Question

What is the Root mean square velocity and average velocity?

Answer 1

Hint: The object is moving fast or slow this depends upon the speed and velocity of that object. As sometimes we have to conclude that which object is moving fast from one another there concept of speed and velocity is very useful.

Complete answer:
Velocity of an object defines the rate of change of position with respect to time and velocity is a scalar quantity i.e. it depends upon the direction of an object. The SI unit of velocity is metre per second.
Root mean square velocity which is abbreviated as RMS value is the square root of the mean of squares of velocity of individual gas molecules whereas velocity of gas molecules can be given by the formula $\dfrac{3RT}{M}$where R = molar gas constant, T = temperature in kelvin, M = Molar mass of the gas. So root mean square velocity is shown by the formula
\[{{v}_{rms}}=\sqrt{\dfrac{3RT}{M}}\]i.e. square root of velocity of gas molecules.
Average velocity is defined as the arithmetic mean of the mean of the velocities of different molecules of a gas at a given temperature which can be represented by \[{{v}_{av}}\]and the formula of average velocity is as follows:
\[{{v}_{av}}=\sqrt{\dfrac{8RT}{\pi M}}\]
Hence in this way we can define root mean square velocity and average velocity if we know the velocity of gas molecules.

Note:
Velocity of gas molecules is generally based on the concept of kinetic theory of gas molecules which generally gives the relationship between pressure, density and temperature on the basis of atomic or molecular models of gases.