Which of the following statement(s) (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?

Correct answer: A. U _ rms is doubled when its temperature is increased four times U _ rms = 3RT M , E _ av = (3)/(2)RT If temperature is made 4 times, U _ rms between twice. Avg. kinetic energy ( F _ av ) is independent of molecular man at a given temperature, U _ rms inversely proportional to the square not of molecular mass.

JEE Advanced 2019Paper 1

Exam: JEE Advanced
Year: 2019
Paper: Paper 1
Subject: Chemistry
Chapter: States of Matter

JEE Advanced 2019 · Paper 1 · Chemistry · States of Matter

Which of the following statement(s) (are) correct regarding the...

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

\left({U}_{rms}\right)

and average translational kinetic energy

\left({ε}_{av}\right)

of a molecule in a gas at equilibrium?

Options

A ${U}_{rms}$ is doubled when its temperature is increased four times
B ${ε}_{av}$ at a given temperature does not depend on its molecular mass
C ${U}_{rms}$ is inversely proportional to the square root of its molecular mass
D ${ε}_{av}$ is doubled when its temperature is increased four times

Correct answer

A. ${U}_{rms}$ is doubled when its temperature is increased four times

Step-by-step solution

{\text{U}}_{\text{rms}} = \sqrt{\dfrac{\text{3RT}}{\text{M}}},

{\text{E}}_{\text{av}} = \dfrac{3}{2}\text{RT}

If temperature is made 4 times,

{\text{U}}_{\text{rms}}

between twice.
Avg. kinetic energy

( {\text{F}}_{\text{av}} )

is independent of molecular man at a given temperature,

{\text{U}}_{\text{rms}}

inversely proportional to the square not of molecular mass.

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