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A composite wall of a furnace has 3 layers of equal thickness having thermal conductivities the ratio of 1 : 2 : 4. What will be the temperature drop ratio across the three respective layer
  • a)
    1 : 2 : 4
  • b)
    4: 2: 1
  • c)
    1 : 1 : 1
  • d)
    log 4 : log 2 : log 1
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A composite wall of a furnace has 3 layers of equal thickness having t...
From the fourier law of heat conduction
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A composite wall of a furnace has 3 layers of equal thickness having t...
Solution:

Given, a composite wall of a furnace has 3 layers of equal thickness having thermal conductivities the ratio of 1 : 2 : 4.

Let the thickness of each layer be 'x' and the temperature difference across the wall be 'ΔT'.

Let Q be the amount of heat flowing through the composite wall.

The rate of heat flow is given by,

Q = (k1A/ x)ΔT1 = (k2A/ x)ΔT2 = (k3A/ x)ΔT3

where A is the area of cross-section.

Let the temperature difference across the first layer, second layer and third layer be ΔT1, ΔT2 and ΔT3 respectively.

We know that,

ΔT1/ x = Q/ (k1A)

ΔT2/ x = Q/ (k2A)

ΔT3/ x = Q/ (k3A)

Dividing the above equations, we get

ΔT1/ ΔT2 = k1/ k2

ΔT2/ ΔT3 = k2/ k3

Multiplying the two equations, we get

ΔT1/ ΔT3 = (k1/ k2) * (k2/ k3) = k1/ k3

Thus, the temperature drop ratio across the three respective layers is 4 : 2 : 1, which is option B.
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