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Question

Is RMS Velocity depends upon pressure of gas or not?

  Or

It is independent of pressure?


Solution

No,Root-mean-square speed is the measure of the speed of particles in a gas which is most convenient for problem solving within the kinetic theory of gases. It is defined as the square root of the average velocity-squared of the molecules in a gas. It is given by the formula

v_{{\mathrm  {rms}}}={\sqrt  {{3RT} \over {M_{m}}}}

where vrms is the root mean square of the speed in meters per second, Mm is the molar mass of the gas in kilograms per mole, R is the molar gas constant, and T is the temperaturein kelvins. Although the molecules in a sample of gas have an average kinetic energy (and therefore an average speed) the individual molecules move at various speeds and they stop and change direction according to the law of density measurements and isolation, i.e. they exhibit property of distribution of speeds. Some move fast, others relatively slow. Collisions change individual molecular speeds but the distribution of speeds remains the same. This equation is derived from kinetic theory of gases using Maxwell–Boltzmann distribution function. The higher the temperature, the greater the mean velocity will be. 


So rms velocity depends on molar mass and temperature ,but it is independent of pressure

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