One mole of an ideal gas in initial state A undergoes a cyclic process $A B C A$, as shown in the figure.…
One mole of an ideal gas in initial state A undergoes a cyclic process $A B C A$, as shown in the figure. Its pressure at $A$ is $p_0$. Choose the correct option(s) from the following
Internal energies at $A$ and $B$ are the same
Work done by the gas in process $A B$ is $p_0 V_0 \ln 4$
Pressure at $C$ is $\frac{p_0}{4}$
Temperature at $C$ is $\frac{T_0}{4}$
Solution
$
\begin{aligned}
& T_A=T_B \quad \therefore U_A=U_B \\
& W_{A B}=(1)(R) T_0 \ln \left(\frac{V_f}{V_i}\right) \\
& =R T_0 \ln \left(\frac{4 V_0}{V_0}\right) \\
& =p_0 V_0 \ln (4)
\end{aligned}
$
Information regarding $p$ and $T$ at $C$ can not be obtained from the given graph. Unless it is mentioned that line $B C$ passes through origin or not.
Hence, the correct options are (a) and (b).
