Which one of the following gases possesses the largest internal energy?

The temperature $(T)$ of one mole of an ideal gas varies with its volume $(V)$ as $T = -\alpha V^3 + \beta V^2$,where $\alpha$ and $\beta$ are positive constants. The maximum pressure of the gas during this process is ............

Two vessels of the same volume contain the same gas at the same temperature. If the pressure in the vessels is in the ratio of $1 : 2$,then

For a mass $m$ of an ideal gas at constant pressure $P$,the volume versus temperature graph is represented by the straight line $B$. If the mass is changed to $2m$ and the pressure is changed to $2P$,which straight line will represent the new state?

Consider the following statements for air molecules in an air-tight container:
$(I)$ The average speed of molecules is larger than root mean square speed.
$(II)$ Mean free path of molecules is larger than the mean distance between molecules.
$(III)$ Mean free path of molecules increases with temperature.
$(IV)$ The rms speed of nitrogen is smaller than oxygen molecule.
Which of the above statements are correct?

One mole of a monoatomic ideal gas undergoes a quasistatic process, which is depicted by a straight line joining points $(V_{0}, T_{0})$ and $(2 V_{0}, 3 T_{0})$ in a $V-T$ diagram. What is the value of the heat capacity of the gas at the point $(V_{0}, T_{0})$?