From the following $V-T$ diagram,we can conclude that:

Two containers of equal volume contain the same gas at pressures $P_1$ and $P_2$ and absolute temperatures $T_1$ and $T_2$ respectively. On joining the vessels,the gas reaches a common pressure $P$ and common temperature $T$. The ratio $P/T$ is equal to

$A$ light container having a diatomic gas enclosed within is moving with velocity $v$. The mass of the gas is $M$ and the number of moles is $n$. The kinetic energy of the gas with respect to the ground is:

An oxygen cylinder of volume $30 \ L$ has $18.20 \ \text{moles}$ of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to $11 \ \text{atm}$ at a temperature of $27^{\circ} \text{C}$. The mass of the oxygen withdrawn from the cylinder is nearly equal to (Given: $R = \frac{100}{12} \ \text{J mol}^{-1} \text{K}^{-1}$, molecular mass of $O_2 = 32 \ \text{g/mol}$, $1 \ \text{atm} = 1.01 \times 10^5 \ \text{Pa}$) (in $\text{kg}$)

An ideal gas filled in a cylinder occupies volume $V$. The gas is compressed isothermally to the volume $V/3$. Now,the cylinder valve is opened and the gas is allowed to leak keeping temperature same. What percentage of the number of molecules should escape to bring the pressure in the cylinder back to its original value (in $\%$)?

$\frac{1}{2}$ mole of helium gas is contained in a container at $S.T.P.$ The heat energy needed to double the pressure of the gas,keeping the volume constant (specific heat of the gas $= 3 \; J \; g^{-1} \; K^{-1}$) is ...... $J$.