At constant pressure,equal amounts of heat are supplied to a monatomic gas and a diatomic gas separately. The ratio of the increases in internal energies of the two gases is

The difference between volume and pressure coefficients of an ideal gas is

Match Column $- I$ and Column $- II$ and choose the correct match from the given choices.

Column $- I$	Column $- II$
$(A)$ Root mean square speed of gas molecules	$(P)$ $\frac{1}{3} n m \bar{v}^{2}$
$(B)$ Pressure exerted by ideal gas	$(Q)$ $\sqrt{\frac{3 RT}{M}}$
$(C)$ Average kinetic energy of a molecule	$(R)$ $\frac{5}{2} RT$
$(D)$ Total internal energy of $1$ mole of a diatomic gas	$(S)$ $\frac{3}{2} k_{B} T$

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?

One mole of an ideal diatomic gas is taken through the cycle as shown in the figure.
$1 \rightarrow 2$: isochoric process
$2 \rightarrow 3$: straight line on $P-V$ diagram
$3 \rightarrow 1$: isobaric process
The average molecular speed of the gas in the states $1, 2$ and $3$ are in the ratio

The plot that depicts the behavior of the mean free time $t$ (time between two successive collisions) for the molecules of an ideal gas,as a function of temperature $(T)$,qualitatively,is (Graphs are schematic and not drawn to scale)