Two rods, one made of copper and the other steel of the same length and cross-sectional area are joined together. The thermal conductivity of copper is $385 \,Js ^{-1} m ^{-1} K ^{-1}$ and steel is $50 \,Js ^{-1} m ^{-1} K ^{-1}$. If the copper end is held at $100^{\circ} C$ and the steel end is held at $0^{\circ} C$, the junction temperature is ........... $C$ (Assuming no other heat losses)
KVPY 2011, Medium
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(d)
Let junction temperature is $T^{\circ} C$.
Then, assuming no heat loss and steady state,
Heat flow through copper rod per second $=$ Heat flow through steel rod per second
$\Rightarrow \frac{K_{\text {Copper }} A(100-T)}{l}=\frac{K_{\text {steel }} A(T-0)}{l}$
$\Rightarrow \quad K_{\text {Copper }}(100-T)=K_{\text {steel }} \cdot T$
$\therefore$ Area and length of both rods are equal.
$\therefore$ Area and length of both rods are equal.
Substituting values, we get
$385(100-T)=50 \,T$
$\Rightarrow \quad 385 \times 100=(385+50) \,T$
$\Rightarrow \quad T=\frac{385 \times 100}{435} \approx 88^{\circ} C$
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