Why is kinetic energy NOT proportional to degrees F/C

[babacanoosh]

Hello all,
I have a question, that regards a problem I was assigned. The problem is:

Why is kinetic energy NOT proportional to degrees F/C?

-I understand it has something to do with absolute zero Kelivn...not C. Thanks

Any help would be greatly appreciated...I need a response by tomorrow. Thanks again

 

[AbedeuS]

$$PV = \frac{1}{3}Nmv_{rms}^{2}$$
$$PV = nRT$$

Therefore:
$$\frac{1}{3}Nmv_{rms}^{2} = nRT$$

Rearranging:
$$v_{rms} = \sqrt{\frac{3nRT}{Nm}}$$

Since $$N = nN_{a}$$ and $$R = kN_{a}$$ it can be simplified to:

$$v_{rms} = \sqrt{\frac{3nN_{a}kT}{nN_{a}m}} = \sqrt{\frac{3kT}{m}}$$

Therefore:
$$v_{rms}\propto \sqrt{T}$$

EDIT: Similar looking results are found if you doing the same with Boltzmann curves or whatever else tickles your fancy.