PhysicsQ1–1 of 1 questions
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1
PhysicsMediumMCQIIT JEE · 1972
$A$ sphere,a cube,and a thin circular plate,all made of the same material and having the same mass,are initially heated to a temperature of $1000^{\circ}C$. Which one of these will cool first?
A
Plate
B
Sphere
C
Cube
D
None of these
Solution
(A) The rate of cooling is given by the formula $\frac{d\theta}{dt} = \frac{A \varepsilon \sigma (T^4 - T_0^4)}{mc}$.
Since all objects have the same mass $m$,material (same specific heat $c$),and are at the same initial temperature $T$,the rate of cooling is directly proportional to the surface area $A$ of the object $(\frac{d\theta}{dt} \propto A)$.
For a given mass and density,the surface area is largest for a thin circular plate and smallest for a sphere.
Therefore,the plate has the largest surface area,which leads to the fastest rate of cooling.
Thus,the plate will cool first.
Since all objects have the same mass $m$,material (same specific heat $c$),and are at the same initial temperature $T$,the rate of cooling is directly proportional to the surface area $A$ of the object $(\frac{d\theta}{dt} \propto A)$.
For a given mass and density,the surface area is largest for a thin circular plate and smallest for a sphere.
Therefore,the plate has the largest surface area,which leads to the fastest rate of cooling.
Thus,the plate will cool first.
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