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I like Jim Green's web page, ( http://users.sisna.com/jmgreen/FirstLaw.htm
) which basically says that anything that increases entropy is "heat". By
this definition, "energy transferred because of a temperature difference"
is a subset of "heat", but "heat" also includes a paddle wheel turning. In
each of these cases, the work done microscopically from outside the system
translates into a greater kinetic energy in the gas molecules inside the
system.