JEE Physics Practice Question

One mole of an ideal gas expands adiabatically from an initial state $\left(T_{\mathrm{A}}, V_{0}\right)$ to final state $\left(T_{\mathrm{f}}, 5 V_{0}\right)$. Another mole of the same gas expands isothermally from a different initial state $\left(T_{\mathrm{B}}, V_{0}\right)$ to the same final state $\left(T_{\mathrm{f}}, 5 V_{0}\right)$. The ratio of the specific heats at constant pressure and constant volume of this ideal gas is $\gamma$. What is the ratio $T_{\mathrm{A}} / T_{\mathrm{B}}$ ?

1. A.$5^{\gamma-1}$
2. B.$5^{1-\gamma}$
3. C.$5^{\gamma}$
4. D.$5^{1+\gamma}$