MHT CET 2023 Physics question

A sphere, a cube and a thin circular plate all made of same material and having the same mass are heated to same temperature of 200C. When these are left in a room

(A)the sphere reaches room temperature fast
(B)the cube reaches room temperature fast
(C)the circular plate reaches room temperature fastCorrect
(D)all will reach the room temperature simultaneously.

Answer: (C)

Solution

By Newton's/Stefan's law of cooling, the rate of loss of heat is proportional to the exposed surface area, while the heat to be lost depends on mass and specific heat, which are the same for all three bodies. Hence the body with the largest surface area cools fastest. For a given volume a sphere has

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Question ID VK-098283