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Time to reach thermodynamic equilibrum

  1. Oct 31, 2006 #1
    I always wondered why time wasn't more of an issue in thermodynamics. for example, if I have a metal at temperature 600 Kelvin. How would one go about calculating the time it took to reach thermal equailibrium if I put the same metal in an enviornment at 300 Kelvin?
    What would the time to reach thermal equilibrium be a function of?
    how come this question is not addressed in most intro physics books on thermo?

  2. jcsd
  3. Oct 31, 2006 #2
    It usually is. Most intro book I see cover thermal conductivity.


    However, in cases such as what you proposed -- there can be alot of variation. If I run my car for an hour up to operating temp, it will take alot longer to cool off on a -30F calm day than on a -30F windy day. Eventually the car will be at -30F, but because the immediate air around the warm parts wouldn't be moving as much and thus it will be warmer, the gradient is changed.

    But, the link I provided should give you a good estimate as to the time it will take for your metal to cool.
  4. Oct 31, 2006 #3


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    Because it is not as easy as you think, and defeats the whole purpose of presenting basic physics at the Intro level. The rate of heat loss depends on the thermal conductivity coefficient of a material (i.e. the material's property), the geometry of the object (i.e. how much surface area to volume ratio), the volume of the object, the specific heat, etc.. etc. In other words, you will be distracted from the basic physics of thermodynamics if you have to tackle such a thing.

    There are plenty of simplified scenario that we present in intro physics. Don't believe me? Why don't you look at the magnetic field from a circular loop of wire. You'll notice that you are always asked about the field along the axis of the loop, never anywhere off axis, as if it doesn't exist. Why do you think that is?

    If we were to give you the whole thing in one shot, you'll never get out of intro physics alive.

  5. Oct 31, 2006 #4
    thanks a lot.
    as to question about magnetic field off the axis-whats the answer?
    or good websites would be great also

  6. Oct 31, 2006 #5
    I think you end up with elliptic integrals in your solution, look up Chapter 5.5 of the third edition of Jackson's E&M book.

    Basically, what happens when you remove high symmetry is you get much tougher math problems. Most E&M problems, when they can even be written in a relatively simple form, have solutions in terms of expansions of spherical harmonics or Bessel functions or some other such thing, and even THOSE solutions are tractable because the problem has some symmetry to it.

    The point that ZapperZ is making, in his gruff way, is that at the introductory level it's more important for you to study the physics than it is to worry about the math. At the higher levels you get to see the math, but it's important that you become fluent in mathematics along the way so that, when you see an infinite series of special functions, you just shrug and say "Oh, that's just expansion in spherical harmonics" rather than being some horrific thing.
  7. Oct 31, 2006 #6


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    For a mechanical engineering major, heat transfer is typically a senior-year level course.
  8. Oct 31, 2006 #7
    Because that is by definition, NOT thermodynamics.

    Thermodynamics deals with steady state equilibrium processes. Heat transfer deals with the transient analysis.
  9. Nov 1, 2006 #8


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    Right, good point - and thermodynamics is taught first. Kinda like how statics is taught before dynamics.
  10. Nov 1, 2006 #9
    Ok i read the wiki article and it helped a lot. but i want to learn to calculate the time.
    let's take a simplified model:
    say we have a rectangular solid with
    volume 2 by 13 by 2 meters=52 m^3
    Surface area = 2lw + 2lh + 2wh= 2*2*3+ 2*2*4 + 2*3*4= 52 m^2
    Volume/Surface area= 1
    The wind speed is 3 m/s everywhere.
    the rectangular solid is somehow cooled to 10 kelvin and then immediately introducted to a region with temperature 300 kelvin.
    we can take the mass of the solid to be 1 kg and the specific heat of the material to be 377 J/kg/Kelvin -> brass
    is there anything else i need to get the time?
    how would one go about doing this problem?
  11. Nov 2, 2006 #10
    Sorry, but the explination is above you right now. The answer is there is no 'one' method to solving this problem. It is going to depend on many factors, such as: flow conditions, thermal resistivity, can you assume lumped capacitance? Do you want an analytic solution? An engineering solution?

    Point being, just wait until your in a heat transfer course. If I just tell you the answer it would be pointless with no background.
    Last edited: Nov 2, 2006
  12. Dec 1, 2006 #11
    What’s about the fluctuation theorem. It is seem to be valid on the non-equilibrium stationary state. Does anyone can explain me for this theorem?
  13. Dec 10, 2006 #12
    It seems cyrusabdollahi was taking thermodynamics to mean specifically equilibrium thermodynamics. The fluctuation theorem is indeed applicable to systems both close to and far away from equilibrium. It is similar to the Green-Kubo relations, but with the addition that it applies to situations far away from equilibrium. The fluctuation theorem simply gives us the probability that entropy will flow in the opposite direction predicted by the second law in a system that is away from equilibrium over a finite time.
  14. Dec 10, 2006 #13
    Many thanks for your explanations, Lonewolf. By the way, could you please recommend me some books to read to understand this theory, because as I know, this is a new theory, which has recently been given by Evans, Cohen and Morris in 1993? Is this true?
  15. Dec 10, 2006 #14
    Yes, those are the guys who came up with the idea. The reference for the original article is Physical Review E 50: 1645–1648., 1994. As for books, I can't think of any that contain a kind of exposition of the theory. There's a review article published somewhere, but I can't remember in which journal or in what year it was published, so I'll dig through my pile of papers and get back to you.

    EDIT: The review paper can be found at http://www.ingentaconnect.com/content/tandf/tadp/2002/00000051/00000007/art00001 [Broken]
    Last edited by a moderator: May 2, 2017
  16. Dec 11, 2006 #15
    Thank you once more time, Lonewolf. However, I can find these papers with the aids of some of my friends, so you don't need to waste your time for it. Wish you all the best.
    Last edited by a moderator: May 2, 2017
  17. Dec 11, 2006 #16


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    I think you mean "thermostatics" a.k.a. equilibrium thermal physics. "Thermodynamics" should refer only to nonequilibrium thermal physics. It's a shame this misusage of terms is still present in textbooks. Perhaps (most) physicists don't like etymology.:frown:

    Thermal conductivity is a transport phenomenon. It can be tackled nicely with the aid of nonequilibrium statistical physics, either classical or quantum.

  18. Mar 20, 2008 #17
    I have the same question as posted before by blumfeld0.
    I want to calculate the time needed for an metal block to reach its thermal equilibrium if I put it in a thermal chamber at -55 deg then at 85 deg.
    I am a mechanical engineer, so please go ahead and explain. I am sure I'll understand whatever you have to say about heat transfer.
  19. Mar 21, 2008 #18
    Well,I think you can use the molecular dynamics to solve this problem.Set the Hamiltonian such as fpu model,phi-4model...,and then calculate the diffusion coefficient by fourier's law.BTW,if you do like this,you can find that abnormal diffusion is emerged in 2D and 1D.
    needing more details you can google with the keywords"thermal conduction" in APS.
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