$A$ 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 $R = 8.32\,J\,mol^{-1}K^{-1}$)

$N$ moles of a diatomic gas in a cylinder are at a temperature $T$. Heat is supplied to the cylinder such that the temperature remains constant but $n$ moles of the diatomic gas get converted into monoatomic gas. What is the change in the total kinetic energy of the gas?

The plot that depicts the behavior of the mean free time $t$ (time between two successive collisions) for the molecules of an ideal gas,as a function of temperature $(T)$,qualitatively,is (Graphs are schematic and not drawn to scale)

$A$ balloon carries a total load of $185\; \text{kg}$ at normal pressure and temperature of $27^{\circ} \text{C}$. What load will the balloon carry on rising to a height at which the barometric pressure is $45\; \text{cm}$ of $\text{Hg}$ and the temperature is $-7^{\circ} \text{C}$? Assume the volume is constant. (in $\text{kg}$)

$A$ monoatomic gas of mass $4.0 \, g$ is kept in an insulated container. The container is moving with a velocity of $30 \, m/s$. If the container is suddenly stopped,then the change in temperature of the gas (where $R$ is the gas constant) is given by $\frac{x}{3R}$. The value of $x$ is ..........

$CO_2$ $(O - C - O)$ is a triatomic gas. The average kinetic energy of $1\,g$ of the gas is: (where $N$ is Avogadro's number,$k$ is Boltzmann's constant,and the molar mass of $CO_2 = 44\,g/mol$)