Heat and Thermodynamics 3 Question 39
39. A solid sphere of copper of radius $R$ and a hollow sphere of the same material of inner radius $r$ and outer radius $R$ are heated to the same temperature and allowed to cool in the same environment. Which of them starts cooling faster?
(1982, 2M)
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Answer:
Correct Answer: 39. Hollow sphere
Solution:
- Net rate of heat radiation $\left(\frac{d Q}{d t}\right)$ will be same in both the cases, as temperature and area are same.
Therefore, from equation
$$ m s\left(-\frac{d \theta}{d t}\right)=\frac{d Q}{d t} \quad \text { or } \quad-\frac{d \theta}{d t} \propto \frac{1}{m} $$
The hollow sphere will cool faster as its mass is less.
