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Two bars of thermal conductivities K and 3K and lengths I 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 $\frac{K^{2}}{l}$ respectively (see figure), then the temperature $φ$
of the interface is

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50°C

60°C

$\frac{100}{3} ° C$

$\frac{200}{3} ° C$

answer is C.

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Detailed Solution

Temperature of interface

$θ = \frac{K_{1} θ_{1} l_{2} + K_{2} θ_{2} l_{1}}{K_{1} l_{2} + K_{2} l_{1}} = \frac{K \times 0 \times 2 + 3 K \times 100 \times 1}{K \times 2 + 3 K \times 1}$

= $\frac{300 K}{5 K} = 60 ° C$

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