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## Homework Statement

A quantity of helium gas is held in a square box 1 m length. The measured macroscopic pressure of the gas is 1000 Pa. An atom of helium makes 500 collisions per second with the wall of the container travelling at an average velocity perpendicular to a wall of a container. Assuming that collisions with the wall are elastic and there are no collisions or potential interaction between the atoms, calculate the kinetic energy of one atom in this system.

## Homework Equations

P=(N m vmean^2)/3V

where

m=mass of one atom

vmean=mean speed

V=volume

N= I am unsure of exactly what this is, I assume it is the number of atoms striking the inside surfaces.

## The Attempt at a Solution

1.There are 500 collisions per second on the wall of this cube. This means that there are 6*500 collisions overall in the cube: 3000 collisions per second overall and therefore 3000 atoms in total colliding with the inside surfaces of the cube.

2. The mass of an He atom is equal to 4.002602u= 6.644*10^-27 kg

3. The cubes volume is 1m*1m*1m=1*m^3

3. P=(N m vmean^2)/3V.

V=1

m=6.644*10^-27

N=3000

P=1000

1000=(3000*(6.64*10^-27)vmean^2)/3(1)

1000=1000*(6.64*10^-27)vmean^2)

1=(6.64*10^-27)vmean^2

1/(6.64*10^-27) = vmean^2= 1.51*10^26

therefore vmean= 1.23*10^13 m/s

1.23*10^13 m/s > c

oh dear.

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