Building a Definition for Heat - Comments

[Multiple_Authors]

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Building a Definition for Heat

Continue reading the Original PF Insights Post.

 

[Chestermiller]

"Suppose that after we have compressed the piston, we release it. Intuitively, we would expect the piston to recoil back, and this is exactly what happens; the gas expands and does [an equal amount of] work on the piston against atmospheric pressure. "

This is not quite correct. It is only correct if both the compression and expansion are done reversibly, which certainly is not the case if expansion occurs adiabatically against constant atmospheric pressure.

 

[Jeff Rosenbury]

We may not say "The body has work.", but it isn't unreasonable to ask how much work we can get out of a body.

Saying a body has heat may be clear. Or it may need some extra precision to make the meaning clear. Which depends on the context and the audience. We create formal definitions so we can be precise when needed.

Thank you for this definition.

 

[Ronie Bayron]

Analysis on boundary, surrounding and system might clear out confusions. Both work and heat are boundary phenomena. There is no work if mass or energy does not cross over higher or lower system boundary.

Potential energy is not work, but change in potential energy is Work. Like wise 500ton metals at 500 deg. C does not have heat energy unless there exist a difference of temperature in system(500 ton metal) and surrounding.

 

[Chestermiller]

Analysis on boundary, surrounding and system might clear out confusions. Both work and heat are boundary phenomena. There is no work if mass or energy does not cross over higher or lower system boundary.

In a closed system, no mass crosses the boundary of the system, but still, work can be done.

Potential energy is not work, but change in potential energy is Work. Like wise 500ton metals at 500 deg. C does not have heat energy unless there exist a difference of temperature in system(500 ton metal) and surrounding.

You are saying that heat cannot be transferred to a system unless there is a temperature gradient at the boundary, correct? Certainly, at the boundary, the temperature of the system must match the temperature of the surroundings (i.e., temperature is continuous at the boundary).

 

[Ronie Bayron]

In a closed system, no mass crosses the boundary of the system, but still, work can be done.

Yes, one example is sterling engine. Note that what I said was " mass or energy". Also my apology for stating "higher or lower system boundary." It should be higher or lower system states.

Work can be done on a close system, given that boundary either expands or collapses, otherwise it's useless. It's like heating an LPG tank, no matter how much heat you apply on it, you can't expect any work until it explodes.

You are saying that heat cannot be transferred to a system unless there is a temperature gradient at the boundary, correct? Certainly, at the boundary, the temperature of the system must match the temperature of the surroundings (i.e., temperature is continuous at the boundary).

No, it's appropriate to say at the boundary the temperature is in between hot and cold reservoir (whichever is hotter - system or surrounding or vice versa)

 

[Chestermiller]

No, it's appropriate to say at the boundary the temperature is in between hot and cold reservoir (whichever is hotter - system or surrounding or vice versa)

Temperature is a continuous function of spatial position during an irreversible change, including at the interface between conductive solids and at the interface between real world reservoirs. However, the temperature gradient (heat flux) at the interface does not have to be continuous. Do you agree with this statement?

Chet

 

[Ronie Bayron]

Temperature is a continuous function of spatial position during an irreversible change, including at the interface between conductive solids and at the interface between real world reservoirs. However, the temperature gradient (heat flux) at the interface does not have to be continuous. Do you agree with this statement?

Chet

My apology Chet, your q is quite deep. I am not sure I got 100% of what you mean. Could you rephrase or give example, perhaps?

 

[Chestermiller]

My apology Chet, your q is quite deep. I am not sure I got 100% of what you mean. Could you rephrase or give example, perhaps?

At time zero, you place a hot conductive semi-infinite solid slab in contact with an identical cold conductive semi-infinite solid slab, and let nature take its course. What do the temperature profiles look like within the two solids at times t > 0? Is the temperature a continuous function of spatial position, including at the boundary? Is the temperature gradient continuous at the boundary? Is the heat flux continuous at the boundary? What are the temperatures in the slabs far from the boundary? What are the the temperatures at the boundary?

Chet

 

[Ronie Bayron]

At time zero, you place a hot conductive semi-infinite solid slab in contact with an identical cold conductive semi-infinite solid slab, and let nature take its course. What do the temperature profiles look like within the two solids at times t > 0? Is the temperature a continuous function of spatial position, including at the boundary? Is the temperature gradient continuous at the boundary? Is the heat flux continuous at the boundary? What are the temperatures in the slabs far from the boundary? What are the the temperatures at the boundary?

Chet

The profile looks like this at the boundaries or the interface of two conducting surfaces. I'm actually lost by the term "continuous", my apology "english" is not my native tounge.

 

[Chestermiller]

The profile looks like this at the boundaries or the interface of two conducting surfaces. I'm actually lost by the term "continuous", my apology "english" is not my native tounge.

Yes. This is more like it. I just wanted to clarify what you were saying. By continuous, what I mean is that the temperature does not change by a finite amount when one crosses the boundary between the two materials.

 

[Let'sthink]

I tend to agree with the Starter, but before I read the other comments i would like to submit my composite view of work and heat by saying that both relate to transfer of energy between two systems. Heat is the transferred energy as a result of temperature difference and work is the transfer of energy where temperature is not directly involved. This kind of thinking for work and heat is most suited in the perview of Thermodynamics, which asserts that Heat and work areprocess variables and can be talked about only when two systems are involved. It release the historic mechanistic connection of work with force.

 

[DrDu]

Caratheodory, who tried first to set thermodynamics on an axiomatic basis, tried to avoid the word "heat" altogether, but it is clear that the change of internal energy can be defined as the work done in an adiabatic process, i.e. $\Delta U=W_\mathrm{adiabatic}$. Hence, heat is simply $Q=\Delta U-W$ where W is the work in a general non-adiabatic process.
Adiabaticity can be defined before defining heat or temperature by saying that the system is adiabatically isolated, if its state is independent of the surrounding.
The real content of the first law is then that the adiabatic work starting from a reference state is a state function.
This is a clear macroscopic definition of both internal energy and heat and one does not have to refer to microscopic degrees of freedom .

 

[DrDu]

I therefore, offer you a formal definition of heat:
“Heat is the non-mechanical exchange of energy between the system and surroundings as a result of a difference in temperature”

How would the Peltier effect fit in this definition?

 

[Let'sthink]

As DrDU talks of non-mechanical exchange of energy as heat, one should also consider non-mechanical work when electrical energy does the work on the system. I think that both heat and work should be dealt equivocally in the perview of Thermodynamics and then point out the essential difference. When an electric heater heats up we may losely say that electrical energy is converted to heat energy. But in the perview of Thermodynamics, Electrical energy is transferred to the heater coil increasing its internal energy raising its temperature above the surrounding which flows as heat to the surrounding. Similar arguments can be given for describing Peltier effect.

 

[DrDu]

As DrDU talks of non-mechanical exchange of energy as heat, one should also consider non-mechanical work when electrical energy does the work on the system. I think that both heat and work should be dealt equivocally in the perview of Thermodynamics and then point out the essential difference. When an electric heater heats up we may losely say that electrical energy is converted to heat energy. But in the perview of Thermodynamics, Electrical energy is transferred to the heater coil increasing its internal energy raising its temperature above the surrounding which flows as heat to the surrounding. Similar arguments can be given for describing Peltier effect.

Thats not the point I wanted to make. You don't need external coils or the like for the Peltier effect. A heat flow may also be driven by purely mechanical forces without a temperature gradient.
We know for more than 100 years by now (e.g. from the works of Pierre Curie in 1886) some basic principles of linear irreversible thermodynamics:
General currents like heat current, mass current, electrical current, chemical reactions are driven by generalized forces like temperature gradients, pressure gradients, electrical potential gradients and chemical potential gradients. The important point is now that the linear relation between currents and forces is non-diagonal, i.e. in general, e.g. a pressure difference will not only drive a mass current but also a heat current even without the slightest temperature gradient.

 

[Let'sthink]

I beg to differ DrDu. "pressure difference will not only drive a mass current but also a heat current" here. does this statement not make heat the state variable? Heat Current means heat was here and now it is there!