$CO_2$ $(O-C-O)$ is a triatomic gas. The mean kinetic energy of one gram of the gas will be (where $N$ is Avogadro's number,$k$ is Boltzmann's constant,and the molecular weight of $CO_2 = 44$).

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.	$(ii)$ $\frac{3}{2}RT$
	$(iii)$ $\frac{3}{2}k_BT$

Two identical bulbs are filled with gas at $N.T.P.$ One bulb is placed in ice and the other in a hot bath, such that the pressure becomes $1.5$ times the initial pressure. What is the temperature of the hot bath in $^\circ C$?

This question has Statement-$1$ and Statement-$2$. Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement-$1$: The internal energy of a perfect gas is entirely kinetic and depends only on the absolute temperature of the gas and not on its pressure or volume.
Statement-$2$: $A$ perfect gas is heated keeping pressure constant and later at constant volume. For the same amount of heat,the temperature rise of the gas at constant pressure is lower than that at constant volume.

If a gas is heated at constant pressure,its isothermal compressibility

Which graph represents the variation of $PV$ with $V$ for a fixed mass of an ideal gas at constant temperature?