{V_{rms}} denotes root mean square speed, bar V average speed and {Vₘ} most probable speed o

English

Gujarati

Hindi

12.Kinetic Theory of Gases

normal

${V_{rms}}$ denotes the root mean square speed, $\bar V$ the average speed and ${V_m}$the most probable speed of gas molecules. Out of the following which one is the correct answer ?

A

${V_{rms}} > \bar V > {V_m}$

B

${V_{rms}} < \bar V < {V_m}$

C

${V_{rms}} > \bar V < {V_m}$

D

${V_{rms}} < \bar V < {V_m}$

Solution

$ \mathrm{v}_{\mathrm{rms}} =\sqrt{\frac{3 \mathrm{kT}}{\mathrm{m}}}=1.732 \sqrt{\frac{\mathrm{kT}}{\mathrm{m}}} $

$ \overline{\mathrm{v}} =\sqrt{\frac{8 \mathrm{kT}}{\pi \mathrm{m}}}=1.596 \sqrt{\frac{\mathrm{kT}}{\mathrm{m}}} $

$ \mathrm{v}_{\mathrm{m}}=\sqrt{\frac{2 \mathrm{kT}}{\mathrm{m}}}=1.414 \sqrt{\frac{\mathrm{kT}}{\mathrm{m}}} $

$ \therefore \mathrm{V}_{\mathrm{ms}}>\overline{\mathrm{v}}>\mathrm{v}_{\mathrm{m}} $

Standard 11

Physics

Share

Similar Questions

Heat is supplied to a di-atomic gas at constant pressure. The ratio of $\Delta Q:\Delta U:\Delta W$ is

normal

An air bubble doubles its radius on raising from the bottom of water reservoir to be the surface of water in it. If the atmospheric pressure is equal to $10\, m$ of water, the height of water in the reservoir is ….. $m$

medium

The following graph shows two isotherms for a fixed mass of an ideal gas. The ratio of $r.m.s.$ speed of the molecules at temperatures $T_2$ and $T_1$ is

normal

One mole of ideal monoatomic gas $\left( {\gamma = 5/3} \right)$ is mixed with one mole of diatomic gas $\left( {\gamma = 7/5} \right)$. What is $\gamma $ for the mixture ? $\gamma $ denotes the ratio of specific heat at constant pressure to that at constant volume

normal

An ideal gas is trapped inside a test tube of cross-sectional area $20 \times 10^{-6} \,\,m^2$ as shown in the figure. The gas occupies a height $L_1$ at the bottom of the tube and is separated from air at atmospheric pressure by a mercury column of mass $0.002\,\, kg$. If the tube is quickly turned isothermally, upside down so that $L_2$ mercury column encloses the gas from below. The gas now occupies height $L_1$ in the tube. The ratio $L_1$ is [Take atmospheric pressure $= 10^5 Nm^{-2}]$

normal