The root mean square velocity, vrms , the average velocity, vm and the most probable velocity, v

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The root mean square velocity, vrms , the average velocity,...

The root mean square velocity, $v_{\text {rms }}$, the average velocity, $v_{m}$ and the most probable velocity, $v_{m p}$ of the molecules of the gas are in the order: (a) $v_{\mathrm{mp}}>v_{\mathrm{w}>} v_{\mathrm{rax}}$ (b) $v_{\text {rms }}>v_{w\rangle} v_{m p}$ (c) $v_{a v}>v_{\text {mp }} v_{\text {rms }}$ (d) $v_{\text {mip }}>v_{\text {rms }} v_{x v}$

The root mean square velocity, $v_{\text {rms }}$, the average velocity, $v_{m}$ and the most probable velocity, $v_{m p}$ of the molecules of the gas are in the order:
(a) $v_{\mathrm{mp}}>v_{\mathrm{w}>} v_{\mathrm{rax}}$
(b) $v_{\text {rms }}>v_{w\rangle} v_{m p}$
(c) $v_{a v}>v_{\text {mp }} v_{\text {rms }}$
(d) $v_{\text {mip }}>v_{\text {rms }} v_{x v}$

Key Concepts

Kinetic Theory of Gases

This theory provides a framework for understanding the properties of gases based on the motions of their molecules. It relates temperature to the average kinetic energy of the molecules and gives rise to statistical speed distributions such as the Maxwell-Boltzmann distribution.

Maxwell-Boltzmann Distribution

The Maxwell-Boltzmann distribution describes the statistical distribution of speeds for molecules in an ideal gas. It shows how many molecules have a particular speed at a given temperature, and it forms the basis for defining various characteristic speeds like the most probable, average, and rms speeds.

Most Probable Speed

The most probable speed is the speed at which the Maxwell-Boltzmann distribution peaks, meaning it is the speed at which the greatest number of molecules are most likely to be found. It is typically the lowest among the characteristic speeds derived from the distribution.

Average Molecular Speed

The average molecular speed is the mean of all molecular speeds weighted by the Maxwell-Boltzmann distribution. It is calculated by integrating the speed over the distribution and tends to lie between the most probable and the rms speeds.

Root Mean Square (RMS) Velocity

The root mean square velocity is the square root of the average of the squares of the speeds of all the gas molecules. It is directly related to the average kinetic energy of the gas molecules and therefore is always the highest among the three characteristic speeds.

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