Question

How does heat capacity change with temperature?

Answer 1

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.

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.