The following data is obtained for $1 \ mole$ of a gas. The gas behaves as an ideal gas in the pressure range (in $bar$):

$P \ (bar)$	$\frac{PV}{RT}$
$1$	$1$
$2$	$1$
$3$	$1$
$4$	$1.5$
$5$	$2.0$

Hydrogen gas is present in compartment $A$ and compartment $B$ as shown in the following figure. If the valve is opened,then the final pressure in the compartments is ............. $atm$. [Assume the temperature of each vessel remains constant at its initial value]

At $300 \ K$ temperature,the pressure and volume of a gas are $1 \ bar$ and $10 \ L$ respectively. If the pressure becomes $2 \ bar$,calculate the volume of the gas at the same temperature. (in $L$)

Containers $A$ and $B$ contain the same gas. The pressure,volume,and temperature of the gas in $A$ are twice the corresponding values of the gas in $B$. The ratio of the number of molecules of gas in $A$ to that in $B$ is ...

If $P$ is pressure and $\rho$ is density of a gas,then $P$ and $\rho$ are related as

When an ideal gas undergoes unrestrained expansion,no cooling occurs because the molecules