Question

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 options given below:

• A. Statement I is false but Statement II is true
• B. Both Statement I and Statement II are true
• C. Both Statement I and Statement II are false
• D. Statement I is true but Statement II is false

Answer 1

The Correct Option is D

Statement I: The root mean square (RMS) speed of gas molecules is given by: \[ v_{\text{rms}} \propto \sqrt{T} \] Let \(T_1 = -73^\circ C = 200 \, \text{K}\) and \(T_2 = 527^\circ C = 800 \, \text{K}\). The ratio of RMS speeds is: \[ \frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}} = \sqrt{\frac{800}{200}} = \sqrt{4} = 2 \] Thus, the RMS speed doubles, and Statement I is true.
Statement II: For an ideal gas, the product of pressure and volume is given by: \[ PV = nRT \] The translational kinetic energy is: \[ \text{Translational KE} = \frac{3}{2} nRT \] Since \(PV \neq \frac{3}{2}nRT\), Statement II is false.