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## Homework Statement

A tyre contains gas at a pressure of 150 kPa. If the gas has a density of 2.0 kg m

^{-3}, find the root mean square speed of the molecules.

## Homework Equations

These are the equations I believe to be relevant:

[tex]c_{rms} = \frac{\sqrt{<c^2>}}{N}[/tex]

[tex]pV = \frac{1}{3}Nm<c^2>[/tex]

[tex]p = \frac{1}{3}ρ<c^2>[/tex]

## The Attempt at a Solution

[tex]\frac{3p}{ρ} = <c^2>[/tex]

[tex]\frac{3 * 150000}{2} = <c^2> = 225000ms^{-1}[/tex]

But I'm not sure how to work out N as I don't any volume or temperature. I'm not quite sure how they get their answer in the back of the book which is 474 ms

^{-1}(which is the square root of 225000) meaning that N = 1? How can that be?

Thank you for reading!

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