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**1. Homework Statement**

A thermally conducting, uniform and homogeneous bar of length L, cross section A, density p

and specific heat at constant pressure cp is brought to a nonuniform temperature distribution by contact at one end with a hot reservoir at a temperature TH and at the other end with a cold reservoir at

a temperature TC. The bar is removed from the reservoirs, thermally insulated and kept at constant pressure. Show the change in entropy is

ΔS = Cp ( 1 + ln(Tf) + (Tc/(Th-Tc))lnTc - (Th/(Th-Tc))lnTh )

**3. The Attempt at a Solution**

I am sorry in advance for my very poor english, but I am studying entropy more in-depth, however I cannot seem to understand where the double integral arises in this problem and if it can be avoided. I have done the problem, and my set-up is identical except I used a single integral only.

http://www.scribd.com/doc/12398371/Problem-Solution-Thermodynamics#scribd

The solution is here on page 50, or it might be page 61,62 for some of you.

Plain and simple, why do I need to integrate over the rod's length as well (dx) ?