$A$ gas obeys $P^2V = \text{constant}$. The initial temperature and volume are $T_0$ and $V_0$. If the gas expands to a volume of $2V_0$,the final temperature is:

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

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

Find the amount of work done to increase the temperature of one mole of an ideal gas by $30^o\ C$ if it is expanding under the condition $V \propto T^{2/3}$. $[R = 1.99 \ cal/mol-K]$

During an experiment, an ideal gas is found to obey a condition $VP^2 = \text{constant}$. The gas is initially at a temperature $T$, pressure $P$, and volume $V$. The gas expands to volume $4V$. Which of the following statements is correct?

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