The root mean square velocity of one mole of a monoatomic...

The root mean square velocity of one mole of a monoatomic gas having molar mass $\mathrm{M}$ is $\mathrm{u}_{\mathrm{rms}}$ - The relation between the average kinetic energy (E) of the gas and $\mathrm{u}_{\mathrm{rms}}$ is: (a) $\mathrm{u}_{\mathrm{rms}}=\sqrt{(3 \mathrm{E} / 2 \mathrm{M})}$ (b) $\mathrm{u}_{\mathrm{mas}}=\sqrt{(2 \mathrm{E} / 3 \mathrm{M})}$ (c) $\mathrm{u}_{\mathrm{rms}}=\sqrt{(2 \mathrm{E} / \mathrm{M})}$ (d) $\mathrm{u}_{\mathrm{mas}}=\sqrt{(\mathrm{E} / 3 \mathrm{M})}$

The root mean square velocity of one mole of a monoatomic gas having molar mass $\mathrm{M}$ is $\mathrm{u}_{\mathrm{rms}}$ -
The relation between the average kinetic energy (E) of the gas and $\mathrm{u}_{\mathrm{rms}}$ is:
(a) $\mathrm{u}_{\mathrm{rms}}=\sqrt{(3 \mathrm{E} / 2 \mathrm{M})}$
(b) $\mathrm{u}_{\mathrm{mas}}=\sqrt{(2 \mathrm{E} / 3 \mathrm{M})}$
(c) $\mathrm{u}_{\mathrm{rms}}=\sqrt{(2 \mathrm{E} / \mathrm{M})}$
(d) $\mathrm{u}_{\mathrm{mas}}=\sqrt{(\mathrm{E} / 3 \mathrm{M})}$

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Key Concepts

Root Mean Square (RMS) Velocity

RMS velocity is a statistical measure that represents the square root of the average of the squares of the velocities of particles in a gas. It is vital in linking the microscopic motion of particles with the macroscopic properties of the gas, such as temperature and pressure.

Average Kinetic Energy

Average kinetic energy describes the mean energy due to the motion of particles in a system. In the context of kinetic theory, it is directly proportional to the absolute temperature and, for an ideal gas, is related to the RMS velocity by the expression (1/2) times the mass of a particle times the square of the RMS velocity.

Kinetic Theory of Gases

The kinetic theory of gases provides a framework for understanding the behavior of gases by considering them as a collection of particles in constant, random motion. It connects macroscopic observables like temperature and pressure with microscopic quantities such as particle mass and velocity, and underpins relationships like the one between kinetic energy and RMS velocity.

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