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

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$. Assertion $A$: If the average kinetic energy of $H_2$ and $O_2$ molecules, kept in two different sized containers are same, then their temperatures will be same. Reason $R$: The r.m.s. speed of $H_2$ and $O_2$ molecules are same at same temperature. Choose the correct answer from the options given below.

The average translational kinetic energy and the $r.m.s.$ speed of molecules in a sample of oxygen gas at $300 \, K$ are $6.21 \times 10^{-21} \, J$ and $484 \, m/s$ respectively. The corresponding values at $600 \, K$ are nearly (assuming ideal gas behaviour):

At a temperature of $300 \ K$,the average translational kinetic energy and $rms$ speed of a sample of oxygen gas are $6.21 \times 10^{-21} \ J$ and $484 \ m/s$ respectively. At $600 \ K$,these values will be respectively: (Assume ideal gas behavior)

Speed of sound in a gas is $v$ and $r.m.s.$ velocity of the gas molecules is $c.$ The ratio of $v$ to $c$ is

$A$ 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$)