Temperature and average translational kinetic energy of an ideal gas molecule (14-13)

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Question

Boltzmann constant

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Review

We can learn something no less important by comparing Equation 14-12 with the ideal gas law in terms of number of molecules, Equation 14-6: $pV = NkT$ , or $p = (N/V)kT$ . In order for both Equations 14-6 and 14-12 to be correct, it must be true that $(2/3)K_{\mathrm{translational,\ average}} = kT$ , or

In words, Equation 14-13 says that the average translational kinetic energy of a molecule in an ideal gas is directly proportional to the Kelvin temperature of the gas. This justifies the statement we made in Section 14-2 about the physical meaning of temperature.