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# Thermal physics exam question watch

1. I have calculated answers for these questions but there is no mark scheme available and for b) should I use 3/2kT = 1/2mCrms^2 or 3/2nRT = 1/2mCrms^2 ?

A sample of air has a density of 1.24 kgm^-3 at a pressure of 1.01x10^5 Pa and a temperature of 300K.

a) Calculate the mean kinetic energy of an air molecule under these conditions.
b) Calculate the mean square speed for the air molecules.
c) Explain why, when the temperature of the air is increased to 320K, some of the molecules will have speeds much less than that suggested by the value you calculated in part b).
2. (Original post by G.Y)
b) Should I use 1.5kT = 0.5mc^2 or 1.5nRT = 0.5Mc^2?

Density 1.24 kgm^-3, pressure 1.01*10^5 Pa, temp 300 K.
Note 2nd eqn is just scaled up from the 1st i.e) 1.5NkT = 0.5Nmc^2 => 1st eqn (/ by N).

No M, n, N (air quantities), so use 1st eqn. What do you use for mass of air molecule? Try weighted average of oxygen/nitrogen molecules.

For c) note 1) molecules have wide range of speeds/ke 2) very large no. cover the range 3) speed distrib has greater spread at higher temp.
3. (Original post by Physics Enemy)
Note 2nd eqn is just scaled up from the 1st i.e) 1.5NkT = 0.5Nmc^2 => 1st eqn (/ by N).

No M, n, N (air quantities), so use 1st eqn. What do you use for mass of air molecule? Try weighted average of oxygen/nitrogen molecules.

For c) note 1) molecules have wide range of speeds/ke 2) very large no. cover the range 3) speed distrib has greater spread at higher temp.
Thank you for c)
Question gives you the density of air so I'm assuming they want you to calculate m (mass of molecule) from m = pV (density x volume) but first to calculate V you need to use pV = nRT or pV = NkT and you don't have / can't work out values for n or N. Very confused.
4. (Original post by G.Y)
Thank you for c)
Question gives you the density of air so I'm assuming they want you to calculate m (mass of molecule) from m = pV (density x volume) but first to calculate V you need to use pV = nRT or pV = NkT and you don't have / can't work out values for n or N. Very confused.
The V in pV = nRT = NkT is for the container, for a large no. of molecules of an ideal gas. Guess you could estimate the volume of an air molecule by treating it as a sphere, radius ~ 1.85*10^-10 m.
5. (Original post by Physics Enemy)
The V in pV = nRT = NkT is for the container, for a large no. of molecules of an ideal gas. Guess you could estimate the volume of an air molecule by treating it as a sphere, radius ~ 1.85*10^-10 m.
So I found this other equation for density. P = pM/RT (p = pressure M = molar mass). Could rearrange to find M. Substitute M into m = M/Na to find the mass of an air molecule. Then use 3/2kT = 1/2mCrms^2 to find the mean square speed. A lot of effort for 3 marks.

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