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A partition wall has two layers A and B in contact, each made of different material. They have the same thickness but the thermal conductivity of layer A is twice that of layer B. If the steady state temperature difference across the wall is 60 K, then the corresponding difference across the layer A is
  • a)
    10 K
  • b)
    20 K
  • c)
    30 K
  • d)
    40 K
Correct answer is option 'B'. Can you explain this answer?
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A partition wall has two layers A and B in contact, each made of diffe...
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A partition wall has two layers A and B in contact, each made of diffe...
Given:
- The partition wall has two layers A and B.
- The thickness of both layers A and B is the same.
- The thermal conductivity of layer A is twice that of layer B.
- The steady state temperature difference across the wall is 60 K.

To find:
The corresponding temperature difference across layer A.

Solution:
1. Understanding the problem:
- We have a partition wall with two layers A and B.
- The temperature difference across the wall is 60 K.
- We need to find the temperature difference across layer A.

2. Understanding the concept:
- Thermal conductivity is a measure of a material's ability to conduct heat.
- Higher thermal conductivity means the material can conduct heat more easily.
- In this problem, layer A has twice the thermal conductivity of layer B.

3. Applying the concept:
- Since both layers have the same thickness, the temperature difference across each layer will depend on their thermal conductivities.
- Let's assume the temperature difference across layer B is ΔTB.
- Since layer A has twice the thermal conductivity of layer B, the temperature difference across layer A, ΔTA, will be twice that of layer B.

4. Calculating the temperature differences:
- Let's assume the temperature difference across layer B is ΔTB.
- As per the given information, the temperature difference across the wall is 60 K.
- So, the temperature difference across layer A, ΔTA, will be twice that of layer B, i.e., 2ΔTB.
- Therefore, 2ΔTB + ΔTB = 60 K.
- Simplifying the equation, we get 3ΔTB = 60 K.
- Dividing both sides by 3, we get ΔTB = 20 K.
- Therefore, the temperature difference across layer A, ΔTA, will be 2 times ΔTB, i.e., 2 * 20 K = 40 K.

5. Answer:
The corresponding temperature difference across layer A is 40 K. Therefore, the correct answer is option B.
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A partition wall has two layers A and B in contact, each made of different material. They have the same thickness but the thermal conductivity of layer A is twice that of layer B. If the steady state temperature difference across the wall is 60 K, then the corresponding difference across the layer A isa)10 Kb)20 Kc)30 Kd)40 KCorrect answer is option 'B'. Can you explain this answer?
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