How does heat capacity change with temperature?

1 Answer
Truong-Son N.
Dec 7, 2015

It depends on the compound. It tends to increase as temperature increases.

For example, methane gas has a heat capacity equation:

#C_p = A + BT + CT^2 + DT^3 + E/T^2#

where #T# is the temperature in #"K"# divided by #1000#. At #298. - 1300. "K"#, we have the following values for methane only:

#A = -0.703029#
#B = 108.4773#
#C = -42.52157#
#D = 5.862788#
#E = 0.678565#
#F = -76.84376#

So if you plug in these values for a specific temperature, you get the heat capacity. If you plot this for multiple temperatures, you get essentially a hyperbolic curve.

![webbook.nist.gov)

So, over #"5200 K"#, the specific heat capacity changed by about #"70 J/mol"*"K"# (it's a gas, so that's why it changed so much).

For a liquid, as you can imagine, the change is less drastic because the entropy is much lower for a liquid than a gas, or for a solid than a liquid.

Related questions
See all questions in Specific Heat
Impact of this question
3676 views around the world
You can reuse this answer
Creative Commons License