Question

According to Newton's law of cooling, the rate of cooling is proportional to $ {(\Delta \theta )^n} $ , where $ \Delta \theta $ is the temperature difference between the body and the surroundings and $ n $ is equal to
A. Three
B. Two
C. One
D. Four

Answer 1

Hint: In the above question they have asked about Newton's law of cooling theorem. To solve this we must know the law of rate of cooling. And using the theorem we will be able to tell the value of n.

Complete step by step answer:
Definition- According to Newton’s law of cooling, the rate of loss of heat from a body is directly proportional to the difference in the temperature of the body and its surroundings. Newton’s law of cooling (or heating) states that the temperature of a body changes at a rate proportional to the difference in temperature between the body and its surroundings. Given that such a difference in temperature is small and the nature of the surface radiating heat remains constant. To put it in simpler terms, we may say that the hotter an object is, the quicker it cools down.
By temperature difference, we mean any phenomenon which leads to the flow of energy into a system or flow of energy from any system into the surrounding area. In the former case, the object heats up, whereas in the latter, the object cools down. Newton’s Law of Cooling leads to the often cited equation of exponential decline over time.
We can state the rate of cooling as $ \dfrac{{d\theta }}{{dt}} \propto \Delta \theta $
Therefore the answer is option (C).

Note:
Limitations of Newton's Law of Cooling:
1) The difference in temperature between the body and surroundings must be small,
2) The loss of heat from the body should be by radiation only,
3) The major limitation of Newton’s law of cooling is that the temperature of surroundings must remain constant during the cooling of the body.