Two metallic blocks M₁ and M₂ of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of M₂ is K then the thermal conductivity of M₁ will be :
[Assume steady state heat conduction]

Solution

Physics sir · 4 steps

In steady state the same heat current flows through both blocks, so set KΔ T/L equal for the two.

1. Read the figure. M₁ is 16 cm long, running from 100 °C to the 80 °C junction, so Δ T₁ = 20 °C. M₂ is 8 cm long, running from 80 °C to 0 °C, so Δ T₂ = 80 °C.
2. Same heat current. In steady state no heat piles up at the junction. The heat per second H = (KA Δ T)/L is therefore the same in both blocks, and the area A cancels.

   (K₁ × 20)/16 = (K × 80)/8

3. Solve. The right side is 10K and the left side is 1.25 K₁. So K₁ = 10K/1.25 = 8K.
4. So. The thermal conductivity of M₁ is 8K, which is option (b).

The idea to keep. For blocks in series, the heat current is common, so KΔ T/L is equal across each block. A small temperature drop over a long block means that block conducts very well.

Answer from the NTA final answer key. Solution by PrepWiser.