Question

For an ideal gas, consider only $(p-V)$ work on going from initial state $A$ to final state $C$. The final state $C$ can be reached by either of two paths as shown below. Which of the option is correct? (Take $\Delta S$ as change in entropy and was work done.)

• A. $\Delta S_{A \rightarrow C}=\Delta S_{A \rightarrow B}+\Delta S_{A \rightarrow C}$
• B. $W_{A \rightarrow B \rightarrow C}=W_{A \rightarrow B}$
• C. $W_{A \rightarrow B \rightarrow C}=W_{A \rightarrow B}+W_{B} \rightarrow C$
• D. Both (a) and (b)

Answer 1

Answer: (D)

Since, entropy is a state function and work done $(W)$ is a path function and, therefore
$\Delta S_{A \rightarrow C}=\Delta S_{A \rightarrow B}+\Delta S_{A \rightarrow C}$ is true but
$\Delta W_{A \rightarrow B \rightarrow C}=W_{A \rightarrow B}+W_{B \rightarrow C}$ is not true.
Moreover, $W_{B} \rightarrow C=p \Delta V=0$
as change in $B \rightarrow C$ is isochoric.
Therefore, $W_{A \rightarrow B \rightarrow C}=W_{A \rightarrow B}$ is true