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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

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`R_(Al)=(L)/(KA)=(1)/(10^-4xx200)=(10^4)/(200)`
Similary `R_("steel")=(10^4)/(50)` and `R_("copper")=(10^4)/(400)`
Let temperature of common junction be T. Then from Kirchhoff's current laws,
`i_(A1)+i_(steel)+i_(Cu)=0`
`implies(T-12)/(R_A1)+(T-51)/(R_(steel))+(T-4)/(R_(Cu))=0`
`implies(T-12)200+(T-50)50+(t-4)400`
`implies4(T-12)+(T-50)+8(T-4)=0`
`implies13T=48+50+32=130`
`impliesT=10^@C`
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