Given below are the four cases in which certain heat transfer is taking place : 1. Ice is melting in a glass full of water 2. Water is boiling in an open container 3. A metal rod is heated in a furnace 4. A cup of coffee is allowed to cool on a table In which of the above cases, the Newton's Law of Cooling is applicable?
- A.1 only
- B.4 only
- C.1 and 4 only
- D.1, 2 and 3
Correct answer
Explanation
The correct answer is B, 4 only. Newton's law of cooling describes a hot body losing heat to cooler surroundings, which is exactly what a cup of coffee on a table does.
The law states that the rate at which a body loses heat is proportional to the difference between its temperature and that of its surroundings, provided the difference is small. So hot coffee cools quickly at first and then more slowly as it nears room temperature, and its temperature falls along an exponential curve. The law assumes the body is cooling without any change of state and without an outside source of heat.
A and C are wrong because melting ice absorbs heat at a constant 0 degrees C; it is a change of state, so its temperature does not follow the law. D is wrong because the boiling water stays at 100 degrees C while it changes into vapour, and the rod in a furnace is being heated by a hot source, not cooling freely, so the law does not apply to cases 1, 2 or 3.
Exam tip: rate of cooling is proportional to (body temperature minus surroundings temperature), for small differences.
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