Question

Assertion :A solid sphere and a hollow sphere of same material and same radius are kept at same temperatures in atmosphere. Rate of cooling of hollow sphere will be more. Reason: If all other conditions are same, then rate of cooling is inversely proportional to mass of body.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

A solid sphere provides resistance to heat flow from inside to outside through it due to the material present inside it. This resistance is absent for a hollow sphere because the mass is practically present at its boundary. Rate of cooling is inversely proportional to mass. This statement is true and can be proved by conservation of energy. So if the hollow sphere is lighter than the solid sphere, then this reason is acceptable. But when they are of the same mass, then it does not explain why solid sphere has a slower rate of cooling than the hollow sphere. The proof is simple:

$mc\frac{dT}{dt}=hA(T-T_s)\Rightarrow \frac{dT}{dt}\propto \frac{1}{m}$

where: $m$ is mass, $c$ is specific heat capacity, $T_s$ is the temperature of surrounding, $A$ is exposed surface area and $h$ is heat transfer coefficient.

Thus, both A and B are acceptable as answers.