An external house wall is built from two layers placed in contact over the entire…

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

Problem

An external house wall is built from two layers placed in contact over the entire area: • Layer 1: brick, thickness

12\,\text{cm}

, thermal conductivity

0.8\,\text{W}\,\text{m}^{-1}\,\text{K}^{-1}

• Layer 2: expanded polystyrene insulation, thickness

3.0\,\text{cm}

, thermal conductivity

0.03\,\text{W}\,\text{m}^{-1}\,\text{K}^{-1}

The inner face of the wall is at

25\,^{\circ}\text{C}

and the outer face is at

5\,^{\circ}\text{C}

. The wall area is

15\,\text{m}^2

. (i) Derive an expression for the equivalent thermal conductivity of two slabs joined face to face. (ii) Using the derived expression, determine the overall rate of heat loss through the described wall. (iii) If the house owner can either double the thickness of the brick layer or of the insulation layer, which choice will reduce the heat loss more? Support your conclusion with calculations.

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