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Homework Help: Heat flow in a rod

  1. Feb 22, 2013 #1
    1. The problem statement, all variables and given/known data

    A very simple problem, but part of an assignment regarding heat flow. The question is:

    A 15 cm rod is insulated at one end, the other is in contact with a reservoir of temperature 37C. By thinking of the physics, after a long time, what is the temperature at the point 5 cm and 10 cm from the insulated end?

    2. Relevant equations


    3. The attempt at a solution

    So I will say that I was sick for a while and missed a week of class. I've been catching up so I'm somewhat familiar with things. Obviously this question is very simple, but I have been thinking of the following questions:

    What does "insulated at one end" mean? It is 0 C? Does the reservoir stay at 37C forever? If so, then after a long time, the entire rod would be 37C. This is probably not the case. If the reservoir transfers and loses it's heat, then after a long time, the rod will reach a uniform, final temperature. This, however, depends on the temperature at the other "insulated" end, doesn't it? Or would the temperature distribution be 12.333 C at 5 cm, 24.666 C at 10 cm, and 37 C at 15 cm?

    Basically, since I missed some class, I am unfamiliar with some of the basic ideas that most students would have been informed about in class. So how do I figure out (by "thinking of the physics" as opposed to calculating) what the temperature will be at various points, given the information above?

    Thanks in advance for any help.
  2. jcsd
  3. Feb 22, 2013 #2
    Hi stripes :smile:

    Generally, in thermodynamic problems the term "reservoir" does in fact mean that it stays the same temperature for ever.

    Why should "insulated" imply some specific temperature (zero as you suggested)? Are you familiar with the term "adiabatic"? What does it mean?
  4. Feb 22, 2013 #3
    I just took a guess, I wasn't sure. But of course none of the heat will leave the other end of the rod.

    So given that the reservoir stays at 37C forever, the rod would eventually be 37C at every point, correct? That's just how it works, isn't it? Just like when the end of time comes, the universe will cool to 2K or whatever the figure is.
  5. Feb 22, 2013 #4
    I don't know about the universe, but your analysis of the rod problem is spot on.
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