Boltzmann's constant

Also called k_B, Boltzmann constant

Boltzmann's constant sets the energy per kelvin in a single atom's average kinetic energy, 1.38 times 10 to the minus 23 joules per kelvin. It is the per-atom counterpart of the universal gas constant.

Per atom, rather than per mole. That is the whole distinction between kBk_B and RR, and it decides which form of a thermodynamics equation to reach for. The AP Physics 2 table of information prints

kB=1.38×10−23 J/Kk_B = 1.38 \times 10^{-23}\ \text{J/K}

and it turns up in three lines of the sheet's thermal physics box: PV=NkBTPV = Nk_BT, Kavg=32kBTK_{\text{avg}} = \tfrac{3}{2}k_BT and U=32NkBTU = \tfrac{3}{2}Nk_BT. In each one, what sits beside it is a count of atoms, NN, or a single atom.

A number for it. At T=300T = 300 K,

Kavg=32(1.38×10−23)(300)=6.2×10−21 JK_{\text{avg}} = \tfrac{3}{2}(1.38 \times 10^{-23})(300) = 6.2 \times 10^{-21}\ \text{J}

which is 0.0390.039 eV using the sheet's 1 eV=1.60×10−191\ \text{eV} = 1.60 \times 10^{-19} J. That is about sixty times smaller than the 2.32.3 eV a green photon carries, which is why a room-temperature object radiates in the infrared rather than in visible light.

The link to RR is one multiplication by Avogadro's number, since a mole is N0N_0 atoms:

R=N0kB=(6.02×1023)(1.38×10−23)=8.31R = N_0k_B = (6.02 \times 10^{23})(1.38 \times 10^{-23}) = 8.31

Mind the subscript. The sheet writes kBk_B with one because a bare kk elsewhere on the same page is the Coulomb constant, 9.0×109 N⋅m2/C29.0 \times 10^9\ \text{N} \cdot \text{m}^2/\text{C}^2, and kk again is thermal conductivity in Q/Δt=kAΔT/LQ/\Delta t = kA\Delta T/L. Three constants, one letter.

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