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Change of variables in heat equation

  1. Dec 4, 2009 #1
    dTB/dt = -k(TB-TM).
    TM is held constant.

    (TB-TM) = Q, so:
    dTB/Q = -kdt.

    How would I change this equation so that instead of integrating wrt to TB, I can instead integrate wrt Q?
  2. jcsd
  3. Dec 4, 2009 #2


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    That's a simple "linear" substitution. Since TB= Q+ TM, dTB/dt= dQ/dt. Your equation becomes just dQ/dt= -kQ.
  4. Dec 6, 2009 #3
    Wow, I really should've been able to do that myself. Thanks a lot though, thats a big help
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