I guess you mean speed, because the average velocity is normally 0.Viona said:What is the meaning of the average velocity of gas molecules calculated by Boltzmann distribution (in kinetic theory of gases)?
It depends. Check the parameters that enter into the calculation of the average speed. Provided that these parameters are equal, then the average speed will be the same.Viona said:Does all molecules have the same average velocity?
No.Viona said:Does all molecules have the same average velocity?
anorlunda said:No.
I don't understand your question. Using an average calculation in any circumstance is needed only when the values are not all equal.
I think I am confused: is the average velocity calculated using Boltzmann distribution is similar to, for example, measuring the velocity for one molecule many times and take the average?cjl said:The average thermal speed is useful for a number of things, but I don't really understand what the question is here. As for your question about all molecules, are you asking if different molecular species have the same average velocity? If so, then generally no. In a gas volume at a given temperature, the average kinetic energy of all molecules is the same (assuming it has reached equilibrium), so the average velocity of any gas species will scale with the inverse square root of the molecular mass.
Viona said:I think I am confused: is the average velocity calculated using Boltzmann distribution is similar to, for example, measuring the velocity for one molecule many times and take the average?
https://en.wikipedia.org/wiki/Ergodic_hypothesismjc123 said:I believe the instantaneous average speed over all the molecules is equal to the time-average for a single molecule, but I'm not sure I could prove it.
The Boltzmann distribution is a statistical distribution that describes the distribution of energy among particles in a system. It is commonly used in physics to describe the behavior of gas molecules.
The average velocity of gas molecules can be calculated by taking the square root of the average of the squared velocities of all the gas molecules in the system, as described by the Boltzmann distribution.
The Boltzmann distribution allows scientists to predict the behavior of gas molecules in a system, such as their average velocity, which is important in understanding and studying various physical phenomena, such as gas pressure and temperature.
The average velocity of gas molecules is affected by temperature, mass of the gas molecules, and the size of the container they are in. These factors can all influence the distribution of energy among the gas molecules, as described by the Boltzmann distribution.
Yes, the Boltzmann distribution is applicable to all types of gases, as long as they are in thermal equilibrium and follow the laws of classical mechanics. It is a fundamental concept in statistical mechanics and is widely used in the study of gases.