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Question

The ends of copper rod of length 1 m and area of cross section 1 cm2 are maintained at 0C and 100C. At the centre of the rod there is a source of heat of power 25 W. Thermal conductivity of copper is 400 W/m-K. In steady state, the temperature at the section of rod at which source is supplying heat, will be

A
150.50C
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B
325.75C
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C
206.25C
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D
126.25C
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Solution

The correct option is C 206.25C
According to the energy balance, the rate of heat generated would be equal to the rate of heat conducted through the rod at steady state.



Hence we can write,
25=H1+H2
25=kA0.5(T100)+kA0.5(T0)
25×0.5400×1×104=2T100
2T=12504+100
T=206.25C

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