Answer Show  RMS velocity is used in place of average velocity because typical gas molecules move in all directions and have net zero velocity. Answer: Root mean square velocity (RMS value)is the square root of the mean of squares of the velocity of individual gas molecules. \(\begin{array}{l}v_{rms}= \sqrt{\frac{3RT}{M}}\end{array} \) Where vrms= Root-mean-square velocity M = Molar mass of the gas (Kg/mole) R= Molar gas constant T = Temperature in Kelvin. Average velocity is the arithmetic mean of the velocities of different molecules of a gas at a given temperature. \(\begin{array}{l}v_{av}= \sqrt{\frac{8RT}{\pi M}}\end{array} \) Where R = Gas constant T = Temperature (in K) M = Molar mass of the gas Refer more
The molecular velocities like average velocity, root mean square velocity, and most probable velocity are well discussed here: Average velocityAverage velocity is the arithmetic mean of the various velocities of the molecules. It is symbolically represented by vav or v. If c1, c2, c3, …………cn are the velocities of individual molecules in a gas and ‘n’ is the total number of molecules present in the gas, then the average molecular velocity is given by The value of average velocity calculated from Maxwell’s law of distribution is where R = Gas constant, T = Temperature (in Kelvin scale), and M = Molar mass of the gas Thus by substituting the values of R, T, π, and M in the above equation, average velocity can be calculated. Root mean square velocityThe square root of the mean of squares of each gas molecule’s velocity is known as the root mean square velocity (r.m.s). It is denoted by μ or vrms. If c1, c2, c3, …………cn are the velocities of individual molecules in a gas, and ‘n’ is the total number of molecules present in the gas, then root mean square velocity (r.m.s.) is given by The Kinetic Gas Equation can be used to calculate the RMS velocity u at a given temperature as where R = Gas constant, T = Temperature (in Kelvin scale), and M = Molar mass of the gas Thus, root mean square velocity can be calculated by putting the value of R, T, and M in the above equation. Most Probable VelocityMost probable velocity is defined as the velocity possessed by the largest number of molecules in a gas. It is denoted by vmp or α. According to Maxwell’s law of distribution of molecular velocities, the most probable velocity is given by the expression. This is the required formula for most probable velocity of gas molecules. Relation between Average Velocity, Root mean square Velocity and Most Probable VelocityAs we know,
Average velocity is the arithmetic mean of the various velocities of the molecules.
mean velocity of gas molecules is also called average velocity and is defined as the arithmetic mean of the various velocities of the molecules.
average velocity of gas molecules is proportional to the temperature.
The distance traveled by a molecule in a given gas per unit of time is known as molecular velocity.
Three types of velocities are considered in the study of the kinetic molecular theory of gases. They are average velocity, r.m.s, and most probable velocity.
|
What do you mean by root mean square velocity average velocity and most probable velocity give equation also?
Postagens relacionadas
direito autoral © 2024 estudarpara Inc.
