$N$ 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?

Fill in the blanks:
$(i)$ At low $......$ and high $......$ temperature,real gases behave as an ideal gas.
$(ii)$ $......$ is a measure of the average kinetic energy of a gas.
$(iii)$ The kinetic energy of a gas with mass $m$ is $E$. Its momentum will be $......$.
$(iv)$ At $......$ temperature,$v_{rms}$ will be double that of $v_{rms}$ at $0^{\circ} C$.

Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure $90 \text{ kPa}$ and temperature $400 \text{ K}$. Keeping the temperature of one vessel constant at $400 \text{ K}$,the temperature of the second vessel is raised to $500 \text{ K}$. The final pressure in the vessels is . . . . . . $\text{ kPa}$.

For a diatomic gas,the change in internal energy for a unit change in temperature at constant pressure and constant volume is $U_1$ and $U_2$ respectively. The ratio $U_1 : U_2$ is

The ratio of the speed of sound in a monatomic gas at $27^{\circ} C$ and the root-mean-square (rms) speed of the molecules of the same gas at a temperature of $127^{\circ} C$ is

Which one of the following gases possesses the largest internal energy?