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Three slabs of materials 1, 2 and 3 with thermal conductivities k1 > k2 > k3 are stacked in series to form a wall, and the left face is 20 deg C hotter than the right face. The three arrangements differ only in the ordering of the slabs: (a) 1-2-3, (b) 1-3-2, (c) 3-1-2. How does the temperature drop dT across material 1 compare among the three cases?

1. dTa > dTb > dTc
2. dTa = dTb = dTc
3. dTa = dTb > dTc
4. dTa = dTb < dTc

Correct answer: dTa = dTb = dTc

Solution

All three walls are the same three slabs in series, so they have the same total resistance and the same heat current; the drop across material 1 depends only on its own resistance, which is unchanged, so the drops are equal.

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