One kg of a diatomic gas is at a pressure of $8 \times 10^4 \; N/m^2$. The density of the gas is $4 \; kg/m^3$. What is the energy (in $\times 10^4 \; J$) of the gas due to its thermal motion?

Two thermally insulated vessels $1$ and $2$ contain air at temperatures $(T_1, T_2)$,volumes $(V_1, V_2)$,and pressures $(P_1, P_2)$. If the valve connecting them is opened,what will be the equilibrium temperature of the system?

$A$ vessel containing nitrogen gas is supplied a heat of $498 \,J$, so as to raise the temperature of the gas by $40^{\circ} C$ at constant pressure. The mass of nitrogen gas in the vessel is (Molecular mass of nitrogen $= 28 \,g/mol$; Universal gas constant $= 8.3 \,J \,mol^{-1} \,K^{-1}$) (in $\,g$)

$A$ gas in container $A$ is in thermal equilibrium with another gas in container $B$. Both contain equal masses of the two gases in the respective containers. Which of the following can be true?

$A$ fixed mass of gas at constant pressure occupies a volume $V$. The gas undergoes a rise in temperature so that the r.m.s. velocity of the molecules is doubled. The new volume will be

$A$ 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