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A wall has two layers A and B ach made of different materials. Both layers have the same thickness. The thermal conductivity of the material of A is twice that of B. Under thermal equilibrium, the temperature difference across the wall is 36∘C. The temperature difference across the layer A is:
- a)21º C
- b)35º C
- c)12º C
- d)57º C
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A wall has two layers A and Bach made of different materials. Both lay...
Consider two walls 'A' and 'B' of thickness 't' each, and thermal conductivity of ' 2K ' and 'K' respectively.
The temperatures at the left of A=Ta, The temperatures at the right of B=Tb, The temperature at the junction
= T.
The temperatures at the left of A=Ta, The temperatures at the right of B=Tb, The temperature at the junction
= T.
Heat flow is a constant in steady state:
Equating heat flow for both walls we get:
Which simplifies to: 
Also given that the temperature difference between the walls is 36º C
Combining the two equation in T,Ta,Tb and eliminating Tb
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Community Answer
A wall has two layers A and Bach made of different materials. Both lay...
Understanding the Problem
To analyze the temperature difference across two layers in a wall, we need to apply the concept of thermal conductivity and heat conduction.
Given Information
- Layer A has thermal conductivity (kA) = 2 * kB (where kB is the thermal conductivity of layer B).
- The total temperature difference across the wall (ΔT_total) = 36°C.
Key Concepts
- The heat transfer through the layers can be expressed using Fourier's law of heat conduction:
Q = (k * A * ΔT) / d, where Q is the heat transfer rate, A is the area, ΔT is the temperature difference, and d is the thickness.
Temperature Differences in Layers
- Let the temperature difference across layer A be ΔTA and across layer B be ΔTB.
- Since both layers are of equal thickness (d), the ratio of the temperature differences will be inversely proportional to their thermal conductivities.
Setting Up the Ratios
- Since kA = 2 * kB, we can write:
ΔTA / ΔTB = kB / kA = 1 / 2.
- This implies ΔTA = (1/2) * ΔTB.
Using Total Temperature Difference
- We also have:
ΔTA + ΔTB = ΔT_total = 36°C.
- Substituting ΔTB = 2 * ΔTA into the equation gives:
ΔTA + 2 * ΔTA = 36°C.
- This simplifies to:
3 * ΔTA = 36°C, leading to:
ΔTA = 12°C.
Conclusion
The temperature difference across layer A (ΔTA) is 12°C, which is option 'C'.
To analyze the temperature difference across two layers in a wall, we need to apply the concept of thermal conductivity and heat conduction.
Given Information
- Layer A has thermal conductivity (kA) = 2 * kB (where kB is the thermal conductivity of layer B).
- The total temperature difference across the wall (ΔT_total) = 36°C.
Key Concepts
- The heat transfer through the layers can be expressed using Fourier's law of heat conduction:
Q = (k * A * ΔT) / d, where Q is the heat transfer rate, A is the area, ΔT is the temperature difference, and d is the thickness.
Temperature Differences in Layers
- Let the temperature difference across layer A be ΔTA and across layer B be ΔTB.
- Since both layers are of equal thickness (d), the ratio of the temperature differences will be inversely proportional to their thermal conductivities.
Setting Up the Ratios
- Since kA = 2 * kB, we can write:
ΔTA / ΔTB = kB / kA = 1 / 2.
- This implies ΔTA = (1/2) * ΔTB.
Using Total Temperature Difference
- We also have:
ΔTA + ΔTB = ΔT_total = 36°C.
- Substituting ΔTB = 2 * ΔTA into the equation gives:
ΔTA + 2 * ΔTA = 36°C.
- This simplifies to:
3 * ΔTA = 36°C, leading to:
ΔTA = 12°C.
Conclusion
The temperature difference across layer A (ΔTA) is 12°C, which is option 'C'.
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A wall has two layers A and Bach made of different materials. Both layers have the same thickness. The thermal conductivity of the material of Ais twice that ofB. Under thermal equilibrium, the temperature difference across the wall is36C. The temperature difference across the layerAis:a)21º Cb)35º Cc)12º Cd)57º CCorrect answer is option 'C'. Can you explain this answer?
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