An LPG (Liquified Petroleum Gas) cylinder weighs 15.0 kg when empty. When full, it weighs 30.0 kg and shows a pressure of 3.0 atm . In the course of usage at $27^{\circ} \mathrm{C}$, the mass of the full cylinder is reduced to $24 \cdot 2 \mathrm{~kg}$. The volume of the used gas in cubic metre at the normal usage condition ( atm and $27^{\circ} \mathrm{C}$ ) is (assume LPG to be normal butane and it behaves ideally)
The compressibility factor for a van der Waal gas at high pressure is
The root mean square (rms) speed of X$$_2$$ gas is x m/s at a given temperature. When the temperature is doubled, the X$$_2$$ molecules dissociated completely into atoms. The root mean square speed of the sample of gas then becomes (in m/s)
Case - 1 : An ideal gas of molecular weight M at temperature T.
Case - 2 : Another ideal gas of molecular weight 2M at temperature T/2.
Identify the correct statement in context of above two cases.