V_1\). |
\(C\rightarrow A\) | Isochoric change leading to change of pressure from \(P_2\) to \(P_1\). |
Total work done in the complete cycle \(ABCA\) is:
1. \(0\)
2. \(nRT(\ln 2-\frac{1}{2})\)
3. \(nRT\ln 2\)
4. \(nRT(\ln 2+\frac{1}{2})\)
1. | \(W_1>W_2\) |
2. | \(W_1<W_2\) |
3. | \(W_1=W_2\) |
4. | \(W_1\) and \(W_2\) cannot be compared unless the temperatures are known. |
1. | \(U_0\) | 2. | \({\Large\frac23}U_0\) |
3. | \(U_0\mathrm{ln}2\) | 4. | \({\Large\frac23}U_0\mathrm{ln}2\) |