Question:
Which of the following statement(s) is(are) correct regarding the root mean square speed ($U_{rms}$) and average translational kinetic energy $\left(\varepsilon_{av}\right)$ of a molecule in a gas at equilibrium ?
Which of the following statement(s) is(are) correct regarding the root mean square speed ($U_{rms}$) and average translational kinetic energy $\left(\varepsilon_{av}\right)$ of a molecule in a gas at equilibrium ?
Updated On: Jun 14, 2022
- $U_{rns}$ is doubled when its temperature is increased four times
- $\varepsilon_{av}$ is doubled when its temperature is increased four times
- $\varepsilon_{av}$ at a given temperature does not depend on its molecular mass
- $U_{rns}$ is inversely proportional to the square root of its molecular mass
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The Correct Option is D
Solution and Explanation
$\bar{E}_{K} = \frac{3}{2}KT$ Average kinetic energy depends only on absolute temperature
K = Boltzmann constant
$U_{rms} = \sqrt{\frac{3RT}{M}}$
$U_{rms} \propto \sqrt{T}$
$U_{rms} \propto \frac{1}{\sqrt{M}}$
Using above formulae, correct statements are (A, C, D).
K = Boltzmann constant
$U_{rms} = \sqrt{\frac{3RT}{M}}$
$U_{rms} \propto \sqrt{T}$
$U_{rms} \propto \frac{1}{\sqrt{M}}$
Using above formulae, correct statements are (A, C, D).
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Concepts Used:
States of Matter
The matter is made up of very tiny particles and these particles are so small that we cannot see them with naked eyes.
There are three States of Matter:
The three states of matter are as follows:
Solid State:
- The solid-state is one of the fundamental states of matter.
- Solids differ from liquids and gases by the characteristic of rigidity.
- The molecules of solids are tightly packed because of strong intermolecular forces; they only oscillate about their mean positions.
Liquid State:
- The molecules in a liquid are closely packed due to weak intermolecular forces.
- These forces are weaker than solids but stronger than that of gases.
- There is much space in between the molecules of liquids which makes their flowing ability easy.
Gaseous State:
- In this state of matter, distances between the molecules are large (intermolecular distance is in the range of 10-7-10-5 cm.
- The intermolecular forces experienced between them are negligible.
- Thus, translatory, rotatory and vibratory motions are observed prominently in gases.