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Kinetic theory of gasses

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In a mixture of hydrogen and oxygen gases at the same temperature, which molecules move faster and why?

This is a question from a CONCEPTUAL physics class (no mathematical explanation please) in the chapter Heat Transfer

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Solution Summary

A conceptual explanation that does not involve calculations.

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This part is the "hand-waving" conceptual explanation:

The temperature of the gas is proportionally related to its kinetic energy (the energy of motion). It depends ONLY on the temperature.
The higher the temperature, the higher the kinetic energy.

Corollary:
Two gas molecules that "have" the same temperature have the same kinetic energy. (Statement #1)

On the other hand:

The kinetic energy of an object is proportional to its mass and proportional to the square of its velocity.

Between two object with the same velocity but different masses, the heavier object will have more kinetic energy.

...

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