The figure shows a polytropic process for an ideal gas. The work done by the gas in process $AB$ is

An ideal gas with heat capacity at constant volume $C_V$ undergoes a quasistatic process described by $p V^{\alpha} = \text{constant}$ in a $p-V$ diagram,where $\alpha$ is a constant. The heat capacity of the gas during this process is given by

One mole of an ideal monoatomic gas at temperature $T_0$ expands slowly according to the law $P = kV$ ($k$ is a constant). If the final temperature is $2T_0$,the heat supplied to the gas is:

An ideal gas is subjected to a thermodynamic process $PV^{2.5} = 0.40$,where $P$ is in $Pa$ and $V$ is in $m^3$. What is the slope of the $P-V$ curve with volume plotted against the $x-$axis at $V = 1 \, m^3$?

Hydrogen gas is undergoing a process given by $PV^2 = \text{constant}$. The ratio of work done by the gas to the change in its internal energy is

$A$ gas obeys the relation $P^2V = \text{constant}$. The initial temperature and volume are $T_0$ and $V_0$. If the gas expands to a volume $2V_0$, what will be its final temperature?