# Does heat capacity change with volume?

Jul 27, 2018

Yes; heat capacity, in units of $\text{J/"^@ "C}$, or $\text{J/K}$, is an extensive property, and does scale with volume. This is why you should watch your units.

On the other hand, specific heat capacity, sometimes given as ${c}_{s}$, in units of $\text{J/g"^@ "C}$ or $\text{J/g"cdot"K}$, is an intensive property, completely independent of the amount of substance, and depends only on its identity.

It is often seen in the equation for heat flow through a substance that causes a temperature change:

q = overbrace(m underbrace(c_s)_"Specific Heat Capacity")^"Heat Capacity"DeltaT

Thus, this quantity for water is ${c}_{s , {H}_{2} O \left(l\right)} = \text{4.184 J/g"^@ "C}$ at ${25}^{\circ} \text{C}$ regardless of the sample size, for copper is ${c}_{s , C u \left(s\right)} = \text{0.385 J/g"^@ "C}$ at ${25}^{\circ} \text{C}$ regardless of the sample size, etc.