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The outer face of a rectangular slab of ...

The outer face of a rectangular slab of equal thickness of iron and brass are maintained at `100^(@)C` and `0^(@)C`, respectively. Find the temperature of the interface. The conductivities of iron and brass are 14 and `126 Wm^(-1) K^(-1)` respectively.

Text Solution

Verified by Experts

The correct Answer is:
`[10^(@)C]`
If T is temperature of the interface of iron and brass slabs, then
`(dQ)/(dt)=K_(1)(A(100-T))/(Delta x) =(K_(B)A(T-0))/(Delta x)`
or `K_(1)(100-T)=K_(B)T`
or `(100-T)/(T)=(K_(B))/(K_(1))=(126)/(14)=9` or `T=10^(@)C`
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Knowledge Check

  • The outer faces of a rectangular slab made of equal thickness of iron and brass are maintained at 100^(@)C and 0^(@)C respectively. The temperature at the interface is (Thermal conductivity of iron and brass are 0.2 and 0.3 respectively)

    A
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    `40^(@)C`
    C
    `50^(@)C`
    D
    `70^(@)C`

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    B
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    C
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    D
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  • Three metal rods made of copper, aluminium and brass, each 20 cm long 4cm in diameter, are placed end to end with aluminium between the other two. The free ends of copper and brass are maintained at 100 and 0^(@)C respectively. Assume that the thermal conductivity of copper is twice that of aluminium and four times that of brass. The approximately equilibrium temperatures of the copper-aluminiu and aluminium-brass junctions are respectively.

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    B
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    D
    `86^(@)` and `57^(@)C`

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