According to the kinetic molecular theory, the average kinetic energy of gas particles is proportional to the absolute temperature of the gas. This can be expressed using the following equation, where k represents the Boltzmann constant. The Boltzmann constant is simply the gas constant R divided by Avogadro’s constant (NA).
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Kinetic Energy of Gas Formula
The kinetic energy of ideal gas is given as E=3/2KT, where E is the average kinetic energy of the gas, T is the temperature of the gas in Kelvin, and K is the Boltzmann constant, whose value is 1.381×10−23m2⋅kg⋅s−2⋅K−1 = 1.381×10−23J/K.
Important Points
- The temperature of a gas can be related to the internal motion of the molecules.
- The average kinetic energy of a gas molecule is KE=(3/2)×KT where K is the Boltzmann constant.
- KE=(3/2)×1.381×10−23J/K×273K=5.66×10−21J.
- The average kinetic energy of gas particles is proportional to the absolute temperature of the gas, and all gases at the same temperature have the same average kinetic energy.
- The mass of one molecule (m) can be calculated from Avogadro’s number (NA) and the Molecular mass of gas (M) with the relation: m = M/NA.