Heat Flow at Equilibrium

Name: Rachel
Status: student
Grade: 9-12
Location: IL

Question: Is it possible for heat to flow between two objects with
the same internal energy?
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Yes.  But the amount of energy flowing in each direction is equal so,
there is no net flow between the bodies.

R. Avakian
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Rachel,
It is possible because internal energy is not temperature.  Two objects
of different size or different material can have the same internal
energy but different temperatures.  When in contact, heat will flow from
the object with the higher temperature to the object with the lower
temperature.

One thing to remember here is that "heat flow" as stated is a total
effect.  In reality, some heat does flow from cold to hot, but much more
will flow from hot to cold.  The total effect is heat from the hotter
object to the colder object.

Dr. Ken Mellendorf
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The answer is absolutely yes! The driving force for heat transfer is
temperature, not internal energy. Internal energy is an 'extensive property'
-- which means it depends on the amount of material present. Internal energy
includes not only the kinetic energy of molecules (related to temperature),
but also the potential energy stored in chemical bonds. If you double the
amount of a given material, you also double the internal energy. Temperature
is an 'intensive property' -- it does not depend on the amount of material
present. If you have material of a given temperature, it is the same
temperature if you add or take away the same material. So, if you have two
materials at the same temperature, there is no driving force for heat
transfer. However, you can have two materials with different temperatures,
but the same internal energy, and there would be heat transfer. The two
materials will be in thermal equilibrium when they reach the same
temperature, not the same internal energy.

Hope this helps,
Burr Zimmerman
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Sure it is possible.  Heat flows from objects at high temperature to
objects at low temperature.  Internal energy is an extensive quantity:
it depends on how much stuff you have.  So for the simplest example,
let us say you have a kilogram of water and ten kilograms of water, each
with the same internal energy.  Which has the higher temperature?  The
one-kilogram sample!  So it will transfer heat to the ten-kilogram
sample, given the chance.

Richard Barrans, Ph.D., M.Ed.
Department of Physics and Astronomy
University of Wyoming

PS
I guess i was not very clear in describing my scenario.  Internal energy 
E is basically total energy of the sample.  The first law of thermodynamics

Delta E = q + w 

is a conservation of energy statement: the change in internal energy E is 
equal to the heat added to the system q plus the work done on the system w.  
So yes, if you have a one-kilogram sample of water and a ten-kilogram sample 
of water both at the same temperature, the ten-kilogram sample will have more 
internal energy and can melt more ice cubes (or, in my preferred demonstration, 
boil more liquid nitrogen).

In the scenario I described in my previous response, I was proposing a case in 
which two samples had different masses but the same internal energy, so the one 
with the least mass had more energy per mass.  More concretely, If you place a 
hot cup of tea in contact with an iceberg, the tea will transfer heat to the 
iceberg, even though the iceberg has much greater internal energy due to its 
much greater mass.  Perhaps that would have been a better illustration to 
begin with.

Rich Barrons
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Hello,

Yes, it is possible for heat to flow between two objects with the same 
internal energy. Heat will flow if there is a temperature different 
between the two bodies, from the warmer one to the colder one, regardless
of internal energies.

The relation between temperature and internal is not a simple one. It is 
complex because internal energy is the sum of a number of forms of energy 
that molecules in a body have  (such as the kinetic energy due to the 
(translational, rotational, vibrational) motion of molecules, the potential 
energy of the molecules, the energy in all the chemical bonds, etc.) whereas 
temperature is related to only one of these energies, namely the translational 
kinetic energy. So, two bodies can have an identical internal energy but 
tremendously different temperatures (with heat flowing from the warmer one 
to the colder one irrespective of their internal energy).

Consider, for example, the example of a hot stream of gas passing over 
cooler water. Water heats up even though liquids, such as water, generally 
have a lot more internal energy than a gas. Thus, not only heat can flow
 from two objects with the same internal energy, but also actually heat 
 can flow from one with a lower internal energy to one with higher internal 
 energy.

Ali Khounsary, Ph.D.
Advanced Photon Source
Argonne National Laboratory
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