# Entropy and temperature

1. Dec 21, 2013

### iScience

in my thermo class when we were formalizing the definition of temperature ($\frac{1}{T}$=$\frac{âˆ‚S}{âˆ‚U}$), we drew out all the combinations of various slopes and concavities of the âˆ‚S/âˆ‚U graphs.

http://imgur.com/cR4V8K8

The shape of this graph i figure should be a reflection of the inherent nature of the material. so, my question is, what properties of the material determines the shape of this graph?

Last edited: Dec 21, 2013
2. Dec 21, 2013

### itaischles

I think the graph should be monotonically increasing since the temperature is the slope. Furthermore, the second derivative should also be considered since it relates to the heat capacity.