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: Proof of heat flow direction?

  1. Jan 19, 2008 #1
    "Proof" of heat flow direction?

    Hi everyone, I have a homework problem that basically says to prove that heat is conducted from a high temperature area to a low temperature area:

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

    Consider a one-dimensional conductor, stretching from x=0 to x=L. The two ends are maintained at T_0 and T_L. The four sides of the conductor are insulated. The temperature distribution along the conductor is steady.

    q_0 represents the heat that enters through the x=0 cross section. Assume q_0 is position, so heat is conducted in the positive x-direction.

    Invoke the 2nd law to prove that q_0 flows toward lower temperatures, for example, by showing that T_L cannot be greater than T_0

    2. Relevant equations

    2nd Law of thermodynamics

    3. The attempt at a solution

    My attempt is as follows:

    I have the 2nd Law in the following form:

    http://img338.imageshack.us/img338/9004/problem11qw8.jpg [Broken]

    I have come across this equation in my text (Heat Transfer, Bejan, 1993) as well:

    http://img237.imageshack.us/img237/6189/problem12ks5.jpg [Broken]

    I wish to substitute this equation into the "q" part of the 2nd Law. From here, in order for the "dS/dt" term to be greater than or equal to zero (Entropy always increasing), the T_0 - T_L term must be greater than zero, therefore, T_0 must be greater than T_L.

    Does this make sense? I'm not sure what to do about the summation term in the form of the 2nd law that I have. Do I only pick the "0" position and forget about the "L" position?

    Thanks in advance for your help.
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Jan 20, 2008 #2


    User Avatar
    Science Advisor
    Gold Member

    Your question got me curious, so I pulled out my old statistical physics text (berkeley physics course-volume 5 by F. Reif). Heres a couple of quotes that may help?
    Last edited: Jan 20, 2008
  4. Jan 20, 2008 #3
    Thank you for the reply. I agree with the quotes you have listed, but I am unsure as to how they help. I agree that they discuss the means by which entropy increases, but I am unsure as to how the increase in entropy relates to the diffusion of heat from a high temperature area to a low temperature area.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook