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A wall has two layers A and B, each made of different material. Both the layers have the same thickness. The thermal conductivity of the meterial 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)6°C
- b)12°C
- c)18°C
- d)24°C
Correct answer is option 'B'. Can you explain this answer?
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A wall has two layers A and B, each made of different material. Both t...
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A wall has two layers A and B, each made of different material. Both t...
Understanding the Problem
We have a wall with two layers, A and B, each having the same thickness. The thermal conductivity of layer A is double that of layer B. Given that the total temperature difference across the wall is 36°C, we need to find the temperature difference across layer A.
Thermal Conductivity Relationship
- Let the thermal conductivity of layer B be K.
- Then, the thermal conductivity of layer A is 2K.
Temperature Gradient Concept
- According to Fourier's law of heat conduction, the heat transfer rate through both layers will be equal at thermal equilibrium.
- The temperature difference across each layer is inversely proportional to its thermal conductivity.
Heat Transfer Calculation
- Let the temperature difference across layer A be ΔTA and across layer B be ΔTB.
Using the relationship of thermal conductivity:
- The heat conduction equation can be expressed as:
ΔTA / ΔTB = K_B / K_A
- Since K_A = 2K_B, we can express it as:
ΔTA / ΔTB = K / 2K = 1/2
Setting Up the Equations
- Since the total temperature difference is 36°C:
ΔTA + ΔTB = 36°C
- From the previous relationship:
ΔTA = (1/2)ΔTB
Solving the Equations
1. Substitute ΔTA into the total temperature equation:
- (1/2)ΔTB + ΔTB = 36°C
- (3/2)ΔTB = 36°C
2. Solve for ΔTB:
- ΔTB = 36°C * (2/3) = 24°C
3. Now find ΔTA:
- ΔTA = (1/2) * 24°C = 12°C
Conclusion
The temperature difference across layer A is 12°C, confirming that the correct answer is option 'B'.
We have a wall with two layers, A and B, each having the same thickness. The thermal conductivity of layer A is double that of layer B. Given that the total temperature difference across the wall is 36°C, we need to find the temperature difference across layer A.
Thermal Conductivity Relationship
- Let the thermal conductivity of layer B be K.
- Then, the thermal conductivity of layer A is 2K.
Temperature Gradient Concept
- According to Fourier's law of heat conduction, the heat transfer rate through both layers will be equal at thermal equilibrium.
- The temperature difference across each layer is inversely proportional to its thermal conductivity.
Heat Transfer Calculation
- Let the temperature difference across layer A be ΔTA and across layer B be ΔTB.
Using the relationship of thermal conductivity:
- The heat conduction equation can be expressed as:
ΔTA / ΔTB = K_B / K_A
- Since K_A = 2K_B, we can express it as:
ΔTA / ΔTB = K / 2K = 1/2
Setting Up the Equations
- Since the total temperature difference is 36°C:
ΔTA + ΔTB = 36°C
- From the previous relationship:
ΔTA = (1/2)ΔTB
Solving the Equations
1. Substitute ΔTA into the total temperature equation:
- (1/2)ΔTB + ΔTB = 36°C
- (3/2)ΔTB = 36°C
2. Solve for ΔTB:
- ΔTB = 36°C * (2/3) = 24°C
3. Now find ΔTA:
- ΔTA = (1/2) * 24°C = 12°C
Conclusion
The temperature difference across layer A is 12°C, confirming that the correct answer is option 'B'.
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A wall has two layers A and B, each made of different material. Both the layers have the same thickness. The thermal conductivity of the meterial 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 isa)6°Cb)12°Cc)18°Cd)24°CCorrect answer is option 'B'. Can you explain this answer?
Question Description
A wall has two layers A and B, each made of different material. Both the layers have the same thickness. The thermal conductivity of the meterial 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 isa)6°Cb)12°Cc)18°Cd)24°CCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A wall has two layers A and B, each made of different material. Both the layers have the same thickness. The thermal conductivity of the meterial 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 isa)6°Cb)12°Cc)18°Cd)24°CCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wall has two layers A and B, each made of different material. Both the layers have the same thickness. The thermal conductivity of the meterial 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 isa)6°Cb)12°Cc)18°Cd)24°CCorrect answer is option 'B'. Can you explain this answer?.
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