

Energy in a System
Name: Michael
Status: educator
Grade: 912
Country: USA
Date: Spring 2012
Question:
I am a high school chemistry teacher with a quick question about entropy, which may be only one of semantics  I am hoping you might be able to help. . I think the problem boils down to if we consider all the energy in a system (E=mc2), can all that be turned into work? The details are this:
In discussing entropy, the isothermal, free expansion of a gas into a vacuum is an often used example (q=0,w=0). After the gas has expanded numerous texts and web sites (an MIT web site in this case) explains that " some ability to do work has been lost" and that "the property that is used to measure the change in ability to get work out of a system (delta)T is the entropy." ( http://web.mit.edu/16.unified/www/FALL/thermodynamics/thermo_7.htm )
SO (sorry for the long intro) What is the definition then of energy? If energy is the "capacity to do work", and the total energy of the system did not change during a free gas expansion (is that true?), but it has less capacity to do work then I am confused. How can the capacity to do work go down, but the energy remain the same? Energy IS the capacity to do work after all... is not it? Even if I expand the definition and say energy is the capacity to do work or release heat, q=0 for the isothermal expansion, so it is irrelevant. How can the capacity to do work go down, but the energy remain the same?
Probably I am misunderstanding the definition either of energy or work (maybe the energy can still do work, just not practical or directional work)... If so, how should I be defining energy? Any help or insight would be greatly appreciated. Again, I know it is likely semantics, but I would like to pin it down.
Replies:
I will let the chemists give a more detailed answer to this one. From a physics point of view, energy is a conserved quantity that flows when there is a change.
Also, Gregg Swackhamer has written an excellent article on some of the misconceptions of work.
http://modeling.asu.edu/modeling/MakingWorkWork.pdf
Nathan A. Unterman
Hi Michael,
There are two concepts here: internal energy  the invented term to keep track of changes in the energy of a system as a function of heat and work, and entropy  a measure of the energy that is not available to do work.
In defining deltaE as equal to q + w, and in an adiabatic expansion against a vacuum, q = 0 and w = 0, then, yes the internal energy of the system has not changed. However, in that expansion, the entropy of the system increased, so while internal energy has remained the same, a portion of that energy is now not available to do work.
Maybe I am not clear, internal energy and entropy are independent variables, just because one goes up or down, does not mean the other does also.
Take, for example, solution formation. For this process, w=0, but it can be endothermic (+q) or exothermic (q) [This, by the way, is why we speak of enthalpy of solution formation and not internal energy of solution formation.] However, whether the solution formation is endo or exothermic, the entropy of the system increases (there are more microstates in the system when solute and solvent molecules can be randomly arranged). So, here is an example of the system's "ability to do work" decreasing  regardless of whether the system gained or lost energy.
Whether the system has high or low energy (E), increased or decreased in energy (deltaE), does not mean that the energy is available for use (S).
Greg (Roberto Gregorius)
Canisius College
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Update: June 2012

