Three moles of an ideal monotomic gas performs a cycle \(A B C D A\) as shown in the figure. The temperatures of the gas at the states \(A, B, C\) and \(D\) are \(400 \mathrm{~K}, 800 \mathrm{~K}, 2400 \mathrm{~K}\) and \(1200 \mathrm{~K}\), respectively. The work done by the gas during this cycle is (\(R\) is universal gas constant)

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Given, number of moles of an ideal monoatomic gas, \(n=3\), temperature of the gas of state \(A, T_A=400 \mathrm{~K}\), temperature of the gas at state \(B, T_B=800 \mathrm{~K}\), temperature of the gas at state \(C, T_C=2400 \mathrm{~K}\), and temperature of the gas at state \(D, T_D=1200 \mathrm{~K}\), Now, work done by the gas during this cycle is, \(W=n R \Delta T\) ( \(\therefore\) Work done in a isothermal process) So, \(W_{\text {nct }}=W_{A \rightarrow B}+W_{B \rightarrow C}+W_{C \rightarrow D}+W_{D \rightarrow A}\) \(\begin{aligned} & W_{\text {net }}=n R\left[\left(T_B-T_A\right)+\left(T_C-T_B\right)+\left(T_D-T_C\right)-\left(T_D-T_A\right)\right] \\ & W_{\text {net }}=3 R[0+(2400-800)+0-(1200-400)] \\ & W_{\text {net }}=3 R \times[1600-800] \\ & W_{\text {net }}=3 R \times 800, W_{\text {net }}=2400 R \end{aligned}\) So, the work done by the gas during, \(A \rightarrow B \rightarrow C \rightarrow D\) cycle is \(W_{\text {net }}=2400 R\).

Three moles of an ideal monotomic gas performs a cycle \(A B C D A\) as shown in the figure. The…

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