The average kinetic energy of one molecule of an ideal gas at $27^{\circ} C$ and $1 \ atm$ pressure is

The total kinetic energy $(KE)$ of $1 \ mol$ of a monoatomic ideal gas at $27 \ ^oC$ is ........ $cal$.

$X$ and $Y$ are two volatile liquids with molar weights of $10 \ g \ mol^{-1}$ and $40 \ g \ mol^{-1}$ respectively. Two cotton plugs,one soaked in $X$ and the other soaked in $Y$,are simultaneously placed at the ends of a tube of length $L = 24 \ cm$. The tube is filled with an inert gas at $1 \ atmosphere$ pressure and a temperature of $300 \ K$. Vapours of $X$ and $Y$ react to form a product which is first observed at a distance $d \ cm$ from the plug soaked in $X$. Take $X$ and $Y$ to have equal molecular diameters and assume ideal behaviour for the inert gas and the two vapours.
$1.$ The value of $d$ in $cm$,as estimated from Graham's law,is:
$(A) \ 8 \ (B) \ 12 \ (C) \ 16 \ (D) \ 20$
$2.$ The experimental value of $d$ is found to be smaller than the estimate obtained using Graham's law. This is due to:
$(A)$ larger mean free path for $X$ as compared to that of $Y$.
$(B)$ larger mean free path for $Y$ as compared to that of $X$.
$(C)$ increased collision frequency of $Y$ with the inert gas as compared to that of $X$ with the inert gas.
$(D)$ increased collision frequency of $X$ with the inert gas as compared to that of $Y$ with the inert gas.
Give the answer for question $1$ and $2$.

If the average kinetic energy $(K.E.)$ of $CO_2$ at $27\,^oC$ is $E$,what is the average kinetic energy of $N_2$ at the same temperature?

The total kinetic energy of $0.6 \ mol$ of an ideal gas at $27 \ ^oC$ is .......... $J$.

According to the kinetic theory of gases,for a diatomic molecule: