That's a really interesting observation. If you mean that the coffee in
the coffee maker takes longer to cool down than the hot coffee in the
cup, that makes a lot of sense. If you mean that the coffee in the cup
cools down slower if it's from the coffee maker, I'm surprised.
The coffee maker has a big carafe (or something like that) which
also heats up as the coffee is made, and it holds more than a cup.
There isn't as much surface per volume of all that hot stuff as there
is for a single cup. Since heat leaves via the surface, you expect the
cup to cool more quickly.
There shouldn't be any difference in the 'quality of heat' of the
coffee from different sources. There can be special cases of materials
which have hidden 'degrees of freedom' (internal chemical properties,
structures of little crystals. etc) which can be different even though
the ordinary temperature is fixed. Then as those materials equilibrate,
energy is traded with those internal modes, so the initial state of
those modes affects how quickly the material cools. However, there
isn't anything like that in a cup of coffee.
You should try a carefully controlled experiment, using a
thermometer. It's important to use the same kinds of cups at the same
temperature. If it's impractical to heat up the cups to the temperature
of the coffee (say, pouring hot coffee into a cup from a coffee maker
doesn't involve heating up the cup the way sticking the cup in the
microwave will), then you should pour both kinds of heated, stirred
coffee into two cold cups (using styrofoam cups may be the easiest way
to reduce the effect of the cup temperature -- a styrofoam cup has a
very low heat capacity). Stirring helps even out nonuniformities in the
temperature distribution in the coffee. There really shouldn't be any
nonuniformities in the temperature distribution in the coffee from the
coffee maker, as these heat from the bottom and convection currents
stir the coffee already. But the coffee int he microwave may be heated
on top more than on the bottom (or maybe the other way around,
depending on the pattern of standing waves in your microwave and the
electrical conductivity of your coffee). If the microwaved coffee is
hot on top and colder on the bottom, convection won't even it out (like
the water in a lake or the ocean on a sunny day -- it's much warmer
near the surface).
(published on 10/22/2007)