# Pressure exerted by a gas (derivation using the kinetic theory of gases)

• Bheshaj
In summary: . so basically you are saying that the average force on the wall is the average of the force exerted by the gas particles that bump into it over time?thanks. so basically you are saying that the average force on the wall is the average of the force exerted by the gas particles that bump into it over time?
Bheshaj
In the derivation of finding pressure exerted by a gas using kinetic theory of gases I am not understanding why the time between two collisions is taken as the time for rate of change of momentum when a particle bounces back from the wall. please help me

I think you misquote. Any reference ? The duration of the collision with the wall is the time in which the momentum changes.

Bheshaj
BvU said:
I think you misquote. Any reference ? The duration of the collision with the wall is the time in which the momentum changes.
BvU said:
I think you misquote. Any reference ? The duration of the collision with the wall is the time in which the momentum changes.
see this

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Something gave in in my neck when I tried to read this. Have to go to the hospital first ...

So where is this quote ? I see ##\Delta t = {2L\over |u|} ## for the time to go to the left wall and back again ...

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Here in the lower left corner its given that force is change in momentum upon time. where he writes the change in momentum and divides it by time between two collisions as given above it.

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They don't have a microscope here in the hospital to read your fine print. Can you be bothered to learn some ##\LaTeX## in order to post legibly ?

Last edited:
But if I have to guess he now averages the change in momentum from the gas particles that bump into the wall, to calculate the average force on the wall.

Its because yoy want to find average force exerted by the molecule. How u find average force? See u find the time in which this repears aka time period. The collision with wall PQRS repeats. Now find the average force in this time. If u were to find instantaneous force u have to divide by time of collision which is very small.

You are giving Maharashtra HSC? I am also giving it.

Bheshaj
Its because yoy want to find average force exerted by the molecule. How u find average force? See u find the time in which this repears aka time period. The collision with wall PQRS repeats. Now find the average force in this time. If u were to find instantaneous force u have to divide by time of collision which is very small.

You are giving Maharashtra HSC? I am also giving it.
yeah, me too thanks

BvU said:
But if I have to guess he now averages the change in momentum from the gas particles that bump into the wall, to calculate the average force on the wall.
thanks

## 1. What is the kinetic theory of gases?

The kinetic theory of gases is a model that explains the behavior of gases at a molecular level. It states that gases are made up of tiny particles in constant, random motion and that the pressure exerted by a gas is a result of the collisions between these particles and the walls of their container.

## 2. How is pressure exerted by a gas calculated using the kinetic theory?

The pressure exerted by a gas can be calculated using the formula P = 1/3 * n * m * c^2, where P is pressure, n is the number of gas molecules, m is the mass of each molecule, and c is the average speed of the molecules. This formula is derived from the kinetic theory of gases.

## 3. What is the relationship between temperature and pressure in the kinetic theory of gases?

According to the kinetic theory, as the temperature of a gas increases, the average speed of its molecules also increases. This leads to more frequent and forceful collisions with the walls of the container, resulting in an increase in pressure.

## 4. How does the volume of a gas affect its pressure according to the kinetic theory?

The kinetic theory states that as the volume of a gas decreases, the molecules are more confined and have less space to move around. This leads to an increase in the frequency of collisions with the container walls, resulting in an increase in pressure. Conversely, as the volume of a gas increases, the pressure decreases.

## 5. What assumptions are made in the kinetic theory of gases?

The kinetic theory of gases makes several assumptions, including that the gas particles are in constant, random motion, that the particles have negligible volume, and that there are no attractive or repulsive forces between particles. It also assumes that the collisions between particles and the container walls are elastic, meaning there is no loss of energy during the collision.

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