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 ${100}^{\circ }\text{C}$ and then allowed to cool at the temperature of the room. Which of these will cool down first –

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

Answer 1

The correct option is B Plate

$\because$ From the definition of specific heat
$Q=mc\Delta \theta \Rightarrow \Delta \theta =\frac{Q}{mc}$ ... (1)
and from stefan’s law
$Q$ or $E=\in A\sigma [T^4-T_0^4]$
From equation (1) and (2)
$\Delta \theta =\frac{\in A\sigma [T^4-T_0^4]}{mc}$
$\Delta \theta \propto A$
more surface area $\Rightarrow$ more cooling.
As plate, sphere and material are made of same material and have same mass, they have same volumes.
$\because$As thickness of plate is small, area of plate is largest, so it will cool first.