Given below are two statements:
Statement I: The temperature of a gas is -73 °C. When the gas is heated to 527 °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:

We analyze each statement: Statement I: The temperature changes from $$-73°C = 200 \text{ K}$$ to $$527°C = 800 \text{ K}$$. The root mean square speed is given by $$v_{rms} = \sqrt{\frac{3RT}{M}}$$, so $$v_{rms} \propto \sqrt{T}$$. $$\frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}} = \sqrt{\frac{800}{200}} = \sqrt{4} = 2$$. The rms speed is doubled. Statement I is TRUE.

Statement II: For an ideal gas, $$PV = nRT$$ and the translational kinetic energy is $$KE = \frac{3}{2}nRT$$. Therefore $$PV = \frac{2}{3}KE$$, which means $$PV \neq KE$$. The product of pressure and volume equals $$\frac{2}{3}$$ of the translational kinetic energy, not equal to it. Statement II is FALSE.

The correct answer is Option B: Statement I is true but Statement II is false.