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Two infinite parallel plates are placed at a certain distance apart. An infinite radiation shield is inserted between the plates without touching any of them to reduce heat exchange between the plates. Assume that the emissivities of plates and radiation shield are equal. The ratio of the net heat exchange between the plates with and without the shield is
[2014]
- a)1/2
- b)1/3
- c)1/4
- d)1/8
Correct answer is option 'A'. Can you explain this answer?
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Two infinite parallel plates are placed at a certain distance apart. A...
here, n = 1
∴
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Two infinite parallel plates are placed at a certain distance apart. A...
Introduction:
In this scenario, two infinite parallel plates are placed at a certain distance apart. An infinite radiation shield is inserted between the plates without touching any of them to reduce heat exchange between the plates. The emissivities of plates and radiation shield are equal.
Explanation:
When two objects are at different temperatures, heat transfer occurs between them. The rate of heat transfer depends on factors such as the temperature difference, the surface area of contact, and the emissivity of the objects.
Heat Exchange Between Plates Without Shield:
Without the radiation shield, heat exchange between the plates occurs through radiation. The rate of heat transfer between the plates is given by the Stefan-Boltzmann law:
Q = εσA(T₁⁴ - T₂⁴)
Where Q is the net heat transfer, ε is the emissivity (assumed to be equal for both plates), σ is the Stefan-Boltzmann constant, A is the surface area of the plates, T₁ is the temperature of one plate, and T₂ is the temperature of the other plate.
Since the plates are at the same temperature and have equal emissivities, the net heat transfer between them is zero.
Heat Exchange Between Plates with Shield:
When the radiation shield is inserted between the plates, it reduces heat exchange between them. The radiation shield acts as a barrier to the thermal radiation, preventing direct heat transfer.
The net heat transfer between the plates with the shield can be calculated by considering the heat transfer between each plate and the shield. Since the emissivities of the plates and the shield are equal, the rate of heat transfer between each plate and the shield is the same.
Therefore, the net heat transfer between the plates with the shield is half of the heat transfer between each plate and the shield.
Hence, the ratio of the net heat exchange between the plates with and without the shield is 1/2. Therefore, the correct answer is option A.
In this scenario, two infinite parallel plates are placed at a certain distance apart. An infinite radiation shield is inserted between the plates without touching any of them to reduce heat exchange between the plates. The emissivities of plates and radiation shield are equal.
Explanation:
When two objects are at different temperatures, heat transfer occurs between them. The rate of heat transfer depends on factors such as the temperature difference, the surface area of contact, and the emissivity of the objects.
Heat Exchange Between Plates Without Shield:
Without the radiation shield, heat exchange between the plates occurs through radiation. The rate of heat transfer between the plates is given by the Stefan-Boltzmann law:
Q = εσA(T₁⁴ - T₂⁴)
Where Q is the net heat transfer, ε is the emissivity (assumed to be equal for both plates), σ is the Stefan-Boltzmann constant, A is the surface area of the plates, T₁ is the temperature of one plate, and T₂ is the temperature of the other plate.
Since the plates are at the same temperature and have equal emissivities, the net heat transfer between them is zero.
Heat Exchange Between Plates with Shield:
When the radiation shield is inserted between the plates, it reduces heat exchange between them. The radiation shield acts as a barrier to the thermal radiation, preventing direct heat transfer.
The net heat transfer between the plates with the shield can be calculated by considering the heat transfer between each plate and the shield. Since the emissivities of the plates and the shield are equal, the rate of heat transfer between each plate and the shield is the same.
Therefore, the net heat transfer between the plates with the shield is half of the heat transfer between each plate and the shield.
Hence, the ratio of the net heat exchange between the plates with and without the shield is 1/2. Therefore, the correct answer is option A.
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Two infinite parallel plates are placed at a certain distance apart. A...
here, n = 1
∴
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Two infinite parallel plates are placed at a certain distance apart. An infinite radiation shield is inserted between the plates without touching any of them to reduce heat exchange between the plates. Assume that the emissivities of plates and radiation shield are equal. The ratio of the net heat exchange between the plates with and without the shield is[2014]a)1/2b)1/3c)1/4d)1/8Correct answer is option 'A'. Can you explain this answer?
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