An ideal gas expands according to the law $P^2 V = \text{constant}$. The internal energy of the gas

An ideal gas undergoes a quasi-static,reversible process in which its molar heat capacity $C$ remains constant. If during this process the relation of pressure $P$ and volume $V$ is given by $PV^n = \text{constant}$,then $n$ is given by (Here $C_p$ and $C_v$ are molar specific heat at constant pressure and constant volume,respectively):

The $P-V$ diagram of a monoatomic gas is a straight line passing through the origin. The molar heat capacity of the gas in this process will be:

The figure shows a process $AB$ undergone by $2$ moles of an ideal diatomic gas. The process $AB$ follows the relation $VT = \text{constant}$. Given $T_1 = 300 \text{ K}$ and $T_2 = 500 \text{ K}$ ($R$ is the gas constant).

One mole of an ideal monoatomic gas expands along the polytropic process $PV^3 = \text{constant}$ from volume $V_1$ to $V_2$. The molar specific heat capacity for this process is given by $C = C_V + \frac{R}{1-n}$. The total heat absorbed during the process can be expressed as:

$A$ monoatomic gas is taken through a process $TP^{-1/3} = \text{constant}$. If heat is given to the gas, what happens to its temperature?