One mole of an ideal monatomic gas undergoes a process described by the equation $PV^3 = \text{constant}$. The heat capacity of the gas during this process is

$A$ diatomic gas follows the equation $PV^m =$ constant during a process. What should be the value of $m$ such that its molar heat capacity during the process is equal to $R$?

The volume of $1 \; mole$ of an ideal gas with the adiabatic exponent $\gamma$ is changed according to the relation $V = \frac{b}{T}$,where $b$ is a constant. The amount of heat absorbed by the gas in the process if the temperature is increased by $\Delta T$ will be:

An ideal gas undergoes a polytropic process given by the equation $PV^n = \text{constant}$. If the molar heat capacity of the gas during this process is the arithmetic mean of its molar heat capacity at constant pressure $(C_P)$ and constant volume $(C_V)$, then the value of $n$ is ..............

One mole of an ideal gas undergoes a process $PV^3 = \text{constant}$, where $P$ and $V$ are pressure and volume respectively. Let $W$ be the work done by the gas as its temperature is increased by $\Delta T$. The value of $|W|$ is ($R$ is the universal gas constant).

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):