# How does heat capacity change with temperature?

Dec 7, 2015

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

For example, methane gas has a heat capacity equation:

${C}_{p} = A + B T + C {T}^{2} + D {T}^{3} + \frac{E}{T} ^ 2$

where $T$ is the temperature in $\text{K}$ divided by $1000$. At $298. - 1300. \text{K}$, 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 $\text{5200 K}$, the specific heat capacity changed by about $\text{70 J/mol"*"K}$ (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.