book_cover_big.gifRecently I got a few questions from Dr.  Wang who read my book. I believe that his questions are excellent and that the answers to his questions will help other readers of this blog site as well to understand entropy. I had some e-mail exchanges with Dr. Wang and I am happy that he agreed that I post parts of our conversation.

 Question: Is heat the ONLY energy form being of dispersion? In addition to heat, do we know one more energy form being of the ability to dispersion?

Answer: Heat, being fundamentally atomic or molecular in nature through vibrations, translations and rotations (remember the simple ideal gas result that 1/2 mv2 = 3/2kT), is indeed a form of energy that is very abundant. Thus in many energy transformations it is difficult to prevent that some part of the energy is transformed in heat! Once heat is generated it is difficult to prevent that part of it leaks away into the environment.

The dispersion of energy refers to the tendency of energy to spread out in space. Indeed for heat this will happen because the atoms and molecules can propagate heat their movements to their neighbors: a bar of iron will conduct the heat from the hot end to the cold end till the temperature is even across the bar. Dispersion is not limited to heat only, for example electromagnetic radiation or magnetic fields will spread out as well.

Question: Is it possible to have entropy increase during the transformation of energies without the involvement of heat, for example, between two non-heat energies?

Answer: Yes, the best example I can come up with are fuel cells. In the cell you convert chemical energy directly in electrical while the entropy of the entire system will increase. But, and that is important, because no heat is directly involved the efficiency of a fuel cell in generating electricity can be much higher then conventional power plants.

Another example can be found in my book on page 173. There you can see how the expansion or mixing of a gas in an isolated system will lead indeed to a higher entropy. Thus the entropy of a system can increase without any change in energy of that system.

A related phenomenon in this respect is the Demon of Maxwell. I have spent a few words on that extremely unraveling thought experiment in the book as well.

Question: Is entropy more fundamental than energy?

Answer: This is a real interesting question, I never thought about that. I would say that energy represents a quantity that never changes and must be therefore quite fundamental. This is basically the First Law of thermodynamics. Entropy says something about the quality of that energy quantity. As long as entropy increases (or can increase) there are gradients (of energy of temperature or of species concentrations) present. As long as gradients are present, life is possible. Thus from that point of view entropy is perhaps the more fundamental one (at least from our planet’s viewpoint) because the presence of energy alone is not enough to enable life. Life needs energy gradients.

Question: Will the increase in entropy SURELY lead to the transformation efficiency less than 100%?

Answer: Here we need to be careful how we phrase this. Since energy is constant, transformations from one form to the others must be 100%. However, if our objective is to transform a given quantity of energy fully into another single form (for instance heat into work) then the increase in entropy will certainly limit the transformation efficiency as an amount TΔS will be no longer “available” to us as that amount has become more “diffuse”.

Question: How about the transformation among energies without the involvement of heat?

Answer: See my remark above for the fuel cells.

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Copyright © 2007  John Schmitz