According to Newton's law of cooling, the heat energy lost per unit area of a body depends on the I. Surface…

Analyze the question

We need the factors on which the heat lost per unit area of a body depends, according to Newton's law of cooling.

Concept

Newton's law of cooling says that the rate of heat loss of a body is proportional to its excess temperature over the surroundings (for small temperature differences):

dQ/dt ∝ (θ − θ₀)

In full, the rate of heat loss is:

dQ/dt = h A (θ − θ₀)

where

• A is the surface area,
• h is a constant depending on the nature of the surface (colour, polish, roughness, etc.),
• (θ − θ₀) is the excess temperature over the surroundings.

Solution

Because the question asks for heat lost per unit area, divide by A:

(dQ/dt)/A = h (θ − θ₀)

• I. Surface area: it cancels out when we talk about "per unit area", so it is not a factor.
• II. Nature of the surface: it enters through h, so it is a factor.
• III. Temperature of the surface: the absolute temperature alone is not what matters. The law depends on the difference from the surroundings, so this is not the factor.
• IV. Excess temperature over the surroundings: this is a factor.

So only II and IV apply.

Answer: B (II and IV only)

Tip: When you see "per unit area", remove area from the list of factors. Also remember that Newton's law of cooling always involves the excess temperature, not the temperature of the body alone.