The resultant of a experimental run of a force (N) vs temperature (K) gives me a slope of 0.0039x - 1.0929. The slope has a (∂f/∂T)l = (∂S/∂l)T
Equation (11) attached as PNG file
We can obtain all the quantities of the right side of Eq. (11) by studying the force at difference temperatures for given extensions. A plot of f versus T has a slope (∂f/∂T)l and the intercept gives the energy change with length at a given T. As we have seen, the term -(∂f/∂T)l = (∂S/∂l)T gives the entropy change with length at a given T. It is thus possible to investigate whether f is determined principally by (∂U/∂l)T or (∂S/∂l)T
The Attempt at a Solution
My issue is really just trying to figure out what wins. the intercept i'm assuming is the ∂U of energy they are talking about, and that the slope at a given temperature that overcomes the intercept energy and that would be the tipping point where force is determined by one and not the other. I'm assuming that the negative intercept is our restoring force.
So am I correct in this line of thinking, or am I way off?