Two Rods A and B of Different Materials Are Welded Together As Shown In Fig. If Their Thermal Conductivities Are k1 and k2 , The Thermal Conductivity Of The Composite Rod Will Be                                                         

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Question

Two rods A and B of different materials are welded together as shown in Fig. If their thermal conductivities are k1 and k2 , the thermal conductivity of the composite rod will be

                                                        

Solution

Correct option is

 

 

If the ends of the rods are maintained at temperatures  and , the rate of flow of heat through each rod is given by

                          

 And                  

Where A is the cross-sectional area of each rod and d is the length of each rod. Now the cross-sectional area of the composite rod is 2A. If k is the thermal conductivity of the composite rod, the rate of heat flow is

                           

But                       Therefore

     

or                      ).

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