Heat Capacity at Constant Volume or Pressure
Most recent answer: 12/15/2019
- George Kourtis (age 54)
In beginning courses we show the difference between Cp and Cv as simply coming from the work an ideal gas does as it expands. That's fine for ideal gases but it misses most of the story for liquids. (This very issue made for some interesting discussions as a group of us worked on the materials for a thermal physics course, because we had to learn it ourselves.)
Let's say you heat the liquid at fixed volume, measuring Cv. Not let it expand (or contract!) isothermally doing work (maybe negative!) until its internal pressure matches what the initial pressure was.You know for sure that the work done can't be the only term in the energy flow, because if it were then for liquids that happen to contract when heated (like water between 0° and 4° C) you'd end up with Cp < Cv. That would violate a theorem. For the liquid the internal energy of all the strongly interacting particles also depends strongly on volume. It's that change that gives most of the difference between Cp and Cv.
As for the match between Cp of the gas and Cv of the liquid, I think that's a coincidence, although I'm not sure.
(published on 12/15/2019)