In reading my own message, posted an hour ago, I see that
something is missing. So let me add it now.
It is true that we never know which part of dU, gained by an
object, came in the form of d'Q and which came in the form
of d'W. This is like not knowing which part of water in the
Atlantic Ocean came from which river. Or like not knowing
which part of dU came as d'Q from object A and which came
as d'Q from object B. Why should this be an argument
against saying that heat is a form of energy?
Should we go one step further and say that mechanical, or
any other, work is also a form of energy? My work of 200
joules done against friction becomes heat and my work of
800 joules , done at the same time against gravity, becomes
potential energy. Exactly 1000 joules of chemical energy
was lost (step by step) by my body in the process of pulling
this sled uphill. First it was chemical energy, then it was
work, and finally it became heat and potential energy. Why
should this interpretation be rejected? What is wrong with
saying that work and heat are forms of energy?
I guess what some will answer this question by pointing
out at the time factor. Chemical energy existed in my body
up to a moment at which it was converted into thermal energy
and into potential energy. Therefore no time is left for it to
exist in the form of d'Q and d'W. I will accept this argument;
dQ' and d'W are very special in that respect. That is why we
should not call them exact differentials.