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If two gasses are in thermal equilbrium, do their molecules have same amount of Kinetic energy?

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    $\begingroup$ Yes, that is the definition $\endgroup$ – Bruce Lee Jan 13 '16 at 7:07
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    $\begingroup$ you need to provide more details : their molecules and same are ambiguous . Strictly speaking, never 2 molecules will have the same KE. And statistically, it depends from many factors, beginning by the kind of samples you consider, the gasses thermal properties and why not, the isotopes. $\endgroup$ – user46925 Jan 13 '16 at 10:29
  • $\begingroup$ @BruceLee Doesn't this depend on the number of degrees of freedom? $\endgroup$ – Norbert Schuch Jan 13 '16 at 11:07
  • $\begingroup$ @NorbertSchuch, by molecules, i thought that the question only referred to translational kinetic energy. Yup it should depend on the number of degrees of freedom. The total KE does depends on it. $\endgroup$ – Bruce Lee Jan 13 '16 at 11:14
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    $\begingroup$ @igael i think the question referred to only translational kinetic energy as viewed from its intonation. Thanks for pointing out other features. $\endgroup$ – Bruce Lee Jan 13 '16 at 11:17
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Two bodies in thermal equilibrium are at the same temperature. See the Zeroth law of thermodynamics.

Temperature is a direct function of average molecular Kinetic energy - by definition. There is no dependence on anything else like degrees of freedom etc.

There are other forms of molecular thermal energy storage - rotation and vibration about molecular bonds as two examples - and the total amount of energy stored internally in a molecule does depend on the total number of degrees of freedom of the molecule. The sum of the translational kinetic energy and all these other stored energies is referred to as internal energy U. That is where the confusion above originates. The total internal energies of the two gasses can be very different even though their average translational kinetic energies and thus their temperatures are the same.

So, YES - the translational kinetic energies of the two gasses in thermal equilibrium with each other will be equal. If their molecular masses are different, their molecular speeds will also be different. Their internal energies may be very different.

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