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Relationship Between Kinetic Energy and Temperature

  1. Jan 24, 2014 #1
    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 [itex]\bar{T} = kT[/itex]. 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. jcsd
  3. Jan 24, 2014 #2

    Simon Bridge

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    "##\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
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