Question

A sphere, a cube and a thin circular pate are heated to the same temperature. If they are made of same material and have equal masses, determine which of these three object cools the fastest and which one cools the slowest?
A. Temperature of sphere drops to room temperature at last
B. Temperature of cube drops to room temperature at last
C. Temperature of thin circular plate drom to room temperature at last
D. Temperatures of all the three drop to room temperature at the same.

Answer 1

Correct Answer - A
`(dT)/(dt)=(epsilon A sigma)/(mc)(T^(4)-T_(0)^(4))=(e A sigma)/(V rho c)(T^(4)-T_(0)^(4))`
`:.` Rate of cooling `R prop A`
(As masses are equal, volume ofn each body must be equal because material is same)
i.e., rate of cooling depends on the area of cross section and we know that for a given volume the area of cross section will be minimum for sphere. It means the rate of cooling will be minimum in case of sphere.
So he temperature of sphere drops to room temperature at last.