What is the specific heat of a gas in an isothermal process and an adiabatic process?

One mole of a diatomic ideal gas undergoes a process shown in $P-V$ diagram. The total heat given to the gas $(\ln 2 = 0.7)$ is (in $P_0 V_0$)

An ideal gas with adiabatic exponent $(\gamma = 1.5)$ undergoes a process in which the work done by the gas is equal to the increase in the internal energy of the gas. The molar heat capacity of the gas for this process is:

An ideal gas with pressure $P$, volume $V$ and temperature $T$ is expanded isothermally to volume $2V$ and a final pressure $P_i$. The same gas is expanded adiabatically to a volume $2V$ then the final pressure is $P_a$. In terms of $\gamma$, the ratio of the two specific heats for the gas, the ratio $P_i/P_a$ is

Match List-$I$ with List-$II$ :

List-$I$	List-$II$
$A$. Isothermal Process	$I$. Work done by the gas decreases internal energy
$B$. Adiabatic Process	$II$. No change in internal energy
$C$. Isochoric Process	$III$. The heat absorbed goes partly to increase internal energy and partly to do work
$D$. Isobaric Process	$IV$. No work is done on or by the gas

Choose the correct answer from the options given below :

One mole of an ideal gas expands adiabatically from an initial state $(T_A, V_0)$ to a final state $(T_f, 5 V_0)$. Another mole of the same gas expands isothermally from a different initial state $(T_B, V_0)$ to the same final state $(T_f, 5 V_0)$. The ratio of the specific heats at constant pressure and constant volume of this ideal gas is $\gamma$. What is the ratio $T_A / T_B$?