# Boltzmann's Constant

**URL:** <https://boards.straightdope.com/t/boltzmanns-constant/19145>\
**Category:** Cecil's Columns/Staff Reports\
**Created:** [May 10, 2000, 6:28pm UTC](https://boards.straightdope.com/t/boltzmanns-constant/19145 "2000-05-10T18:28:28Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![Yossarian](https://avatars.discourse-cdn.com/v4/letter/y/9de0a6/32.png) [@Yossarian](https://boards.straightdope.com/u/Yossarian)\
**Post date:** [May 10, 2000, 6:28pm UTC](https://boards.straightdope.com/t/boltzmanns-constant/19145/1 "2000-05-10T18:28:28Z")

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In the mailbag column,

[http://www.straightdope.com/mailbag/memc2.html](http://www.straightdope.com/mailbag/memc2.html)

STDSTAFF Karen mentions:

> [@](#):
>
> The c2 is a conversion constant just as m/2 is the conversion constant between kinetic energy and speed2, mg is the conversion constant between potential energy and location, and Boltzmann’s constant k is the conversion constant between heat energy and temperature.

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.