Which of the following statement(s) is (are) correct regarding the root mean square speed $\left(\mathrm{U}_{\text {rms }}\right)$ and average translational kinetic energy ( $\varepsilon_{\text {av }}$ ) of a molecule in a gas at equilibrium ?

(A) $\mathrm{U}_{\text {rms }}$ is doubled when its temperature is increased four times; (B) $\varepsilon_{\mathrm{av}}$ at a given temperature does not depend on its molecular mass; (C) $\mathrm{U}_{\text {rms }}$ is inversely proportional to the square root of its molecular mass

(D) $\varepsilon_{\mathrm{av}}$ is doubled when its temperature is increased four times

JEE Advanced · 2019 · 27 May 2019 · Paper 1 · States of Matter

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Which of the following statement(s) is (are) correct regarding the root mean square speed

(U_{rms})

and average translational kinetic energy (

ε_{av}

) of a molecule in a gas at equilibrium ?

(A) $U_{rms}$ is doubled when its temperature is increased four times✓ Correct
(B) $ε_{av}$ at a given temperature does not depend on its molecular mass✓ Correct
(C) $U_{rms}$ is inversely proportional to the square root of its molecular mass✓ Correct
(D) $ε_{av}$ is doubled when its temperature is increased four times

Answer: (A), (B), (C)

Solution

U_{rms} = \frac{3 R T}{M}

and

ε_{av} = \frac{3}{2} k T

(A) TRUE:

U_{rms} \propto T

. If T increases 4 times,

U_{rms}

doubles.

(B) TRUE:

ε_{av}

depends only on T, not on molecular mass.

(C) TRUE:

U_{rms} \propto \frac{1}{M}

.

(D) FALSE:

ε_{av} \propto T

. If T increases 4 times,

ε_{av}

increases 4 times, not doubles.

JEE Advanced · 2019 · 27 May 2019 · Paper 1 · One or more correct options

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JEE Advanced · 2019 · 27 May 2019 · Paper 1 · States of Matter

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