$A$ 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

An ideal gas mixture filled inside a balloon expands according to the relation $PV^{2/3} = \text{constant}$. The temperature inside the balloon 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

$1 \, \text{mole}$ of a gas expands with temperature as $V = KT^{2/3}$. What is the work done when temperature changes by $30^oC$ (in $R$)?

Consider one mole of an ideal gas in a cylindrical container following the path shown in the $P-V$ diagram. The process follows $PV^{1/2} = \text{constant}$.
$(a)$ Find the work done in taking the gas from state $1$ to state $2$.
$(b)$ If $V_2 = 2V_1$, what is the ratio of temperatures $\frac{T_1}{T_2}$?
$(c)$ The internal energy of one mole of gas at temperature $T$ is $\frac{3}{2}RT$. Find the heat supplied to the gas in taking it from state $1$ to state $2$.

$A$ gas expands in such a way that its pressure and volume satisfy the condition $PV^2 = \text{constant}$. Then the temperature of the gas