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


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