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What is the temperature (in $^oC$) of the steel-copper junction in the steady state of the system shown in Figure Length of the steel rod $=15.0\; cm ,$ length of the copper rod $=10.0\; cm ,$ temperature of the furnace $=300^{\circ} C ,$ temperature of the other end $=0^{\circ} C .$ The area of cross section of the steel rod is twice that of the copper rod. (Thermal conductivity of steel $=50.2 \;J s ^{-1} m ^{-1} K ^{-1} ;$ and of copper $\left.=385 \;J s ^{-1} m ^{-1} K ^{-1}\right)$
$56.98$
$44.4$
$27.15$
$90.45$
Solution
$\frac{K_{1} A_{1}(300-T)}{L_{1}}=\frac{K_{2} A_{2}(T-0)}{L_{2}}$
where $1$ and $2$ refer to the steel and copper rod respectively. For
$A_{1}=2 A_{2}, L_{1}=15.0 cm$
$L_{2}=10.0 cm , K_{1}=50.2 J s ^{-1} m ^{-1}$$K ^{-1}, K_{2}=385 J$
$s ^{-1} m ^{-1} K ^{-1},$ we have
$\frac{50.2 \times 2(300-T)}{15}=\frac{385 T}{10}$
which gives $T=44.4^{\circ} C$
