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Homework Help: Rate of entropy generation (can it be negative?)

  1. Mar 28, 2012 #1


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    1. The problem statement, all variables and given/known data

    The Clausius inequality combined with the defintion of entropy yields an inequality known as the increase of entropy principal, expressed as

    Sgen ≥ 0

    where Sgen is the entropy generated during a process.

    2. Relevant equations

    Sgen ≥ 0

    3. The attempt at a solution

    I know that Sgen cannot be negative, but can the rate of Sgen, [itex]\dot{S}_{gen}[/itex] be negative?
  2. jcsd
  3. Mar 28, 2012 #2
    I do believe. You mean the entropy generates fast at first and slow later. Why not.
  4. Mar 28, 2012 #3


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    That was my thought but I wasn't sure as this whole entropy thing is rather new to me.

    I reasoned that if a car going 50mph slows down to 40mph, it still has a positive velocity, but the velocity derivative (acceleration) is negative. Likewise, Sgen's time rate of change can be negative although entropy generated overall can only be positive. Test on Friday... I hope I'm right!
  5. Jun 26, 2012 #4
    Thermodynamics (Equilibrium) neither entertains (asks) nor answers questions concerning the rates of processes. Rates of processes is irrelevant to find answers to questions in thermodynamics. Once the initial and final states of a system are defined, the process connecting them could be of any rate (could be infinitely fast/slow), the result of the entropy change will be the same.
    It would perhaps be better to write the equation as delta S universe greater than or equal to zero instead of Sgen greater than or equal to zero, to reduce possible ambiguity and misinterpretations.
  6. Jun 26, 2012 #5
    I think what Radhakrishnam is alluding to here is that the constrained form of the Clausius inequality described by you in the OP applies to a closed, adiabatic system (i.e., an isolated system). The entire universe can be regarded as a closed, adiabatic system. The more general form of the Clausius inequality, applicable to closed (but not necessarily adiabatic) systems is dS > dq/T.
  7. Jun 26, 2012 #6


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    That is true. Fair enough. But aside from that, I want to know what happens along the way, not just at the endpoints. If it's not under the umbrella of thermodynamics, in what area of science may my question be asked?

    Entropy Generation Definition:
    Entropy generated (Sgen) during a process is a measure of the irreversibilities of that process.

    Lets say you have a device that is rougher in one area than another and when the parts move in the device, more friction occurs as the parts make contact with the rough area.

    The rate of entropy generation would be positive through this rough patch because the device introduces more irreversibility (friction) here. Then as your parts go back to moving smoothly and they are not touching the rough area, the friction subsides and the rate of entropy generation would be negative.

    Does this make sense? This would make it sound like the rate of entropy generation could be negative.
  8. Jun 27, 2012 #7
    Thermodynamics gives whether a given process under given conditions is possible or impossible, in principle. when a process is known to be possible, the rate at which it is possible to carry out that process in practice depends upon the kinetics which takes into account the presence of catalysts, for example, etc. But that would not help in finding out the rate of generation of entropy.

    Thermodynamics is much simpler to understand and appreciate than what it is projected to be in many books.
  9. Jun 27, 2012 #8
    Here are some suggestions on how to begin to get a handle on what you are looking for:

    1. Bird, Steward, and Lightfoot "Transport Phenomena" has a homework problem that looks at entropy generation in non-equilibrium continua.

    2. Look up non-equilibrium thermodynamics in Wikipedia

    3. Get a book on Statistical Thermodynamics, and get an idea how entropy is expressed in terms of the total number of quantum mechanical states available. Then start looking at how the molecular dynamics guys use statistical thermo to quantify entropy (and other thermodynamic entities) in systems that are not at equilibrium.
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