$A$ monatomic ideal gas undergoes a process in which the ratio of $P$ to $V$ at any instant is constant and equals to $1$. What is the molar heat capacity of the gas?

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

An ideal gas is found to obey $Pv^{\frac{3}{2}} = \text{constant}$ during an adiabatic process. If such a gas initially at a temperature $T$ is adiabatically compressed to $\frac{1}{4}$th of its volume,then its final temperature is

In an $H_2$ gas process, $PV^2 = \text{constant}$. The ratio of work done by the gas to the change in its internal energy is:

An ideal gas expands in such a way that $PV^2 = \text{constant}$ throughout the process.

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: