The time rate of loss of heat by a body is proportional to the

1. Analyze the question The question asks what the rate of heat loss from a body depends on. This is Newton's Law of Cooling.

2. Explain the concept Newton's Law of Cooling states that the rate at which a body loses heat to its surroundings is directly proportional to the difference between the body's temperature and the temperature of its surroundings (provided the temperature difference is small and the surroundings stay constant).

In symbols:

dQ/dt ∝ (θ − θ₀)

or

dQ/dt = k(θ − θ₀)

where:

• θ = temperature of the body
• θ₀ = temperature of the surroundings
• k = a constant that depends on the surface area and nature of the body's surface

3. Solution: checking each option

• A. Temperature of its surroundings: Wrong. The surroundings' temperature alone does not determine the rate of loss. A hot cup of tea loses heat quickly in a cold room even though the room temperature is the same as in a warm room.
• B. Temperature of the body: Wrong. The body's temperature alone is not enough. If the body is at the same temperature as its surroundings, there is no net heat loss however hot both are.
• C. Difference in temperature between the body and its surroundings: Correct. This matches Newton's Law of Cooling exactly.
• D. Ratio of the temperatures: Wrong. The law uses the difference, not the ratio.

4. Answer The correct option is C.

5. Exam tip Remember that heat flows because of a difference in temperature. When the difference is zero (thermal equilibrium), there is no net heat loss. Whenever you see "rate of cooling" in JAMB, think "temperature difference". The cooling curve (temperature against time) is steep at first and flattens out as the body approaches the temperature of its surroundings, because the difference keeps getting smaller.