For a gas,as shown in the $P-T$ graph,the densities at points $A$ and $B$ are $\varrho_0$ and $\frac{4}{3} \varrho_0$ respectively. The value of $Y$ on the pressure $(P)$ axis is

Nitrogen gas $N_2$ of mass $28 \,g$ is kept in a vessel at a pressure of $10 \,atm$ and temperature $57^{\circ} C$. Due to leakage of $N_2$ gas,its pressure falls to $5 \,atm$ and temperature to $27^{\circ} C$. The amount of $N_2$ gas leaked out is .......... $g$.

Column-$I$ represents a graph and Column-$II$ represents a physical quantity or condition that is constant for that graph. Match them correctly:

Column-$I$	Column-$II$
$(a)$ Top graph	$(i)$ Constant pressure
$(b)$ Bottom graph	$(ii)$ Constant volume
	$(iii)$ For ideal gas

Two bulbs of identical volumes connected by a small capillary are initially filled with an ideal gas at temperature $T$. Bulb $2$ is heated to maintain a temperature $2 T$,while bulb $1$ remains at temperature $T$. Assume throughout that the heat conduction by the capillary is negligible. Then,the ratio of final mass of the gas in bulb $2$ to the initial mass of the gas in the same bulb is close to

From the following $P-T$ graph,what inference can be drawn?

At $NTP$,a sample of equal volume of chlorine and oxygen is taken. What is the ratio of the number of molecules?