Is temperature inversely related to the average kinetic energy of a gas?

Answer 1

In an ideal gas of monatomic particles, the average kinetic energy is

<K>=(3/2)*k*T

In a more general ideal gas, the average energy of each particle is

<K>=(d/2)*k*T

where d is the number of degrees of freedom. There isn't a clear distinction between kinetic and potential energy for general degrees of freedom.

For normal (non-negative) temperatures, as temperature increases, so does energy. The exact relation depends on the entropy of the system.

T=dU/dS, where d is the partial derivative.

http://en.wikipedia.org/wiki/Equipartition_theorem

http://en.wikipedia.org/wiki/Ideal_gas

Answer 2

The expression for gas pressure developed from kinetic theory relates pressure and volume to the average molecular kinetic energy. Comparison with the ideal gas law leads to an expression for temperature sometimes referred to as the kinetic temperature.

This leads to the expression

The more familiar form expresses the average molecular kinetic energy:
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It is important to note that the average kinetic energy used here is limited to the translational kinetic energy of the molecules. That is, they are treated as point masses and no account is made of internal degrees of freedom such as molecular rotation and vibration. This distinction becomes quite important when you deal with subjects like the specific heats of gases. When you try to assess specific heat, you must account for all the energy possessed by the molecules, and the temperature as ordinarily measured does not account for molecular rotation and vibration. The kinetic temperature is the variable needed for subjects like heat transfer, because it is the translational kinetic energy which leads to energy transfer from a hot area (larger kinetic temperature, higher molecular speeds) to a cold area (lower molecular speeds) in direct collisional transfer.

Answer 3

KE = (3/2)kT, where k is the constant of proportionality.

Answer 4

Temperature is a measure of the average molecular kinetic energy of a substance. They are one and the same.