$A$ gas has temperature $T$ and volume $V$. At constant pressure,if the temperature is increased by $\Delta T$,the volume increases by $\Delta V$. How does $\delta = \frac{\Delta V}{V\Delta T}$ vary with temperature?

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

Column-$I$ represents physical quantity and Column-$II$ represents formula. Match them correctly:

Column-$I$	Column-$II$
$(a)$ Kinetic energy per unit mole of gas.	$(i)$ $\frac{1}{2}RT$
$(b)$ Kinetic energy per one molecule of gas.	$(ii)$ $\frac{3}{2}RT$
	$(iii)$ $\frac{3}{2}k_BT$

If the pressure of $CO_2$ (real gas) in a container is given by $P = \frac{RT}{2V - b} - \frac{a}{4V^2}$,then the mass of the gas in the container is ...... $g$.

$A$ fixed mass of gas at constant pressure occupies a volume $V$. The gas undergoes a rise in temperature so that the r.m.s. velocity of the molecules is doubled. The new volume will be

Two closed containers of equal volume are filled with air at pressure $P_0$ and temperature $T_0$. Both are connected by a narrow tube. If one of the containers is maintained at temperature $T_0$ and the other at temperature $T$,then the new pressure in the containers will be: