Heat flow from P to QdtdQ=12KA(T−10)Heat flow from Q to SdtdQ=1KA(400−T)At steady state heat flow is same in whole combination12KA(T−10)=KA(400−T)2T−20=400−T3T=420T=140∘
Temp of junction is 140°CTemp at a distance × from end Pis Tx=(130x+10∘)Change in the length dx is dydy=αdx(Tx−10)0∫Δydy=0∫1αdx(130x+10−10)Δy=[2αx2×130]01Δy=1.2×10−5×65Δy=78.0×10−5m=0.78mm