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Question: Answered & Verified by Expert
Two metal cubes $A$ and $B$ of same size are arranged as shown in the figure. The extreme ends of the combination are maintained at the indicated temperatures. The arrangement is thermally insulated. The coefficients of thermal conductivity of $A$ and $B$ are $300 \mathrm{~W} / \mathrm{m}^{\circ} \mathrm{C}$ and $200 \mathrm{~W} / \mathrm{m}^{\circ} \mathrm{C}$, respectively. After steady state is reached, the temperature of the interface will be

PhysicsThermal Properties of MatterJEE Main
Options:
  • A $45^{\circ} \mathrm{C}$
  • B $90^{\circ} \mathrm{C}$
  • C $30^{\circ} \mathrm{C}$
  • D $60^{\circ} \mathrm{C}$
Solution:
2128 Upvotes Verified Answer
The correct answer is: $60^{\circ} \mathrm{C}$
Temperature of interface $T=\frac{K_1 \theta_1+K_2 \theta_2}{K_1+K_2}$
$=\frac{300 \times 100+200 \times 0}{300+200}=60^{\circ} \mathrm{C}$

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