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Question

A solid sphere, a cube and a plate, are made of the same material and all have same mass. These are heated to a temperature 100C and then allowed to cool at the temperature of the room. Which of these will cool down first –

A
Cube
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B
Plate
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C
Sphere
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D
All will cool down simultaneously
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Solution

The correct option is B Plate
From the definition of specific heat
Q=mcΔθΔθ=Qmc ... (1)
and from stefan’s law
Q or E=Aσ[T4T40]
From equation (1) and (2)
Δθ=Aσ[T4T40]mc
ΔθA
more surface area more cooling.
As plate, sphere and material are made of same material and have same mass, they have same volumes.
As thickness of plate is small, area of plate is largest, so it will cool first.

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