About maxwell-boltzmann distribution

In summary, the Maxwell-Boltzmann distribution is a probability distribution used to describe the speeds of particles in a gas at a given temperature. It is derived from two fundamental equations in classical thermodynamics and helps us understand the behavior of particles in a gas at different temperatures. The distribution makes several assumptions about the gas and is used in real-world applications such as in gas turbines, chemical reactions, and the study of atmospheric gases. It is also used in statistical mechanics to model the behavior of particles and understand molecular properties.
  • #1
asdff529
38
0
Base on maxwell-boltzmann distribution,we can calculate the average velocity of gas molecule .
i read a book and it proves like that
average velocity=[itex]\int vf(v) dv[/itex]
I don't understand why we don't have to divide it by N because we should be calculating the average,but not the total.
Would anyone tell me where i went wrong
 
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  • #2
f(v) is a probability distribution, not the total number so you have already divided by N when calculating the probability distribution.
 
  • #3
by multiplying each bin of the velocities, you already normalize the velocity distribution
 

Related to About maxwell-boltzmann distribution

What is the Maxwell-Boltzmann distribution?

The Maxwell-Boltzmann distribution is a probability distribution that describes the speeds of particles in a gas at a given temperature. It is used to predict the average number of particles with a certain speed in a gas, and is based on the principles of classical thermodynamics.

How is the Maxwell-Boltzmann distribution derived?

The Maxwell-Boltzmann distribution is derived from two fundamental equations in classical thermodynamics: the Maxwell-Boltzmann equation and the Boltzmann distribution. These equations describe the relationship between temperature, pressure, and the behavior of particles in a gas.

What is the significance of the Maxwell-Boltzmann distribution?

The Maxwell-Boltzmann distribution is significant because it helps us understand the behavior of particles in a gas at different temperatures. It allows us to predict the average speed of particles in a gas, which is important in many fields such as physics, chemistry, and engineering.

What are the assumptions of the Maxwell-Boltzmann distribution?

The Maxwell-Boltzmann distribution makes several assumptions about the gas, such as that it is an ideal gas, the particles are non-interacting, and that the temperature is constant. These assumptions allow us to simplify the equations and make predictions about the behavior of the gas.

How is the Maxwell-Boltzmann distribution used in real-world applications?

The Maxwell-Boltzmann distribution is used in many real-world applications, such as in the design of gas turbines, chemical reactions, and the study of atmospheric gases. It is also used in the field of statistical mechanics to model the behavior of particles in a gas and to understand the properties of materials at the molecular level.

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