Question

$0.2$ moles of an ideal gas is taken round the cycle $A B C$ as shown in the figure. The path $B \rightarrow C$ is an adiabatic process, $A \rightarrow B$ is an isochoric process and $C \rightarrow A$ is an isobaric process. The temerature at $A$ and $B$ are $T_{A}=300 K$ and $T_{B}=500 K$ and pressure at $A$ is 1 atm and volume at $A$ is $4.9 L$. The volume at $C$ is
(Given : $\gamma=\frac{Cp}{C_{V}}=\frac{5}{3}, R = 8.205 × 10^{-2}\,L \,atm \,mol^{-1}$
$K^{-1}, \left(\frac{3}{2}\right)^{^{2/5}} =0.81$

• A. 6.9 L
• B. 6.6 L
• C. 5.5 L
• D. 5.8 L

Answer 1

Answer: (B)

For A $\rightarrow$ B, Isochoric process
$\frac{P_{A}}{T_{A}}=\frac{P_{B}}{T_{B}}$
$P_{B}=\frac{T_{B}}{T_{A}} P_{A}$
$P_{B}=\frac{500}{300}\times1=\frac{5}{3}\, atm ...\left(i\right)$
For B $\rightarrow$ C, Adiabatic process
$\therefore \frac{T^{\gamma}_{C}}{P_{C}^{\gamma-1}}=\frac{T^{\gamma}_{B}}{P_{B}^{\gamma-1}}$
$T_{C}=\left(\frac{P_{C}}{P_{B}}\right)^{^{\frac{\gamma-1}{\gamma}}}\times T_{B}$
$=\left[\frac{1}{5/3}\right]^{^{\frac{\left(5/3\right)-1}{\left(5/3\right)}}}\times500 \left(Usinig \left(i\right)\right)$
$=\left(\frac{3}{5}\right)^{2/5} \times500 ...\left(ii\right)$
For C $\to$ A, Isobaric process
$\therefore \frac{V_{C}}{T_{C}}=\frac{V_{A}}{T_{A}}$
$V_{C}=V_{A}\times\frac{T_{C}}{T_{A}}=4.9\times\left(\frac{3}{5}\right)^{2/5}\times500\times\frac{1}{300} \left(Using \left(ii\right)\right)$
$V_{c}=4.9\times0.81\times\frac{5}{3}=6.6 L$