An ideal gas expands adiabatically $(\gamma = 1.5)$. To reduce the root-mean-square (r.m.s.) velocity of the molecules $3$ times, the gas has to be expanded by a factor of: (in $\times$)

$A$ 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?

$A$ box contains $N$ molecules of a perfect gas at temperature ${T_1}$ and pressure ${P_1}$. The number of molecules in the box is doubled while keeping the total kinetic energy of the gas the same as before. If the new pressure is ${P_2}$ and temperature is ${T_2}$,then:

$A$ thermally insulated vessel containing monatomic gas is moving with a speed of $30 \, m/s$. If the vessel suddenly stops, the increase in gas temperature is (Molar mass of gas $= 83 \, g/mol$ and $R = 8.3 \, J/K \cdot mol$). (in $ \, K$)

$A$ closed compartment containing gas is moving with some acceleration in a horizontal direction. Neglect the effect of gravity. Then the pressure in the compartment is

When the temperature of an ideal gas is increased by $600 \ K$,the velocity of sound in the gas becomes $\sqrt{3}$ times the initial velocity in it. The initial temperature of the gas is .... $^oC$