# Understanding the concept of temperature vs. mean energy/heat capacity of a system

I need help understanding a concept in thermodynamics.

1. What is the relationship between temperature and mean energy?

2. What is the relationship between temperature and heat capacity?

What I know:

$$B=\frac{1}{kT}$$, where $B$ is the temperature parameter.

$$dB=\frac{-dT}{kT^2}$$

$$\bar E = -\frac{d(lnZ)}{dB}$$, where $\bar E$ is the average energy of the system.

I related the 2 values using the 2 equations and simplified:

$$\bar E \sim -T^2$$

Was this on the right track? Also, can the same thing be done for heat capacity?

• your derivation is wrong..see the rule for multiplication of partial derivatives.. – Bruce Lee Feb 8 '16 at 4:43
• @BruceLee I edited my question. – whatwhatwhat Feb 8 '16 at 17:29