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Consider a solid block of unit thickness for which the thermal conductivity decreases with an increase in temperature. The opposite faces of the block are maintained at constant but different temperatures: $T(x=0)>T(x =1)$. Heat transfer is by steady state conduction in $x$-direction only. There is no source or sink of heat inside the block. In the figure below, identify the correct temperature profile in the block.

  1. $I$
  2. $II$
  3. $III$
  4. $IV$
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