If a gas is heated at constant pressure,its isothermal compressibility

The average translational kinetic energy of ${N}_{2}$ gas molecules at $... {}^{\circ} {C}$ becomes equal to the ${K.E.}$ of an electron accelerated from rest through a potential difference of $0.1 \ V$. (Given ${k}_{B} = 1.38 \times 10^{-23} \ J/K$). (Fill the nearest integer).

An ideal gas is expanding such that $PT^{3} = \text{constant}$. The coefficient of volume expansion of the gas is: (in $/T$)

$0.056 \, kg$ of Nitrogen is enclosed in a vessel at a temperature of $127 \, ^{\circ}C$. The amount of heat required to double the speed of its molecules is $k \, cal$. (Take $R = 2 \, cal \, mole^{-1} K^{-1}$)

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

$2.8 \ g$ of nitrogen gas $(N_2)$ is in a vessel at a temperature of $127^{\circ} C$. The amount of heat energy required to increase the rms speed of the nitrogen molecules by $41.4 \%$ is $(R = 8.31 \ J \ mol^{-1} \ K^{-1})$. (in $J$)