Re: can the specific heat of a gas in a process be negative

This illustrates a common problem, which is that the term "specific heat" 
is often not clearly defined.  It refers to the energy input to a system 
corresponding to a change in temperature, but there are different 
"specific heats" corresponding to different constraints on the system.

The most common (and most useful) definitions are
Cv = dU/dT at constant volume
Cp = dH/dT at constant pressure

I believe that both of these quantities are always positive.

However, there are other "specific heats" one sees occasionally.  One is 
the specific heat defined on a path where vapor-liquid saturation 
conditions are maintained, and this can be a negative number for the vapor 
in some circumstances.  There is also something called the "polytropic 
specific heat" that one sees in very old textbooks in conjunction with 
processes such as you describe, and I think it can also be negative.

In summary, it is essential to define exactly what you mean when you use 
the term "specific heat" (or "heat capacity").  The commonly used 
quantities are always positive, but there are other "specific heats" out 
there which can cause confusion.  I once reviewed a paper for Physical 
Review E in which the author (from a distinguished institute) had fallen 
victim to some of this confusion, so don't feel too bad if it confuses you 
as an undergraduate.