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JEE PHYSICS MCQ: THERMAL PROPERTIES OF MATTER

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Three slabs of thicknesses x1,x2\text{x}_1, \text{x}_2 and x3\text{x}_3 and coefficients of thermal conductivity K1,K2\mathrm{K}_1, \mathrm{K}_2 and K3\mathrm{K}_3 are placed parallel to each other in contact. In steady state the combination behaves as a single slab of material of conductivity K,\mathrm{K}, given by: (Cross section areas are same)
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Correct option: D
x1 K1+x2 K2+x3 K3=x1+x2+x3 K\frac{\mathrm{x}_1}{\mathrm{~K}_1}+\frac{\mathrm{x}_2}{\mathrm{~K}_2}+\frac{\mathrm{x}_3}{\mathrm{~K}_3}=\frac{\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3}{\mathrm{~K}}
Option D (x1 K1+x2 K2+x3 K3=x1+x2+x3 K\frac{\mathrm{x}_1}{\mathrm{~K}_1}+\frac{\mathrm{x}_2}{\mathrm{~K}_2}+\frac{\mathrm{x}_3}{\mathrm{~K}_3}=\frac{\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3}{\mathrm{~K}}) is correct because the thermal resistances add in series, and the equivalent thermal resistance is the sum of individual resistances.

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