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A hollow sphere has inner and outer surface areas of 2 m2 and 8 m2 respectively for a given temperature difference and heat flow across the surface. Considering the material of the sphere as a plane wall of the same thickness, the equivalent mean area normal to the direction of heat flow is
- a)6 m2
- b)5 m2
- c)4 m2
- d)3 m2
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A hollow sphere has inner and outer surface areas of 2 m2 and 8 m2 re...
To find the equivalent mean area normal to the direction of heat flow, we need to compare the heat flow through the hollow sphere and the equivalent plane wall.
Let's assume the thickness of the hollow sphere and the plane wall is the same, denoted by 't'.
Step 1: Calculate the heat flow through the hollow sphere
The heat flow through the hollow sphere can be calculated using the formula:
Q = k*A*(ΔT/d)
where Q is the heat flow, k is the thermal conductivity of the material, A is the surface area, ΔT is the temperature difference, and d is the thickness of the material.
Given:
Inner surface area of the hollow sphere, A1 = 2 m^2
Outer surface area of the hollow sphere, A2 = 8 m^2
Step 2: Calculate the equivalent surface area of the plane wall
The equivalent surface area of the plane wall can be calculated by adding the inner and outer surface areas of the hollow sphere. Since the thickness of the hollow sphere and the plane wall is the same, we can write:
A_eq = A1 + A2
Step 3: Calculate the equivalent mean area normal to the direction of heat flow
The equivalent mean area normal to the direction of heat flow is equal to the equivalent surface area divided by the thickness of the material. Therefore, we can write:
A_mean = A_eq / t
Given that the thickness of the hollow sphere and the plane wall is the same, we can simplify the equation to:
A_mean = (A1 + A2) / t
Substituting the given values, we have:
A_mean = (2 + 8) / t = 10 / t
Therefore, the equivalent mean area normal to the direction of heat flow is 10 / t, which is option C.
Let's assume the thickness of the hollow sphere and the plane wall is the same, denoted by 't'.
Step 1: Calculate the heat flow through the hollow sphere
The heat flow through the hollow sphere can be calculated using the formula:
Q = k*A*(ΔT/d)
where Q is the heat flow, k is the thermal conductivity of the material, A is the surface area, ΔT is the temperature difference, and d is the thickness of the material.
Given:
Inner surface area of the hollow sphere, A1 = 2 m^2
Outer surface area of the hollow sphere, A2 = 8 m^2
Step 2: Calculate the equivalent surface area of the plane wall
The equivalent surface area of the plane wall can be calculated by adding the inner and outer surface areas of the hollow sphere. Since the thickness of the hollow sphere and the plane wall is the same, we can write:
A_eq = A1 + A2
Step 3: Calculate the equivalent mean area normal to the direction of heat flow
The equivalent mean area normal to the direction of heat flow is equal to the equivalent surface area divided by the thickness of the material. Therefore, we can write:
A_mean = A_eq / t
Given that the thickness of the hollow sphere and the plane wall is the same, we can simplify the equation to:
A_mean = (A1 + A2) / t
Substituting the given values, we have:
A_mean = (2 + 8) / t = 10 / t
Therefore, the equivalent mean area normal to the direction of heat flow is 10 / t, which is option C.
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Community Answer
A hollow sphere has inner and outer surface areas of 2 m2 and 8 m2 re...
Mean area for the sphere is geometric mean of inside and outside area.
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A hollow sphere has inner and outer surface areas of 2 m2 and 8 m2 respectively for a given temperature difference and heat flow across the surface. Considering the material of the sphere as a plane wall of the same thickness, the equivalent mean area normal to the direction of heat flow isa)6 m2b)5 m2c)4 m2d)3 m2Correct answer is option 'C'. Can you explain this answer?
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