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Q.

Two metallic blocks $M_{1} a n d M_{2}$ of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity $M_{2}$ is K then the thermal conductivity of $M_{1}$ will be: [Assume steady state heat conduction]

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a

12.5 K

b

10K

c

8K

d

2 K

answer is B.

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Detailed Solution

As Q = constant in series
So, $Q_{M 1} = Q_{M 2}$

$\Rightarrow \frac{(100 - 80)}{16} = \frac{80 - 0}{8} [∴ Q = \frac{T_{1} - T_{2}}{l / k A}] \Rightarrow \frac{20}{16} \times k_{1} A = \frac{80}{8} k_{2} A \Rightarrow k_{2} = \frac{20 \times 8}{16 \times 80} \times k_{1} \Rightarrow k_{2} = \frac{k_{1}}{8} \Rightarrow k_{1} = 8 k_{2} = 8 K [k_{2} = k]$

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