Question

two solid sphere A and B made of the same material have radii rA and rB respectively.Both the spheres are cooled from the same temperature under the conditions valid for Newton's law of cooling.The ratio of the rate of change of temperature in A and B is​

Answer 1

ua/ub = r²(a) / r²(b)

Explanation:

Given: Two solid sphere A and B made of the same material have radii r(a) and r(b), respectively. Both the spheres are cooled from the same temperature under the conditions valid for Newton's law of cooling.

Find: The ratio of the rate of change of temperature in A and B.

Solution:

The rate of change of temperature of a sphere depends on the surface area of the sphere. So let the rate of change of temperature be ua and ub respectively.

Then their ratio ua/ub = Area(a) /Area(b) = 4πr²(a) / 4πr²(b) = r²(a) / r²(b)

So the ratio of rate of change of temperature of the two spheres is equal to the ratio of the squares of their respective radii.