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 $0\,^oC$ and $100\,^oC$ respectively (see figure), then the temperature $\varphi $ of the interface is......... $^oC$
Medium
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Temperature of interface
$\theta=\frac{\mathrm{K}_{1} \theta_{1} l_{2}+\mathrm{K}_{2} \theta_{2} l_{1}}{\mathrm{K}_{1} l_{2}+\mathrm{K}_{2} l_{1}}=\frac{\mathrm{K} \times 0 \times 2+3 \mathrm{K} \times 100 \times 1}{\mathrm{K} \times 2+3 \mathrm{K} \times 1}$
$=\frac{300 \mathrm{K}}{5 \mathrm{K}}=60^{\circ} \mathrm{C}$
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