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Boltzmann constant
Intermediate
Connects energy and temperature.
k_B = 1.38×10⁻²³ J/Kk_B = 1.381×10⁻²³ J/K links temperature to energy per particle: R = N_A k_B. kT is the characteristic thermal energy.
kT at 300 K = 4.14×10⁻²¹ J = 26 meV.
Per molecule, not per mole.
In more detail
The Boltzmann constant k, about 1.38 × 10⁻²³ J/K, links temperature to energy at the molecular level. It equals the gas constant divided by Avogadro's number.
Real-world uses
- Statistical mechanics uses k to convert temperature into energy scales.
- Noise calculations in electronics involve Boltzmann's constant.
- Engineers use Boltzmann's constant to link the energies of particles and sensors to temperature in electronics and physics.
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Frequently asked questions
Why is it so small?
Because molecular energies are tiny compared with everyday energies.
How is it related to R?
k equals R divided by Avogadro's number.
Why is the constant so small?
Because one molecule carries a tiny amount of energy compared with the joules we use in everyday life.
Related topics in Kinetic Theory & Statistical Physics
Ideal gas assumptions · Pressure from molecular collisions · Kinetic interpretation of temperature · RMS speed · Mean free path · Collision frequency