Boltzmann constant
A fundamental constant k_B = 1.38 × 10⁻²³ J/K relating the energy scale of individual particles to temperature. It appears in kinetic theory equations and statistical mechanics. k_B = R/N_A where R is the gas constant.
Formula
kB = R/Nₐ = 1.38 × 10⁻²³ J/K
Real World
Engineers designing the James Webb Space Telescope used the Boltzmann constant to calculate the thermal energy of detector noise, requiring cooling to −233 °C to suppress it.
Exam Focus
Use kB for per-particle calculations and R for per-mole calculations; mixing the two is the most common error in kinetic theory questions.
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