Mastering Heat Capacity Equations for Accurate Temperature Control

[kokos]

I have a problem with heat capacity of different materials. i know that heat capacity is the mount of energy needed in order to rise the temperature of a material by 1 degree, but i also know that different amount of energy is needed to rise the temperature from 0 to 1 degree and different amount of energy is needed to rise the temperature from 100 to 101 degrees.

i know that there are equations that describe the heat capacity of different materials in different temperatures but i can't find any of them.

please help!

 

[nasu]

Yes, the heat capacity depends on temperature. In some materials may be approximately constant over a range of temperature.
To find the explicit dependence you need to decide what "material" are you interested in. There is no general formula valid for everything.
In crystalline solids is pretty much constant around room temperature and decreases for low temperatures. For ideal gas is constant (as long as the gas is ideal).

 

[kokos]

I totally agree with you.
Actually the material I'm interested in is copper. i was looking for a website or something where i can find the equation for the change of heat capacity as a function of temperature.
I would be grateful if you could help me.

Thanks

 

[nasu]

If you are looking for an analytical formula which woks for any temperature I am afraid you may not be able to find one. The models for specific heat produce some integral that has to be calculated numerically in general. For specific temperature domains it can be approximated by an analytical formula. But even then it will have some parameters that may not be easy to find.
You can also take experimental data and try to fit a curve to it. You will end up with some empirical formula that may be what you need.
Data for copper between 6 K and 400 K is given for example here:
http://www.sciencedirect.com/science/article/pii/S0021961404001223

 

[kokos]

thanks a lot!