Question

An ideal gas is taken through the cycle $A \to B \to C \to A$ as shown in the figure. If the net heat supplied to the gas in the cycle is $5\, J$. the magnitude of work done during the process $C \to A$ is

• A. 5 J
• B. 10 J
• C. 15 J
• D. 20 J

Answer 1

Answer: (A)

5 J

Answer 2

An ideal gas is taken through the cycle
$A \rightarrow B \rightarrow C \rightarrow A$ as shown in the figure,

Erom the graph,
$W_{A B} =P \times d V$
$=10 \times(2-1)=10 \,J$
Similarly,
$W_{B C}=P \times(0)=0 \,J$
According to the first law of thermodynamics
$\Delta Q=\Delta U+W$
Here, $\Delta U =0$
$\therefore\, Q =W$
$5 =W_{AB}+W_{B C}+W_{C A}$
$W_{C A} =5-W_{A B}-W_{B C}=5-10-0$
$W_{C A}=-5 \,J$
$\left|W_{C A}\right|=5 \,J$
Hence, the magnitude of work done during the process $C \rightarrow A$ is $5 J$