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

In the kinetic theory of gases,which of these statements is/are true?
$(i)$ The pressure of a gas is proportional to the mean speed of the molecules.
$(ii)$ The root mean square speed of the molecules is proportional to the pressure.
$(iii)$ The rate of diffusion is proportional to the mean speed of the molecules.
$(iv)$ The mean translational kinetic energy of a gas is proportional to its kelvin temperature.

Two identical glass bulbs are interconnected by a thin glass tube. $A$ gas is filled in these bulbs at $N.T.P.$ If one bulb is placed in ice and another bulb is placed in a hot bath,then the pressure of the gas becomes $1.5$ times. The temperature of the hot bath will be ....... $^oC$

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

From a certain apparatus,the diffusion rate of hydrogen has an average value of $28.7 \; cm^3 s^{-1}$. The diffusion of another gas under the same conditions is measured to have an average rate of $7.2 \; cm^3 s^{-1}$. Identify the gas.

For a mass $m$ of an ideal gas at constant pressure $P$,the volume versus temperature graph is represented by the straight line $B$. If the mass is changed to $2m$ and the pressure is changed to $2P$,which straight line will represent the new state?