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COMEDK · Physics · 12. Thermal Properties of Matter

A block of metal A is connected in series with another block of metal B such that the two metal blocks have the same area of cross sections. The thermal conductivity of metal A is K and the free end of metal A is at \(80^{\circ} \mathrm{C}\). The temperature of the interface is \(60^{\circ} \mathrm{C}\) and the free end of metal B is at \(20^{\circ} \mathrm{C}\). Assuming the two metals have the same thickness, the conductivity of metal B is:

  1. A \(2 K\)
  2. B \(\dfrac{K}{2}\)
  3. C \(\dfrac{K}{4}\)
  4. D \(4 K\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\dfrac{K}{2}\)

Step-by-step Solution

Detailed explanation

In a steady state, the rate of heat flow through two blocks connected in series is the same. Let \(A\) be the cross-sectional area and \(L\) be the thickness of each block. The rate of heat flow \(H\) is given by \(H = \dfrac{KA(T_1 - T_2)}{L}\). For metal A, the temperature…
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