# What is the specific heat of copper through its phases?

Specific heat is the amount of heat required to change the temperature of 1 gram of a substance by 1 Celsius.

For instance, the specific heat of water in the solid phase is 2.059 J/gC and 4.184 J/gC in the liquid phase.

That being said, what is the specific heat of copper in all three of its phases (liquid, solid and gas) in J/gC st standard pressure? How would one figure this out?

The NIST Webbook is generally a good place to look for thermochemistry data. You can see here that there are data for all three phases. It looks a bit daunting, but because heat capacity is not constant with temperature, it's expressed as a Shomate equation. Basically, you find the equation that starts with $C^°_p$ and substitute the parameters from the table underneath along with the desired temperature and you can calculate the heat capacity for any temperature within the range shown at the top of the table. (note that these are molar heat capacities and you'll have to convert if you want it in terms of mass)

If you prefer, you can just click View table to get computed values at certain temperatures, which will save you the calculation.

The heat capacity of a material is a measure of the heat energy (in J) that the material (of mass M in g or moles) absorbs or releases for every unit rise or fall in temperature (in °C or K).

Whilst the heat capacity of most materials will generally be different at different temperatures and pressures, as they undergo internal structural changes with temperature, the heat capacity is generally quoted at a given temperature and pressure. These are typically quoted as 'standard conditions' (as defined by the various standard authorities around the world). For example, the National Institute of Standards and Technology (NIST) defines 'standard conditions' as 20°C and 1atm.

Now, copper is a solid below the temperature of 1358 K ​(1085°C) and has a specific heat capacity of 0.386 J/g.K or 24.5 J/mol.K (at 20°C and 1 atm).

Various empirical formulae exist which allow one to calculate the specific heat capacity of copper at other temperatures, based on measurements taken in various experiments and fitting the data to various curves such as cubic splines.

Copper is a liquid between the temperature of 1358K and 2835 K ​(2562°C) with true specific heat capacity of 0.572 J/g/K or 36.33 J/mol.K at a temperature of 1400K.

More accurate values of specific heat are given by suitable curve-fitting formulae, based on experimental data. (See: http://link.springer.com/article/10.1007%2FBF02755998)

Above it's boiling point of 2835 K ​(2562°C) copper vapourises. Copper gas has specific heat capacity of 25.14 (at 3000K) or at other temperatures, given by the Shomate Equation: $c_p(t)=A+Bt+Ct^2+Dt^3+Et^{-2}$

where

$t$ is the temperature in Kelvin / 1000

$A = -80.48635$

$B= 49.35865$

$C=-7.578061$

$D=0.404960$

$E=133.3382$

References:

http://www.nist.gov/data/PDFfiles/jpcrd263.pdf