A sphere, a cube and a thin circular plate all of same...

A sphere, a cube and a thin circular plate all of same material having same mass are initially heated to $200^{\circ} \mathrm{C}$. Which of these will cool fastest?
(a) Circular plate
(b) Sphere
(c) Cube
(d) All of these

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Key Concepts

Newton's Law of Cooling

This principle describes the rate at which an object cools by relating the rate of change in temperature to the difference between the object's temperature and the ambient temperature. It provides a framework for understanding how objects of different shapes and sizes lose heat in an environment where convection and radiation are significant.

Surface Area to Volume Ratio

This ratio is crucial in determining the rate of heat loss because it influences how much surface is available for heat exchange relative to the amount of material (or thermal energy) contained within the object. Objects with a high surface area relative to their volume cool faster as they have more exposure to the cooling medium.

Thermal Mass

Thermal mass refers to an object's ability to store heat energy. It combines the effects of an object's mass and its heat capacity. A lower thermal mass means that an object will experience a faster temperature change for a given amount of heat loss or gain, making this concept important when comparing the cooling rates across objects with the same mass.

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