Does heat capacity change with volume?

Answer 1

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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Answer 2

Serenity Allen

No, heat capacity does not change with volume. Heat capacity is an extensive property that depends on the mass and specific heat capacity of a substance, but not on its volume.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.