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MJCfromCT
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"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:
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
2nd Law of thermodynamics
My attempt is as follows:
I have the 2nd Law in the following form:
http://img338.imageshack.us/img338/9004/problem11qw8.jpg
I have come across this equation in my text (Heat Transfer, Bejan, 1993) as well:
http://img237.imageshack.us/img237/6189/problem12ks5.jpg
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.
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:
Homework Statement
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
Homework Equations
2nd Law of thermodynamics
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
I have come across this equation in my text (Heat Transfer, Bejan, 1993) as well:
http://img237.imageshack.us/img237/6189/problem12ks5.jpg
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.
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