Average kinetic energy of gases

In addition to pressure, one of the quantities that states the macroscopic nature of gas is temperature (T). Gas pressure equation:

Average kinetic energy of gases 1

Combine the equation 1 and the equation 2 :

Average kinetic energy of gases 2

Average kinetic energy of gases 3

This is the equation of the average kinetic energy of gases vs. the absolute temperature of the gas.

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Temperature is directly proportional to the average translational kinetic energy of gas molecules. The larger the temperature, the higher the average translational kinetic energy, the smaller the temperature, the lower the average translational kinetic energy. We can conclude that temperature is a measure of the average kinetic energy of the molecular translation.

Another form of the equation for the average kinetic energy of a gas:

Average kinetic energy of gases 4

n = number mol (mol), R = universal gas constant (R = 8.315 J / mol. K = 8315 kJ / kmol.K), T = absolute temperature (Kelvin), EK = the average translation kinetic energy of the molecule gas (Joule).

Average kinetic energy of gases 5

k = Boltzmann’s constant, R = universal gas constant, NA = Avogadro number, M = molecular mass, m = mass, n = number of moles.

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First, translational kinetic energy is kinetic energy possessed by objects or molecules. Translation movements can be in the form of straight motion, parabolic motion. While the rotational kinetic energy = kinetic energy possessed by objects or molecules that make the rotational motion.

Second, the average translation kinetic energy in the equation above applies only to monatomic gases. Examples of monatomic gases are He (helium), Ar (Argon), etc. In addition to monatomic gas, there are also diatomic gases. Examples of diatomic gases are O2 (oxygen), N2 (nitrogen), CO (carbon monoxide), etc. There are also polyatomic gases. For example CO2 (carbon dioxide) etc. The monatomic gas consists of only one atom; diatomic gas consists of two atoms and polyatomic gas consists of many atoms.

Third, the absolute temperature must be stated on the Kelvin (K) scale. If the temperature is still in the Celsius scale (oC), change it first to the Kelvin (K) scale.

Fourth, equation 1 and equation two above do not only apply to gas substances but also apply to liquids and gas substances.

Example problem :

What is the average translational kinetic energy of molecules in a gas at 40 °C?

Solution :

Average kinetic energy of gases 6

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