Two gases A and B having same initial state (P, V, n, T). Now gas A is compressed to $\frac{\mathrm{V}}{8}$ by isothermal process and other gas $B$ is compressed to $\frac{V}{8}$ by adiabatic process. The ratio of final pressure of gas A and B is (Both gases are monoatomic, $\gamma=5 / 3$ )

Question

Aicharya · Accepted Answer

For isothermal process (gas A) $\begin{aligned} & P_1 V_1=P_2 V_2 \\ \therefore \quad & P_0\left(8 V_0\right)=P_2\left(V_0\right) \\ \Rightarrow & \Rightarrow P_2=8 P_0 \end{aligned}$
For adiabatic process (gas B) $\begin{aligned} & P^\gamma=\text { constant } \\ \therefore \quad & \frac{P_2}{P_1}=(8)^\gamma \\ \therefore \quad & P_2=(8)^\gamma P_0 \end{aligned}$
Hence, $\frac{\left(\mathrm{P}_2\right)_{\mathrm{B}}}{\left(\mathrm{P}_1\right)_{\mathrm{A}}}=\frac{(8)^\gamma \mathrm{P}_0}{8 \mathrm{P}_0}=(8)^{\gamma-1}$ $\begin{aligned} & \frac{\left(P_2\right)_B}{\left(P_1\right)_A}=8^{2 / 3} \\ & =\sqrt[3]{64}=4 \\ \therefore \quad & \frac{\left(P_1\right)_A}{\left(P_2\right)_B}=\frac{1}{4} \end{aligned}$ $\ldots(\text { given }, \gamma=5 / 3)$ *

Two gases A and B having same initial state (P, V, n, T). Now gas A is compressed to $\frac{\mathrm{V}}{8}$…

Solution