Kinetic theory

The kinetic theory of gases is a theory that explains the macroscopic properties of gases by consideration of their composition at a molecular level.

Temperature

The above equation tells us that the product of pressure and volume per mole is proportional to the average molecular kinetic energy. Further, the ideal gas equation tells us that this product is proportional to the absolute temperature. Putting the two together, we arrive at one important result of the kinetic theory: average molecular kinetic energy is proportional to the absolute temperature. The constant of proportionality is 3/2 times Boltzmann's constant, which is the ratio of the gas constant R to Avogadro's number (independent of the gas). This result is related to the equipartition theorem.

Related Topics:
Mole - Ideal gas equation - Temperature - Boltzmann's constant - Gas constant - Avogadro's number - Equipartition theorem

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Thus the kinetic energy per kelvin is:

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• per mole 12.47 J
• per molecule 20.7 yJ = 129 μeV

At standard temperature (273.15 K) we get:

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• per mole 3406 J
• per molecule 5.65 zJ = 35.2 meV

Examples:

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• hydrogen (molecular mass = 2): 1703 kJ/kg
• nitrogen (molecular mass = 28): 122 kJ/kg
• oxygen (molecular mass = 32): 106 kJ/kg