$A$ 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?

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:

Suppose an ideal gas follows the process $VP^3 = \text{constant}$. The initial temperature and volume of the gas are $T$ and $V$ respectively. If the gas expands to $27V$, then its final temperature will be:

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

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

During an experiment, an ideal gas is found to obey an additional law $VP^2 = \text{constant}$. The gas is initially at temperature $T$ and volume $V$. What will be the temperature of the gas when it expands to a volume $2V$?