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