# Determining temperature of a diatomic gas

[SOLVED] Determining temperature of a diatomic gas

1. Assume 3.0 moles of a diatomic gas has an internal energy of 10kJ. Determine the temperature of the gas after it has reached equilibrium (assuming that molecules rotate and vibrate at that tmeperature).

2.Boltzmann's constant and # of moles 6.022x10^23

3.The average kinetic energy per diatomic gas molecule is (5/2) kB T where kB is Boltzmann's constant.
The number of molecules in 3 moles is 3 * 6.022 x 10^23, so I just solved for T:

10000 J = (5/2)* (1.3807 x 10^-23 J/K) * 3 * (6.022 x 10^23) * T

Which, I get 160k, but the answer is suppose to be 115k, which I have no idea what I did wrong, maybe the wrong constant perhaps? No clue. Thanks for any help given :D

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Everything looks fine. I just whipped out my calculator and got the same answer. You *might* be missing something about the internal energy, i.e. maybe you can't equate U = 5/2kT, but off the top of my head it looks fine.

It's possible that the book is wrong. Wouldn't be the first time.

Awesome, thats what I thought it could be a book error. I will go and ask my teacher about this whenever its possible, thanks for your help :+)

alphysicist
Homework Helper
Hi Deoxygenation,

1. Assume 3.0 moles of a diatomic gas has an internal energy of 10kJ. Determine the temperature of the gas after it has reached equilibrium (assuming that molecules rotate and vibrate at that tmeperature).

2.Boltzmann's constant and # of moles 6.022x10^23

3.The average kinetic energy per diatomic gas molecule is (5/2) kB T where kB is Boltzmann's constant.
The number of molecules in 3 moles is 3 * 6.022 x 10^23, so I just solved for T:

10000 J = (5/2)* (1.3807 x 10^-23 J/K) * 3 * (6.022 x 10^23) * T

Which, I get 160k, but the answer is suppose to be 115k, which I have no idea what I did wrong, maybe the wrong constant perhaps? No clue. Thanks for any help given :D
I think the factor of (5/2) is incorrect here. These diatomic molecules are vibrating and rotating, so the degrees of freedome are:

three from translation (x,y,z)
two from rotation (the two axes perpendicular to the line joining the atoms)
two from vibration (kinetic and potential energy)

Each degree of freedom will give (1/2)kT of energy per molecule, and so I think the answer in your book is correct.

Oooo, wow, good thing I came back and check out the question. Ok, thats what must of been wrong. Thank you for finding the error :+)