Q 11-11-082JEE MainJEE Main 2023 (31 Jan, Shift 2)Medium
A hypothetical gas expands adiabatically such that its volume changes from $8$ litres to $27$ litres. If the ratio of final pressure of the gas to initial pressure of the gas is $\dfrac{16}{81}$, then the ratio of $\dfrac{C_p}{C_v}$ will be
Answer: (A) $\dfrac43$
$PV^\gamma=$ constant: $\dfrac{P_2}{P_1}=\left(\dfrac{V_1}{V_2}\right)^\gamma$.
$$\frac{16}{81}=\left(\frac{8}{27}\right)^\gamma\ \Rightarrow\ \left(\frac23\right)^4=\left(\frac23\right)^{3\gamma}\ \Rightarrow\ \gamma=\frac43$$
Solution by Sreeraj P, M.Sc Physics