Question 8

Two metallic blocks $$M_1$$ and $$M_2$$ of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of $$M_2$$ is $$K$$ then the thermal conductivity of $$M_1$$ will be : [Assume steady state heat conduction]

Steady-state condition: $$\left(\frac{\Delta Q}{\Delta t}\right)_1 = \left(\frac{\Delta Q}{\Delta t}\right)_2$$

$$\frac{K_1 A (100 - 80)}{L_1} = \frac{K_2 A (80 - 0)}{L_2}$$

$$\frac{K_1 A (100 - 80)}{L_1} = \frac{K_2 A (80 - 0)}{L_2}$$ $$\implies \frac{K_1}{8} = 10K$$

$$\implies K_1 = 80K \times \frac{16}{20 \times 8} = 8K$$

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