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Three identical rods of length 1m each, ...

Three identical rods of length `1m` each, having cross-section area of `1cm^(2)` each and made of Aluminium, copper and steel respectively are maintained at temperature of `12^(@)C, 4^(@)C` and `50^(@)C` respectively at their separate ends. Find the temperature of their common junction.
`[K_(Cu) = 400 W//m-K, K_(AI) = 200 W//m-K, K_("steel") = 50 W//m-K]`

Text Solution

Verified by Experts

` R_(Al) = (L)/(KA)=(1)/(200xx10^(-4)) = 10^(4)/200`
Similarly `R_(steel) = 10^(4)/50` and ` R_(copper)= (10^(4))/(400)`
Let temperature of common junction = `T`
then from Kirchoff,s current laws, `i_(Al) + i_(steel) +i_(Cu) =0`
` implies (T-12)/(R_(Al)) + (T-51)/R_(steel) + (T-4)/R_(Cu)=0`
` implies (T-12)200+(T-50)50 +(T-4)400=0`
`implies 4(T-12)+ (T-50) + 8(T-4)=0`
` implies 13T=48+52+32=130`
` implies T=10^(@)C`
` (##ALN_PHY_C07(I)_S01_010_S01.png" width="80%">
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