Boltzmann constant

The Boltzmann constant (k or kB) is the physical constant relating temperature to energy.

Role in relating temperature to energy

Given a thermodynamic system at an absolute temperature T, the thermal energy carried by each microscopic "degree of freedom" in the system is on the order of magnitude of kT/2. Room temperature, 300 K (27 °C or 80 °F), corresponds to a kT/2 of 2.07 × 10−21 J, or 13 meV.

Related Topics:
Thermodynamic - Absolute temperature - Order of magnitude - Room temperature - C - F - MeV

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In classical statistical mechanics, homogeneous ideal gases possess

Related Topics:
Classical - Statistical mechanics - Ideal gas

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kT/2 per degree of freedom per atom. Monatomic ideal gases possess 3 degrees of freedom per atom, corresponding to the three spatial directions, which means a thermal energy of 1.5kT per atom. As indicated in the article on heat capacity, this corresponds very well with experimental data. The thermal energy can be used to calculate the root mean square speed of the atoms, which is inversely proportional to the square root of the atomic mass. The root mean square speed at room temperature ranges from 1370 m/s for helium, down to 240 m/s for xenon. The situation is more complicated for molecular gases; diatomic gases, for example, possess approximately 5 degrees of freedom per molecule.

Related Topics:
Atom - Heat capacity - Root mean square - Atomic mass - Helium - Xenon

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