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
Show Solution
Verified By Collegedunia
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).
Was this answer helpful?
0
0
Top JEE Advanced Chemistry Questions
- The molecule that has linear structure is
- Which one among the following does not have the hydrogen bond?
- Carbon tetrachloride has no net dipole moment because of
- On hybridisation of one s and one p-orbital we get
- The IUPAC name of the compound having the formula is
View More Questions
Top JEE Advanced States of matter Questions
- According to kinetic theory of gases, for a diatomic molecule
- Equal weights of ethane and hydrogen are mixed in an empty container at $25^\circ$ C. The fraction of the total pressure exerted by hydrogen is
- Equal weights of methane and hydrogen are mixed in an empty container at $25^\circ$ C The fraction of the total pressure exerted by hydrogen is
- For one mole of a van der Waals' gas when $b = 0$ and $T = 300\, K$. the $pV\, vs \,1/V$ plot is shown below. The value of the van der Waals' constant a (atm $L\, mol^{-2}$)
- Helium atom is two times heavier than a hydrogen molecule. At $298\, K$ the average kinetic energy of a helium atom is
View More Questions
Top JEE Advanced Questions
- Yellow light is used in a single slit diffraction experiment with slit width of 0.6 mm. If yellow light is replaced by X-rays, then the observed pattern will reveal
- The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and the image at a distance of 26 cm from the convex lens, calculate the new size of the image.
- A concave lens of glass, refractive index 1.5 has both surfaces of same radius of curvature R. On immersion in a medium of refractive index 1.75, it will behave as a
- The position vector $\vec{r}$ of a particle of mass $m$ is given by the following equation $\vec{r}(t)=\alpha t^{3} \hat{i}+\beta t^{2} \hat{j}$ where $\alpha=\frac{10}{3} \,ms ^{-3}, \beta=5\, ms ^{-2}$ and $m =0.1 \,kg$. At $t =1\, s$, which of the following statement (s) is (are) true about the particle?
- In an n-p-n transistor circuit, the collector current is 10 mA. If 90% of the electrons emitted reach the collector
View More Questions
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.