An Ice-box Is Made Of Wood 1.75 Cm Thick, Lined Inside With Cork 2 Cm Thick. If The Temperature Of The Inner Surface Of The Cork Is Steady At 0oC And That Of The Outer Surface Is Steady At 12oC, What Is The Temperature Of The Surface? The Thermal Conductivity Of Wood Is 5 Times That Of Cork.                                                          

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Question

An ice-box is made of wood 1.75 cm thick, lined inside with cork 2 cm thick. If the temperature of the inner surface of the cork is steady at 0oC and that of the outer surface is steady at 12oC, what is the temperature of the surface? The thermal conductivity of wood is 5 times that of cork.

                                                         

Solution

Correct option is

10.2oC

 

Let be the temperature of the interface in the steady state. Since the rate of flow of heat through wood and cork must be the same in the steady state, we have

            

Where S is the area of the interface. Thus we have

                      

Or                  

Which gives           T = 10.2oC

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