Question

The wall of a house is made from a layer of wood 3cm thick and a layer of wool which is 5.2 cm thick. The layer of wood faces outside and the layer of wool faces inside. The thermal conductivity of wood is 0.08W/mK and the thermal conductivity of wool is 0.02W/mK. The temperature outside the house is 0oC and the temperature inside the house is 18.7 oC. What is the temperature (in oC) at the contact surface between the wool and the wooden layers?

Answer 1

The the temperature (in °C) at the contact surface between the wool and the wooden layers is T = 16.34°C

Explanation:

Thermal conductivity of wood = 0.08 W/mK

Thermal conductivity of wool = 0.02 W/mK

Temperature outside the house = 0°C

Let temperature at contact surface is T

Rate of flow of heat always remain same therefore

Rate "R" = KA∆T / l

• Where K is thermal conduction.
• Area is A
• ∆T is temperature difference.
• "l" is length of conductance.

R = 0.02 x A ( T -0) / 5.2

R =0.08 x A x (18.7 - 0 ) / 3

3T = 388.96 - 20.8 T

23.8 T = 388.96

T = 388.96 / 23.8

T = 16.34°C

Thus the the temperature (in °C) at the contact surface between the wool and the wooden layers is T = 16.34°C

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