This is highly unconventional. Being unconventional doesn't make it wrong,
but it calls for detailed explanation.
We are being given the new notions of W and Q. This raises many questions:
-- If W is work and Q is work, then W is not the total work. What symbol
shall we use to represent the total work?
-- How are W and Q related to "work" in the sense of F dot ds?
-- Does F dot ds equal W?
-- Does F dot ds equal total work?
-- Does the total work equal W plus Q, or are there other contributions?
I'm mystified. Without a great deal of additional info, I cannot imagine
how the notion
Both Q and W are _work_!
is helpful to anyone.
Jim and I agree that the usual interpretation of the
Delta E = W + Q
equation is broken, but AFAICT we have not reached agreement on how to fix
things. My recommendations can be found at http://www.monmouth.com/~jsd/physics/thermo-laws.htm