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Two bars of thermal conductivities K and...

Two bars of thermal conductivities `K` and `3K` and lengths `1 cm` and `2 cm` respectively have equal cross-sectional area, they are joined lengths wise as shown in the figure. If the temperature at the ends of this composite bar is `0^(@)C` and `K^(2)//l` respectively (see figure), then the temperature `phi` of the interface is

A

`50^(@)C`

B

`100/3.^(@)C`

C

`60^(@)C`

D

`200/3.^(@)C`

Text Solution

Verified by Experts

The correct Answer is:
C
Temperature of interface
`theta = (K_(1)theta_(1)l_(2)+K_(2)theta_(2)l_(1))/(K_(1)l_(2)+K_(2)l_(1)) = (Kxx0xx2+3Kxx100xx1)/(Kxx2+3Kxx1)`
`=(300K)/(5K) = 60^(@)C`.
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