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 200. 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 fast (d) all will reach the room temperature simultaneously

Answer: (c). Same mass and material, so same heat capacity mc; rate of cooling dT/dt ∝ A/mc. For a given volume, the sphere has the least surface area and a thin plate has the largest. Largest area means fastest heat loss, so the plate cools fastest. So the answer is (c) the circular plate reaches room temperature fast.

A sphere, a cube and a thin circular plate all made of same material… | MHT CET 2023 (14 May, Shift 1)

Q77MHT CET 2023 · 14 MAY · SHIFT 1Medium

Thermal Radiation: Black Body, Stefan & Wien

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 $200^\circ\text{C}$ . When these are left in a room.

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Answer: (c)

Same mass and material, so same heat capacity $mc$ ; rate of cooling $\frac{dT}{dt} \propto \frac{A}{mc}$ .
For a given volume, the sphere has the least surface area and a thin plate has the largest.
Largest area means fastest heat loss, so the plate cools fastest.
So the answer is (c) the circular plate reaches room temperature fast.

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