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A rod of length L is perfectly insulated on its sides and made of a material whose thermal conductivity varies with temperature as K = alpha/T, where alpha is a constant. Its ends are held at temperatures T1 and T2 with T2 > T1. Find the steady-state rate of heat flow per unit area along the rod.

1. (alpha/L)*ln(T2/T1)
2. (alpha/L)*(T2 - T1)
3. (alpha/L)*ln(T1/T2)
4. (alpha/L)*(T2/T1)

Correct answer: (alpha/L)*ln(T2/T1)

Solution

With K = alpha/T, integrating q dx = alpha dT/T across the rod gives q = (alpha/L)*ln(T2/T1).

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