Ncert Exercises & Solutions

A sphere, a cube and a thin circular plate, all of the same material and same mass are initially heated to the same high temperature.

1. Plate will cool fastest and cube the slowest

2. Sphere will cool fastest and cube the slowest

3. Plate will cool fastest and sphere the slowest

4. Cube will cool fastest and plate the slowest

(3) Hint: The rate of cooling depends on the surface area of the body.

Consider the diagram where all three objects are heated to the same temperature T.

Step 1: Find the rate of cooling for three bodies in terms of surface area.

We know that density,

ρ = \frac{m a s s}{v o l u m e}

is the same for all three objects. Hence, the volume will also be the same.

As the plate's thickness is the least, the surface area of the plate is maximum. According to Stefan’s law of heat loss, we know that A is the surface area of for object and T is the temperature.

Hence,

H_{s p h e r e} : H_{c u b e} : H_{p l a t e} = A_{s p h e r e} : A_{c u b e} : H_{p l a n t e}

A_{p l a t e}

is maximum, hence, the plate will cool fastest.
As the sphere is having a minimum surface area hence, the sphere cools slowest.

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