# Why use dimensionless heat capacity?

Perhaps this is blindly obvious, but in typical discussions of statistical mechanics (with, say, constant volume) one often finds that, rather than using the heat capacity

$$C_V = \frac{\partial E}{\partial T}\bigg|_V = T\frac{\partial S}{\partial T}\bigg|_V,$$

(where the 2nd equality comes from the 1st Law of Thermodynamics), the dimensionless heat capacity

$$\hat{C}_V = \frac{C_V}{Nk}$$

(where $N$ is the # of particles in the system, and $k$ is the Boltzmann constant) is introduced and used instead. So.... why? How is the dimensionless version more useful than the original?

• This explains the choice to use the specific heat $c_v = C_V/N$, but doesn't really explain why Boltzmann's constant is thrown in there. – dmckee Feb 22 '17 at 17:26