In the mailbag column,
http://www.straightdope.com/mailbag/memc2.html
STDSTAFF Karen mentions:
Umm… Heat Capacity (Cp, for constant pressure), not Boltzmann’s constant (k), is the converstion constant between heat energy and temperature. As in:
dq = Cp dT
(at constant P).
And, of course, also at constant P, it works out for Enthalpy (H) the same way, too:
dH = Cp dT.
Boltzmann’s constant is our bridge between configuration (statistical probability of where everything “is”) and Entropy:
S = k ln W,
where S is the configurational entropy and W is the probability that a system is in it’s most likely state. We could, of course, multiply k by Avogadro’s number (Na) and make the gas constant, R, and then relate temperature to entropy (dS = nR ln (T2/T1)), and link it eventually with our various energies (including thermal energy, q), but I think that–strictly speaking–Karen meant to say that Heat Capacity, not Boltzmann’s constant, is our conversion constant.