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

One mole of an ideal gas at temperature $T_1$ expands according to the law $\frac{P}{V^2} = a$ (constant). The work done by the gas until the temperature of the gas becomes $T_2$ is:

An ideal gas follows a process described by the equation $PV^2 = C$ from the initial $(P_1, V_1, T_1)$ to final $(P_2, V_2, T_2)$ thermodynamic states,where $C$ is a constant. Then:

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:

$0.02 \, mol$ of an ideal diatomic gas with initial temperature $20^{\circ} C$ is compressed from $1500 \, cm^3$ to $500 \, cm^3$. The thermodynamic process is such that $p V^2 = \beta$,where $\beta$ is a constant. Then,the value of $\beta$ is close to (the gas constant,$R = 8.31 \, J / K / mol$).

$A$ gas is found to obey the law $P^2V =$ constant. The initial temperature and volume are $T_0$ and $V_0$. If the gas expands to a volume $3V_0$,its final temperature becomes