# heat capacity constant pressure versus constant volume?

#### [email protected]

##### Member
10+ Year Member
I am having issues understanding a chapter in the EK Physics book in Lecture 5 on Heat Capacity, Phase Change and Colligative Properties. On page 80, they discuss that a constant heat capacity at constant pressure C(p) is greater than constant volume C(v). I agree that at constant pressure, a substance can absorb energy with less change in temperature by expelling some of the energy to the surroundings as work whereas with constant volume all energy goes into heat and may contribute to temperature change.

The next paragraph confuses me though: For a solid or liquid, both of which experience very little change in volume, there is a more important reason why constant volume and pressure heat capacities differ. The intermolecular forces of a solid or liquid are much stronger than those of a gas. Small changes in the intermolecular distances of noncompressible phases result in large changes in intermolecular potential energy. Intermolecular potential energy does not affect temperature, and thus heat is absorbed at constant pressure with less change in temperature than when heat is absorbed at constant volume. Again: C(p) is greater than C(v).

I am confused because the volumes of solids and liquids are more consistent than that of a gas and are less compressible, thus arent their volumes considered to be more constant in relation to gas volumes. I think the paragraph is saying that energy is energy is absorbed as large changes in intermolecular potential energy in solids and liquids but intermolecular potential energy does not affect temperature. In this case, wouldnt C(v) be greater than C(p). I am confused. Can someone help me clear this up? Has EK confused me with another typo?

#### Gauss44

##### Full Member
5+ Year Member
I interpreted that to mean that if the energy doesn't go toward changing the volume (and doesn't go toward intermolecular potential energy), it has to go somewhere else. That somewhere else can be toward a change in temperature. And that more energy can go toward changing the volume of a gas (or toward intermolecular potential energy of a gas) compared to a solid or liquid which is why gas can be more resistant to changing temperature.

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