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Two rods, one of iron and another of alu...

Two rods, one of iron and another of aluminium of equal length and equal cross-sections are connected with each other. The free end of the iron rod is kept at `100" "^(@)C` and the free end of aluminium rod is kept at `0" "^(@)C`. If thermal conductivity of aluminium is four times that of iron, find the temperature of their contact surface in the thermal steady state.

Text Solution

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`((dQ)/(dt))_(Fe)=((dQ)/(dt))_(Al)`
`:.(KA[100-T_(x)])/(L)=(4KA[T_(x)-0])/(L)`
`:.100-T_(x)=4T_(x)`
`:.5T_(x)=100`
`:.T_(x)=20" "^(@)C`
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