$A$ thermally insulated vessel containing monatomic gas is moving with a speed of $30 \, m/s$. If the vessel suddenly stops, the increase in gas temperature is (Molar mass of gas $= 83 \, g/mol$ and $R = 8.3 \, J/K \cdot mol$). (in $ \, K$)

The average translational energy and the rms speed of molecules of a sample of oxygen gas at $300 \ K$ are $6.21 \times 10^{-21} \ J$ and $484 \ m/s$ respectively. The corresponding values at $600 \ K$ are nearly (assuming ideal gas behaviour):

$A$ horizontal uniform glass tube of $100 \ cm$ length, sealed at both ends, contains a $10 \ cm$ mercury column in the middle. The temperature and pressure of air on either side of the mercury column are $31^{\circ} C$ and $76 \ cm$ of mercury, respectively. If the air column at one end is kept at $0^{\circ} C$ and the other end at $273^{\circ} C$, then the pressure of air which is at $0^{\circ} C$ is (in $cm$ of $Hg$):

$A$ vessel of volume $V$ contains an ideal gas having mass density $\rho$ at temperature $T$ and pressure $p$. After a portion of the gas is let out, the pressure in the vessel is decreased by $\Delta p$. The mass of the released gas is

$(a)$ When a molecule (or an elastic ball) hits a massive wall,it rebounds with the same speed. When a ball hits a massive bat held firmly,the same thing happens. However,when the bat is moving towards the ball,the ball rebounds with a different speed. Does the ball move faster or slower?
$(b)$ When gas in a cylinder is compressed by pushing in a piston,its temperature rises. Guess at an explanation of this in terms of kinetic theory using $(a)$ above.
$(c)$ What happens when a compressed gas pushes a piston out and expands? What would you observe?
$(d)$ Sachin Tendulkar used a heavy cricket bat while playing. Did it help him in any way?

The heat energy that must be supplied to $14 \text{ g}$ of nitrogen at room temperature to raise its temperature by $48^{\circ}C$ at constant pressure is ($R$ = gas constant, Molecular weight of nitrogen $(N_2) = 28$) (in $R$)