Given below are two statements :

Statement 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 option given below :

A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown in the figure. Its volume is then reduced to the original volume from E to F by an isobaric process. The total work done by the gas from D to E to F will be

The root mean square speed of smoke particles of mass $$5 \times 10^{-17} \mathrm{~kg}$$ in their Brownian motion in air at NTP is approximately. [Given $$\mathrm{k}=1.38 \times 10^{-23} \mathrm{JK}^{-1}$$]

A vessel contains $$14 \mathrm{~g}$$ of nitrogen gas at a temperature of $$27^{\circ} \mathrm{C}$$. The amount of heat to be transferred to the gas to double the r.m.s speed of its molecules will be :

Take $$\mathrm{R}=8.32 \mathrm{~J} \mathrm{~mol}^{-1} \,\mathrm{k}^{-1}$$.