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In the figure, ABC is a B conducting rod whose lateral surfaces are insulated. The length of the section AB is one-half of that of BC, and the respective thermal conductivities of the two sections are given in the figure. If the ends A and C are maintained at 0⁰C and 70⁰C respectively, the temperature of junction B in the steady state is

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30⁰C

60⁰C

40⁰C

50⁰C

answer is A.

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Detailed Solution

Heat currents in both the rods are equal.

or $H_{C B} = H_{B A}$

or $\frac{θ_{C} - θ_{B}}{(2 l / 3 K A)} = \frac{θ_{B} - θ_{A}}{(l / 2 K A)}$

$∴ \frac{3}{2} (70 - θ_{B}) = 2 (θ_{B} - 0)$

or $θ_{B} = 30^{\circ} C$

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