Given below are two statements:Statement I: T | vedclass

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(B) Analysis of Statement $I$:The root mean square speed $(v_{rms})$ of gas molecules is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$.Initial temperature

Vedclass · Accepted Answer

Statement $I$ is true but Statement $II$ is false.

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(B) Analysis of Statement $I$:The root mean square speed $(v_{rms})$ of gas molecules is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$.Initial temperature $T_1 = -73^{\circ} C = (-73 + 273) K = 200 K$.Final temperature $T_2 = 527^{\circ} C = (527 + 273) K = 800 K$.The ratio of speeds is $\frac{v_{rms,2}}{v_{rms,1}} = \sqrt{\frac{T_2}{T_1}} = \sqrt{\frac{800}{200}} = \sqrt{4} = 2$.Thus,$v_{rms,2} = 2 v_{rms,1}$. Statement $I$ is true.Analysis of Statement $II$:For an ideal gas,the pressure-volume product is $PV = nRT$.The translational kinetic energy $(KE_{trans})$ of an ideal gas is given by $KE_{trans} = \frac{3}{2} nRT$.Therefore,$PV = \frac{2}{3} KE_{trans}$.Since $PV 
eq KE_{trans}$,Statement $II$ is false.

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