$A$ light container having a diatomic gas enclosed within is moving with velocity $v$. The mass of the gas is $M$ and the number of moles is $n$. The kinetic energy of the gas with respect to the ground is:

$A$ 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 a gas is heated at constant pressure,its isothermal compressibility

An ideal gas $(\gamma = 1.5)$ is expanded adiabatically. How many times must the gas be expanded to reduce the root mean square velocity of the molecules $2.0$ times?

When the gas is heated,in which direction will the piston move?

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 . . . . . . $\text{ kPa}$.