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If you check the 5th edition of Serway & Beichner, you'll find that heat is
basically treated as a process, in effect, as a verb. "Heat is the transfer
of energy from one object to another object as a result of a difference in
temperature between the two." pg 581. You can <I>heat</I> an object and
increase its internal energy. Chapter 20 relates the difference between heat
and internal energy to the difference between work and mechanical energy.
You don't talk about the work <I>of</I> a system, just as you shouldn't talk
about the heat of a system.