

$(i)$Average kinetic energy per molecule of $A$ is equal to that of $B$.
$(ii)$ Root mean square value of translational velocity of $B$ is four times that of $A$.
$(iii)$ Pressure exerted by $B$ is eight times of that exerted by $A$.
$(iv)$ Number of molecules of $B$ in the cylinder is eight time that of $A$.
Statements $I:$ The temperature of a gas is $-73^{\circ}\,C$. When the gas is heated to $527^{\circ}\,C$, the root mean square speed of the molecules is doubled.
Statement $II:$ The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules.
In the light of the above statements, choose the correct answer from the options given below :