A wall is to be insulated with two layers: an inner layer of glass wool ( ) and an…

PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

A wall is to be insulated with two layers: an inner layer of glass wool (k1=0.040 W m−1 K−1k_1 = 0.040\,\text{W m}^{-1}\,\text{K}^{-1}) and an outer layer of wood (k2=0.12 W m−1 K−1k_2 = 0.12\,\text{W m}^{-1}\,\text{K}^{-1}). The total available thickness for insulation is 8.0 cm8.0\,\text{cm}. The wall area is 3.0 m23.0\,\text{m}^2, and the steady temperature difference across the wall is expected to be 25 K25\,\text{K}. The heat transfer rate must not exceed 45 W45\,\text{W}. (i) Derive an expression for the heat transfer rate in terms of the individual layer thicknesses. (ii) Using the condition on total thickness, calculate the required thickness of the glass wool layer so that the heat-transfer limit is satisfied. Give your answer in centimetres.

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