# Kinetic Theory of Gases Derivation

• Jimmy87
In summary, the average of the squared velocities of molecules in a gas is obtained by dividing the total force of all molecules by the total number of molecules, which is mathematically required and aligns with the concept of averages. This results in the equation ##\frac{F}{N}## = k ( average squared velocity of one molecule ).
Jimmy87
Hi, I am struggling with a particular point on the derivation of the kinetic theory of gases. Between 5mins and 6mins 30seconds of the video below they discuss how to get a value for the average of the squared velocities of the molecules in the gas. The bit I don't get is why they divide by 'N' on BOTH sides of the equation (i.e. why he divides the force by N). At first I thought he did it to make sure he did it to both sides of the equation but then that doesn't make sense to me. If you add up all the squared velocities and divide through the total number of molecules then you get the average of the squared velocities. So instead of the force being equal to the squared velocity of a single particle it is equal to an average for them all which is fine. But then why would you go and divide the left side by N as well?

If F = k ( sum of the square of each molecule's velocity ) that is the total force for ALL the molecules
So when you divide the RHS by N to get the average velocity, you now have the velocity of ONE typical molecule.
F is much too big for that. It was the force for ALL the molecules combined. So we have to divide that also by N.
Now ##\frac{F}{N}## = k ( average squared velocity of one molecule )

As you said, it is mathematically required that you divide both sides of an equation by the same thing.

It is also what averages are about.
Say F = the total number of chocolates in N boxes

Then ##\frac{F}{N}## = ##\frac{the\ total\ number\ of\ chocolates\ in\ N\ boxes}{N}## = the average number of chocolates in ONE box

Jimmy87

## 1. How is the kinetic theory of gases derived?

The kinetic theory of gases is derived from the assumption that gas molecules are in constant random motion and that their collisions with each other and with the walls of the container are perfectly elastic. This theory is also based on the assumption that the volume of the gas molecules themselves is negligible compared to the volume of the container.

## 2. What is the relationship between the average kinetic energy of gas molecules and temperature?

The average kinetic energy of gas molecules is directly proportional to the temperature of the gas. As the temperature increases, the average kinetic energy of the gas molecules also increases. This is because at higher temperatures, the molecules are moving faster and have more kinetic energy.

## 3. How does the kinetic theory explain gas pressure?

The kinetic theory explains gas pressure by stating that the pressure exerted by a gas is a result of the constant collisions between gas molecules and the walls of the container. The more collisions that occur, the higher the pressure of the gas will be.

## 4. Can the kinetic theory of gases be applied to all types of gases?

Yes, the kinetic theory of gases can be applied to all types of gases, as long as the gas molecules are in constant random motion and their collisions are perfectly elastic. This theory is used to explain the behavior of ideal gases, which do not interact with each other.

## 5. How does the kinetic theory of gases explain gas diffusion?

The kinetic theory of gases explains gas diffusion by stating that gas molecules are in constant random motion and will eventually spread out to fill the entire container. This is due to the collisions between the molecules causing them to move in different directions and distribute themselves evenly throughout the container.

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