$\frac{1}{2}$ 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 ...... $J$.

$A$ monoatomic gas of mass $4.0 \, g$ is kept in an insulated container. The container is moving with a velocity of $30 \, m/s$. If the container is suddenly stopped,then the change in temperature of the gas (where $R$ is the gas constant) is given by $\frac{x}{3R}$. The value of $x$ is ..........

At which temperature will the speed of sound in hydrogen be the same as the speed of sound in oxygen at $100\,^{\circ}C$?

The same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is $1:4$,then:
$A.$ The $r.m.s.$ velocity of gas molecules in the two vessels will be the same.
$B.$ The ratio of pressure in these vessels will be $1:4$.
$C.$ The ratio of pressure will be $1:1$.
$D.$ The $r.m.s.$ velocity of gas molecules in the two vessels will be in the ratio of $1:4$.

An ideal gas has $N$ molecules in a closed box at temperature $T_1$ and pressure $P_1$. If the number of molecules in the box is doubled and the total kinetic energy is kept the same,what will be the new pressure $P_2$ and temperature $T_2$?

$A$ cylinder of fixed capacity $44.8 \, L$ contains helium gas at standard temperature and pressure. What is the amount of heat needed to raise the temperature of the gas in the cylinder by $15.0 \, ^{\circ}C$? $(R = 8.31 \, J \, mol^{-1} K^{-1})$