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The diameter of an iron sphere and the l...

The diameter of an iron sphere and the length of the side of an iron cube are equal. Initially they are at the same temperature. If they take the same amount of heat, whose final temperature will be higher?

Text Solution

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If x be the diameter of the sphere, its volume is,
`V_(1)=(4)/(3)pi((x)/(2))^(2)`
The length of the side of the cube is x.
The volume of the cube is, `V_(2)=x^(3)`
`therefore" "(V_(1))/(V_(2))=((4)/(3)pi(x^(3))/(8))/(x^(3))=(pi)/(6) lt 1" "therefore" "V_(1) lt V_(2)`
Since the volume of the cube is greater than that of the sphere, the mass of the cube is also greater. So, if an equal amount of heat is taken by the cube, its rise in temperature will be smaller, i.e., the rise in temperature of the sphere will be higher.
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