Answer 1:
It's a very good question and I will try to do it
bit by bit.
The answer to your first question
involves the ease at which heat is transferred by
air vs. copper. Air it turns out is a horrible
conductor of heat. Engineers often take advantage
of this.
If you go out by a decent thermos
bottle for coffee and you saw it in half you will
find two walls separated by air with a few joints
for stability. Because the air can't conduct heat
well, the thermos can keep the coffee hot for
hours. The same is true for double panned windows
for houses in which two sheets of glass are
separated by a small amount of air. This design
can save a significant amount of money in heating
costs.
Copper on the other hand is an
incredible good thermal conductor. We actually use
in my research on LEDs and Lasers. Both types of
devices heat up as they work which reduces the
efficiency of the devices and decreases their
reliability. By placing the devices on small
pieces of copper the heat is removed
rapidly.
your are quite right that heat is the
average kinetic energy of a substance, average
translational energy IE the motion of the
particles, in a gas the particles have kinetic
energy, and move about chaotically, and
collectively this energy is the substance's heat
energy/internal energy.
In air, the particles
are free to move as described above. In the
copper, the total heat energy of the particle is
described by the average energy of the particles,
which I suppose are vibrating, not moving about
translationally.
The answer to the next part
of your question really depends on your
experimental set up.
For instance, how much
air is there, is the hot plate still being heated.
The best way to think about the problem is how
much thermal energy is there at the very
beginning. Unless you add to that energy, change
its form, or remove it, you will always have that
energy. No more and no less. So if you had a
100 gram plate, and 1 gram of air. Given enough
time the air and plate would eventually come to
equilibrium in which they have the same amount of
thermal energy, i.e. the same temperature. In
this case the plate wouldn't change temperature
very much.
As a back of the envelope
calculation: (100*86 + 1*80)/101 = 85.94. But if you
had your whole house of air it would go the other
way and the plate would cool to the temperature of
the air. This happens all the time when cooking
and you withdraw a pot from the stove. It all
comes down to thermal conductivity. An
example of
this, say it was really cold last night and you
leave a plastic bucket, and a metal bucket
outside. Eventually they both reach the air's
temperature. If you pick one up which feels
colder? The metal bucket, because it is a good
thermal conductor it can suck your thermal energy
away much faster. But eventually it you held onto
them both, each would draw the same amount of
thermal energy. (Assuming right balance of sizes
etc.) Just one does it faster than the other.
In relation to the last part of the question -
the same thing applies for water as air except for
two things. It is denser which means that it can
absorb more energy per volume, and it has a higher
thermal conductivity, which means it will suck the
heat faster. But thermal equilibrium will still
be reached.
Very good question and I hope this
helped.
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