# Derivation of 1/3nMc^2 = nRT

• sgstudent
In summary: i think the term 'average' is used by people if there are variations in 'individual' events but sum /total of the effect carried out can be averaged over a large number of identical measurements/events. due to large number of molecules in random motion inside the container and colliding with each other as well as with the walls of the container ,an observer can think of averaging over the state of motion rather than takinng individual molecules and adding individual characteristic path , motion and impulse transferred to the wall of the enclosure.in kinetic theory the picture is almost above therefore the average force/average velocity and other terms are being used'one can visit the following toget a clear picture;http://gal

#### sgstudent

In the derivation the first step used F=Δmv/t and for t, they used t=2L/v where L is the distance between one end to the other end of the wall.

But I don't understand why we use 2L as the distance. Isn't the force exerted by that molecule only for the very short period where the molecule is in contact with the wall only? For example when we look at a car crash we look at that short moment when the car comes to a stop from an extremely high speed- shouldn't the same be applied?

sgstudent said:
In the derivation the first step used F=Δmv/t and for t, they used t=2L/v where L is the distance between one end to the other end of the wall.

But I don't understand why we use 2L as the distance

actually they calculate average force and the time interval is between two collisions taken as a round trip by a molecule after hitting a wall.
and there is a factor 2 also for the momentum change
F = delta p = 2 m v(x) x delta t and delta t= 2L/v(x)

drvrm said:
actually they calculate average force and the time interval is between two collisions taken as a round trip by a molecule after hitting a wall.
and there is a factor 2 also for the momentum change
F = delta p = 2 m v(x) x delta t and delta t= 2L/v(x)
Could you explain why using the change in momentum from one end to the other for the duration need (t) would give us the average force? I have not been exposed to the concept of an average force before so I'm not sure how to use it. Thanks!

Last edited:
sgstudent said:
Could you explain why using the change in momentum from one end to the other for the duration need (t) would give us the average force? I have not been exposed to the concept of an average force before so I'm not sure how to use it. Thanks!

i think the term 'average' is used by people if there are variations in 'individual' events but sum /total of the effect carried out can be averaged over a large number of identical measurements/events. due to large number of molecules in random motion inside the container and colliding with each other as well as with the walls of the container ,an observer can think of averaging over the state of motion rather than takinng individual molecules and adding individual characteristic path , motion and impulse transferred to the wall of the enclosure.

in kinetic theory the picture is almost above therefore the average force/average velocity and other terms are being used'
one can visit the following to
get a clear picture;

http://galileoandeinstein.physics.v...dfs/10_1425_web_Lec_31_KineticTheoryGases.pdf

## 1. What is the equation 1/3nMc^2 = nRT used for?

The equation 1/3nMc^2 = nRT is used to calculate the average kinetic energy of gas molecules in a system, known as the internal energy. It is also known as the equipartition theorem.

## 2. How was the equation 1/3nMc^2 = nRT derived?

The equation 1/3nMc^2 = nRT is derived from the kinetic theory of gases, which states that the average kinetic energy of gas molecules is directly proportional to the temperature of the gas. By using the ideal gas law (PV = nRT) and the kinetic energy formula (KE = 1/2mv^2), the equation can be derived.

## 3. What do the variables in the equation 1/3nMc^2 = nRT represent?

The variable n represents the number of moles of gas, M represents the molar mass of the gas, c represents the speed of light, R represents the gas constant, and T represents the temperature in Kelvin.

## 4. Can the equation 1/3nMc^2 = nRT be applied to all gases?

Yes, the equation can be applied to all gases as long as they behave according to the ideal gas law. This means that the gas molecules are not interacting with each other and there are no intermolecular forces present.

## 5. How is the equation 1/3nMc^2 = nRT related to the concept of temperature?

The equation 1/3nMc^2 = nRT shows the direct relationship between the average kinetic energy of gas molecules and temperature. As the temperature increases, the average kinetic energy of the gas molecules also increases. This concept is important in understanding the behavior of gases and their properties.