$A$ $15\,g$ mass of nitrogen gas is enclosed in a vessel at a temperature $27\,^{\circ}C.$ The amount of heat transferred to the gas,so that the rms velocity of the molecules is doubled,is about ...... $kJ$ [Take $R = 8.3\,J/K\,mole$ ]

$A$ cylindrical tube of uniform cross-sectional area $A$ is fitted with two airtight frictionless pistons. The pistons are connected to each other by a metallic wire. Initially, the pressure of the gas is $P_0$ and the temperature is $T_0$; the atmospheric pressure is also $P_0$. Now, the temperature of the gas is increased to $2T_0$. The tension in the wire will be:

$\frac{1}{2}$ mole of helium gas is contained in a container at $S.T.P.$ The heat energy needed to double the pressure of the gas,keeping the volume constant (specific heat of the gas $= 3 \; J \; g^{-1} \; K^{-1}$) is ...... $J$.

Two identical bulbs are filled with gas at $N.T.P.$ One bulb is placed in ice and the other in a hot bath, such that the pressure becomes $1.5$ times the initial pressure. What is the temperature of the hot bath in $^\circ C$?

If a closed container containing gas is in motion and is suddenly stopped,the random motion of the gas molecules will .......

An insulated container contains a monoatomic gas of molar mass $M$. The container is moving with velocity $V$. If it is stopped suddenly, the change in temperature of the gas is ($R$ = gas constant).