Question

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 $400\, K , 800\, K , 2400 \,K$ and $1200 \,K$, respectively. The work done by the gas during this cycle is ( $R$ is universal gas constant)

• A. 1200 R
• B. 3600 R
• C. 2400 R
• D. 2000 R

Answer 1

Answer: (C)

According to the question,

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