Does heat capacity change with volume?

1 Answer
Truong-Son N.
Jul 27, 2018

Yes; heat capacity, in units of "J/"^@ "C", or "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 "J/g"^@ "C" or "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_2O(l)) = "4.184 J/g"^@ "C" at 25^@ "C" regardless of the sample size, for copper is c_(s,Cu(s)) = "0.385 J/g"^@ "C" at 25^@ "C" regardless of the sample size, etc.

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