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If V is the volume of metal in a casting and A its surface area, then the time of solidification will proportional to
- a)V, 1/A
- b)V, 1/A2
- c)V2, 1/A
- d)V2, 1/A2
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
If V is the volume of metal in a casting and A its surface area, then...
Explanation:
Surface area and solidification time:
When a casting solidifies, the heat is transferred from the molten metal to the surrounding environment through its surface. Therefore, the surface area of the casting plays a crucial role in the solidification process. A larger surface area allows for more efficient heat transfer, leading to faster solidification.
Volume and solidification time:
The volume of the casting determines the amount of molten metal that needs to solidify. As the volume increases, more heat needs to be dissipated, resulting in a longer solidification time.
Relationship between volume and surface area:
The surface area of a casting is directly related to its volume. As the volume increases, the surface area also increases. This relationship is given by the formula:
A ∝ V^(2/3)
where A is the surface area and V is the volume.
Relationship between solidification time and surface area:
From the above relationship, we can conclude that the solidification time is inversely proportional to the surface area. As the surface area increases, the solidification time decreases.
Relationship between solidification time and volume:
Since the solidification time is directly proportional to the volume, we can write:
t ∝ V
where t is the solidification time and V is the volume.
Combining the relationships:
We can combine the relationships between volume, surface area, and solidification time as follows:
t ∝ V
t ∝ 1/A^(2/3)
t ∝ V^(1/3) / A^(2/3)
Rearranging the equation, we get:
t ∝ V^(2/3) / A^(2/3)
Comparing this equation with the given options, we can see that the correct answer is option D:
V^2, 1/A^2
Surface area and solidification time:
When a casting solidifies, the heat is transferred from the molten metal to the surrounding environment through its surface. Therefore, the surface area of the casting plays a crucial role in the solidification process. A larger surface area allows for more efficient heat transfer, leading to faster solidification.
Volume and solidification time:
The volume of the casting determines the amount of molten metal that needs to solidify. As the volume increases, more heat needs to be dissipated, resulting in a longer solidification time.
Relationship between volume and surface area:
The surface area of a casting is directly related to its volume. As the volume increases, the surface area also increases. This relationship is given by the formula:
A ∝ V^(2/3)
where A is the surface area and V is the volume.
Relationship between solidification time and surface area:
From the above relationship, we can conclude that the solidification time is inversely proportional to the surface area. As the surface area increases, the solidification time decreases.
Relationship between solidification time and volume:
Since the solidification time is directly proportional to the volume, we can write:
t ∝ V
where t is the solidification time and V is the volume.
Combining the relationships:
We can combine the relationships between volume, surface area, and solidification time as follows:
t ∝ V
t ∝ 1/A^(2/3)
t ∝ V^(1/3) / A^(2/3)
Rearranging the equation, we get:
t ∝ V^(2/3) / A^(2/3)
Comparing this equation with the given options, we can see that the correct answer is option D:
V^2, 1/A^2
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If V is the volume of metal in a casting and A its surface area, then the time of solidification will proportional toa)V, 1/Ab)V, 1/A2c)V2, 1/Ad)V2, 1/A2Correct answer is option 'D'. Can you explain this answer?
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