A rustic cabin has a floor area of 3.50 m × 3.00 m. (is walls, which are 2.50 m tall, are made of wood (thermal conductivity 0.0600 W/m · K) 1.80 cm thick and are further insulated with 1.50 cm of a synthetic material. When the outside temperature is 2.00 °C. it is found necessary to heat the room at a rate of 1.25 kW to maintain its temperature at 19.0°C. Calculate the thermal conductivity of the insulating material. Neglect the heat lost through the ceiling and floor. Assume the inner and outer surfaces of the wall have the same temperature as the air inside and outside the cabin.

Solution 113P Step 1 : In this question we need to find thermal conductivity of the insulating material Data given Area of cabin A = 2{( 3.50 m × 3.00 m) + (3.50 × 2.50 m) + (3.00 m × 2.50 m) } A = 53.5 m 2 Thermal conductivity of wood k = w.0600 W/m K Thickness of cabin w = 1.80 cm = 0.18 m 1 thickness of insulated material = w 1.50 cm 2 The total thickness of the cabin will be w 1 w =21.80 cm + 1.50 cm = 3.3 cm = 0.033 m dQ Rate of heat required dT = 1.25 W/m K Maximum temperature T = 19 C In Temperature outside the cabin T = 2 C O