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 100o C and the aluminium end at 0o C. 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 junctions Cu-Ni and Ni-Al respectively
The correct option is
B
If suppose KNi=K⇒KAl=3K and KCu=6K.
Since all metal bars are connected in series
So (Qt)combination=(Qt)Cu=(Qt)Al=(Qt)Ni
and 3Keq=1KCu+1KAl+1KNi=16K+13K+1K=96K
⇒Keq=2K
Hence, if (Qt)Combination=(Qt)Cu
⇒KeqA(100−0)lCombination=KCuA(100−θ1)lCu
⇒2KA(100−0)(25+10+15)=6KA(100−θ1)25⇒θ1=83.33o C
Similar if (Qt)Combination=(Qt)Al
⇒2KA(100−0)50=3KA(θ2−0)15⇒θ2=20o C