A few problems I have with this article as it stands now== 

 Neither the word equilibrium, nor the word reversible appears in the article. It needs to mention that all definitions involving heat are true only for a reversible transformation, probably voicing it more than the small addition I had left last time, and which was removed. The other definition involving S is true in the differential sense as long as a transformation goes from an equilibrium state to another (not necessarly pasing through a series of equilibrium states), which is the "normal" situation as far as thermodynamics are concerned, so that extra care isn't, I think, needed in this case. Another option is to mention delta Q not as the amount of heat exchanged in an imaginary reversible tranformaiton, rather than the amount of heat actually exchanged by the system, but I don't find this very satisfactorly. 

 The formula at the start should also mention that this is for incompressible bodies. We can either say incompressible, or say "for a liquids and a solids," at the start, introducing incompressibility later. That should remain quite simple. 

 Otherwise C can be derived as a partial derivative of the internal energy. 

 : I agree we should be clear about the importance of reversibility. 

 : With regard to compressible vs. incompressible - I think this article should be about the thermodynamic concept of heat capacity. It should NOT be about the special case of heat capacity for incompressible bodies. On the other hand, to start out with complete generality may not be the best idea, because it can be difficult for a beginner to grasp. I think the introduction could start out by introducing the concept of heat capacity without the idea of holding N-1 parameters constant where N is the dimension of the thermodynamic space you are working in. Then, the introduction could point out the difficulties encountered with the simplistic view when dealing with compressible bodies, and introduce Cp and Cv. Then finally, it could point out the fact that N-1 parameters must be held constant. 
 :where to speak of this is in the "thermodynamics equations" article 

 :I don't think it is too much of a problem to then write the subsequent sections in terms of Cp and Cv  as a compromise between simplicity and generality. A one-dimensional thermodynamic space is too simple, it leaves out too much. Almost all the wikipedia thermodynamics articles are written assuming a 2-dimensional space (P-V or P-T or whatever) and we should do the same. Incompressible bodies have a separate section. A final section could introduce  heat capacities  for spaces with more dimensions as the final generalization. 

 ::Another option is to make the final generalization in the thermodynamics equations article. One I'll edit, but first I have others to finish.Just mention in this article that for the expressions are different for a body who exchanges work with the outside in another form than pressure work.  

 I have a question, since this has become the last place where one speaks: do van der waals effects play a big role for hydrogen, oxygen and nitrogen? Or, are they just half-classical half-quantum ideal gas (depending on the degree of freedoms you are looking at)? We'll need to get that info for the diatomic ideal gas article, so I wondered if someones already knows. It's easy to write bullshit on such questions.  

 Hydrogen, oxygen and nitrogen can be liquefied and solidified. Ideal gases can't. So the nonideal effects play a big role at low temperature.   

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