Relation between Boltzmann's constant $k$ and Avogadro's number? In an online lecture series on statistical mechanics, Leonard Susskind made a passing comment about how Boltzmann's constant is related to Avogadro number, hence why they are the same order of magnitude. Does anyone have any further information about this? I can't see how the two are linked.  
 A: The product of the Boltzmann constant $k_B$ and the Avogadro constant $N_A\approx 6.022 \times 10^{23}\:\rm mol^{-1}$ (not the Avogadro number, which is the same but without the $\rm mol^{-1}$ qualifier) is equal to the molar gas constant:
$$
R = k_B N_A.
$$
The molar gas constant is the constant that shows up in the ideal gas law when it is expressed as $PV = nRT$, with $n$ the amount of gas particles in the volume (i.e. the number of moles in the gas).
This is the form of the ideal gas law that relates most closely with human-sized units (i.e. pressure and volume in SI units, temperature in Kelvin, and amount of gas in moles, where one mole is a decently-human-sized amount of gas), so its value in SI units has a value that is reasonably close to unity:
$$
R \approx 8.3\: \rm J \: mol^{-1} \: K^{-1}.
$$
As Susskind points out, since $N_A$ and $k_B$ need to multiply into a numerical value close to unity in SI units, their individual orders of magnitude is of similar order, with $N_A$ huge and $k_B$ tiny.
