$A$ gas at $27^\circ C$ temperature and $30$ atmospheric pressure is allowed to expand to atmospheric pressure. If the volume becomes $10$ times its initial volume,then the final temperature becomes ...... $^\circ C$.

The temperature of an ideal gas at atmospheric pressure is $300\,K$ and volume is $1\,m^3$. If the temperature and volume both become double,then the pressure will be:

What is the number of molecules in $1 \, litre$ of an ideal gas at $S.T.P.$?

An oxygen cylinder of volume $30 \; L$ has an initial gauge pressure of $15 \; atm$ and a temperature of $27 \; ^{\circ}C$. After some oxygen is withdrawn from the cylinder,the gauge pressure drops to $11 \; atm$ and its temperature drops to $17 \; ^{\circ}C$. Estimate the mass (in $kg$) of oxygen taken out of the cylinder ($R = 8.31 \; J \; mol^{-1} K^{-1}$,molecular mass of $O_{2} = 32 \; u$).

One mole of an ideal gas undergoes a process in which pressure $P$ varies with volume $V$ as $P = 3 - g \left(\frac{V}{V_0}\right)^2$,where $V_0$ and $g$ are constants. The maximum temperature attainable by the ideal gas during this process is ($All$ quantities are in $SI$ units and $R$ is the gas constant).

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