1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Thermodynamics resistance proof

  1. Feb 9, 2009 #1
    1. The problem statement, all variables and given/known data
    Prove that thermal resistance is additive in series

    2. Relevant equations
    where R=L/k

    3. The attempt at a solution

    For two slabs in thermal contact where TC is the outside cold temperature and TH is the outside hot temperature


    The A's cancel out, and after a bit of math, I've gotten the equation down to


    How can I get rid of the T's with no subscript and just be left with R1+R2 on the right side?
  2. jcsd
  3. Feb 9, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Try considering an energy balance at the point between the two slabs.
  4. Feb 9, 2009 #3
    Are you suggesting that these slabs are in dynamic thermal equilibrium? If so, are you suggesting that I simply equate the two heat currents? I will not have "R" involved in my expression then, only R1 and R2...
    I truly want to understand this. Thank you.
  5. Feb 9, 2009 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Yes, the equation applies to steady state conditions only.
  6. Feb 9, 2009 #5


    User Avatar
    Homework Helper

    I'd approach it more simply.

    Heat Flow = ΔT/R

    So R*Heat Flow = ΔT

    The heat flow of R1 is then R1*H = ΔT = (Ti - T1)

    And through R2 is R2*H = (T1 - T2)

    Heat flow for the system then is

    R1*H + R2*H = (Ti - T1) + (T1 - T2) = Ti - T2

    If Rtotal*H for the system is Ti - T2, then Rtotal is (R1 + R2)
  7. Feb 10, 2009 #6
    Thank you very much! That is a lot more straightforward than how I was trying to prove it.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook