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Question

A composite metal bar of uniform section is made up of length 25 cm of copper, 10 cm of nickel and 15 cm of aluminium. Each part being in perfect thermal contact with the adjoining part. The copper end of the composite rod is maintained at 100 and the aluminium end at 0. The whole rod is covered with belt so that there is no heat loss occurs at the sides. If KCu=2KAl and KAl=3KNi, then what will be the temperatures of CuNi and NiAl junctions respectively.


A
Temperature of CuNi is 78.26
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B
Temperature of NiAl is 26.08
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C
Temperature of CuNi is 50.3
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D
Temperature of NiAl is 53.40
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Solution

The correct options are
A Temperature of CuNi is 78.26
B Temperature of NiAl is 26.08

If suppose KNi=KKAl=3K and KCu=6K

Since all metal bars are connected in series

So (Qt)combination=(Qt)Cu=(Qt)Al=(Qt)Ni

and l1+l2+l3Keq=l1KCu+l2KAl+l3KNi=256K+153K+10K

Keq=6023K

Hence, if (Qt)Combination=(Qt)Cu

KeqA(1000)lCombination=KCuA(100θ1)lCu

60KA(1000)23(25+10+15)=6KA(100θ1)25θ1=78.26C

Similar if (Qt)Combination=(Qt)Al

60KA(1000)23×50=3KA(θ20)15θ2=26.08C

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