# Relationship Between Kinetic Energy and Temperature

1. Jan 24, 2014

### Bashyboy

Hello everyone,

I am currently reading the pages from a book called Thermal Physics, which was written by Daniel Schroeder; the pages to which I refer are 10-13. In these pages, he derives the relationship $\bar{T} = kT$. Here is one line that intrigues me,

"So if this model is accurate, the temperature of a gas is a direct measure of the average translational kinetic energy of its molecules."

I was wondering, does anyone know of any experiments that had (or are) been conducted to verify this formula, as I would be very interested in reading an account of these experiments.

Thank you.

2. Jan 24, 2014

### Simon Bridge

"$\bar T=kT$" is nonsense - typo?

The usual relationship for the kinetic temperature of an ideal gas is: $\bar E_K=\frac{3}{2}kT$ ... for a general gas we expect: $\bar E_K\propto kT$ ... where the constant of proportionality is a material property. For simple gasses, it corresponds to roughly half the number of degrees of freedom.

The definitive experiments were done a long time ago.

The distribution of energies follows the Maxwel-Boltzman distribution - and it is this which has been experimentally confirmed. These days it may be found in a college teaching lab. i.e. http://www.cosbkup.gatech.edu/group/chem780/CHAPT1.pdf s1.5.5
... the lead-up is worth the read since the authors make some effort to justify assertions from simple observations where they can.
Anyway - the section shows the student-lab methods of determining the energy distribution of a gas. From there you can confirm the relationship between the mean energy and the temperature.

Last edited: Jan 24, 2014