Newton's law of cooling is valid only for a

1. Analyze the question The question asks about the conditions under which Newton's law of cooling holds.

2. Explain the concept Newton's law of cooling states that the rate of heat loss of a body is directly proportional to the temperature difference between the body and its surroundings:

dQ/dt ∝ (θ − θ₀)

or

dθ/dt = −k(θ − θ₀)

where θ is the body's temperature, θ₀ is the surroundings' temperature, and k is a constant.

The law is an approximation. It works well only when:

• The temperature difference between the body and its surroundings is small (roughly under 30 °C or so).
• Heat loss is mainly by convection (forced or in a steady draught) and conduction, with little radiation.
• The surroundings stay at a constant temperature.

At large temperature differences, radiation becomes dominant. Radiation follows Stefan's law (proportional to T⁴), not a simple linear relationship, so Newton's law breaks down.

3. Solution

• Option B (large temperature range): wrong, because radiation then dominates and the linear relationship fails.
• Option C (free flow range): not a meaningful condition for this law. Newton's law actually applies to forced convection.
• Option D (presence of heat source): wrong, because the law describes a body cooling down, with no heat source supplying energy.
• Option A (small temperature range): correct, because the rate of cooling is proportional to the temperature excess only when that excess is small.

4. Answer The correct option is A.

5. Exam tip Remember: Newton = Normal-small differences. If a question asks when Newton's law applies, think "small temperature difference." For large differences, think Stefan–Boltzmann (T⁴).