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

One kg of a diatomic gas is at a pressure of $8 \times 10^4 \; N/m^2$. The density of the gas is $4 \; kg/m^3$. What is the energy (in $\times 10^4 \; J$) of the gas due to its thermal motion?

The speed of sound in an ideal gas at a given temperature $T$ is $v$. The rms speed of gas molecules at that temperature is $v_{\text{rms}}$. The ratio of the velocities $v$ and $v_{\text{rms}}$ for helium and oxygen gases are $X$ and $X^{\prime}$,respectively. Then,$\frac{X}{X^{\prime}}$ is equal to

Two thermally insulated vessels $1$ and $2$ are filled with air at temperatures $(T_1, T_2)$,volumes $(V_1, V_2)$,and pressures $(P_1, P_2)$ respectively. If the valve joining the two vessels is opened,the temperature inside the vessel at equilibrium will be

$4.0 \, g$ of a gas occupies $22.4 \, L$ at $NTP$. The specific heat capacity of the gas at constant volume is $5.0 \, J K^{-1} mol^{-1}$. If the speed of sound in this gas at $NTP$ is $952 \, m s^{-1}$,then the heat capacity at constant pressure is .... $J K^{-1} mol^{-1}$ (Take gas constant $R = 8.3 \, J K^{-1} mol^{-1}$)

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 $^\circ C$?