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Kinetic theory identifies temperature with molecular motion: the average translational kinetic energy is 1.5kT, independent of the gas. At 300 K that is 6.21e-21 J, or 0.0388 eV - the origin of the kT/e = 25.9 mV thermal voltage in semiconductors. Pressure follows as NkT/V, the microscopic form of the ideal gas law.
Average kinetic energy
KE = 1.5 k T per molecule
Pressure
P = N k T / V
Because temperature is defined by energy per degree of freedom. Heavier molecules simply move more slowly to carry the same energy.
Everywhere in statistical physics - Boltzmann factors, diode equations, reaction rates. At room temperature kT is about 25.7 meV.