# Heat Capacity Numerical Problem

1. Mar 10, 2013

### YAHA

1. The problem statement, all variables and given/known data

I am working on a problem for my Thermal Physics course. In short, its a numerical problem. I had to go through some Excel calculations and end up with two columns of numbers. One, C/Nk, where C-heat capacity, k-boltzmann constant, N-number of particles and the other is kT/eps, where k-Boltzmann constant, T-temperature, eps-some unit of energy. I have sets of numbers in both of these columns, so I can plot C/Nk as a function of kT/eps.

Then, I am am given an experimentally measured C(T) for some real materials and asked to estimate(roughly) the constant eps for each of the materials. How do I go about this? Any hints? I have tried doing some numerical methods, but end up with a mess. There has to be some quick and simple way.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Mar 11, 2013

### Staff: Mentor

Assuming that only $C$ depends on $T$, you can write
$$\frac{C}{Nk} = a \frac{k T}{\epsilon},$$
where $a$ is some proportionality constant. On your graph of $C/Nk$ vs $k T/\epsilon$, find some point where you can find an approximate value for $a$ (hint: the steeper the slope, the smaller the error).

Then, do the same for the experimental values, with $\epsilon$ the unknown, instead of $a$.