The relationship between pressure $P$,volume $V$,and total internal energy $E$ for an ideal gas is:

If $E$ is the kinetic energy per mole of an ideal gas and $T$ is the absolute temperature,then the universal gas constant is given as

$A$ vessel of volume $10 \text{ liters}$ is filled with $H_2$ gas. The total average translational kinetic energy of its molecules is $4.5 \times 10^5 \text{ J}$. The pressure of hydrogen in the vessel is

The temperature at which the kinetic energy of oxygen molecules becomes double its value at $27^{\circ}\,C$ is $............^{\circ}\,C$.

On the basis of the kinetic theory of gases,the mean kinetic energy $(K.E.)$ of $1\, mole$ per degree of freedom is:

Number of molecules in a volume of $4\, cm^{3}$ of a perfect monoatomic gas at some temperature $T$ and at a pressure of $2\, cm$ of mercury is close to $?$
(Given,mean kinetic energy of a molecule (at $T$) is $4 \times 10^{-14}\, erg$,$g=980\, cm/s^{2}$,density of mercury $=13.6\, g/cm^{3}$)