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

The pressure exerted by $6.0 \ g$ of methane gas in a $0.03 \ m^3$ vessel at $129 \ ^oC$ is : (Atomic masses of $C = 12.01, H = 1.01$ and $R = 8.314 \ J K^{-1} mol^{-1}$) :- ................ $Pa$

Using the equation of state $pV = nRT$,show that at a given temperature,the density of a gas is proportional to the gas pressure $p$.

An ideal gas expands against a constant external pressure of $3 \ atm$ from $4 \ dm^3$ to $6 \ dm^3$. The work done during this process is ..... $J$.

$A$ bubble is at the bottom of a lake of depth $h$. As the bubble rises to the surface,its radius increases by a factor of $3$. If the atmospheric pressure is equal to the pressure exerted by a water column of height $\ell$,then $h$ is equal to:

The value of the compressibility factor for an ideal gas is ........ .