$A$ vessel contains $14\,g$ of nitrogen gas at a temperature of $27^{\circ}\,C$. The amount of heat to be transferred to the gas to double the r.m.s. speed of its molecules will be $......J$ (Take $R = 8.32\,J\,mol^{-1}K^{-1}$)

$A$ container holds $10^{26} \text{ molecules/m}^3$ each of mass $3 \times 10^{-27} \text{ kg}$. Assume that $1/6$ of the molecules move with velocity $2000 \text{ m/s}$ directly towards one wall of the container while the remaining $5/6$ of the molecules move either away from the wall or in perpendicular direction,and all collisions of the molecules with the wall are elastic.

Moon has no atmosphere because

$A$ thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $\gamma$. It is moving with speed $v$ and it is suddenly brought to rest. Assuming no heat is lost to the surroundings,its temperature increases by

$A$ very tall vertical cylinder is filled with a gas of molar mass $M$ under isothermal conditions at temperature $T$. The density and pressure of the gas at the base of the container are $\rho_0$ and $p_0$,respectively. Choose the correct statement$(s)$ if gravity is assumed to be constant throughout the container.

One mole of an ideal diatomic gas is taken through the cycle as shown in the figure.
$1 \rightarrow 2$: isochoric process
$2 \rightarrow 3$: straight line on $P-V$ diagram
$3 \rightarrow 1$: isobaric process
The average molecular speed of the gas in the states $1, 2$ and $3$ are in the ratio