Temperature of a body θ is slightly more than the temperature of the surrounding θ0. Its rate of cooling (R) versus temperature of the body (θ) is plotted. Its shape would be
When the temperature of a body exceeds that of its surroundings by only a small amount, Newton's law of cooling applies: the rate of cooling is directly proportional to the temperature excess over the surroundings.
Step 1 — Newton's law of cooling: \(R=-\dfrac{d\theta}{dt}=k(\theta-\theta_0)\), where k is a positive constant.
Step 2 — R is a linear function of θ with positive slope, \(\dfrac{dR}{d\theta}=k\gt 0\), so the graph is a straight line rising with θ.
Step 3 — R becomes zero at \(\theta=\theta_0\), so the line meets the θ axis at the surrounding temperature, not at the origin.
A horizontal line would mean the rate of cooling does not depend on temperature. A curve that falls steeply and flattens is the shape of temperature against time, not of rate against temperature. A line falling with θ would mean a hotter body cools more slowly, which contradicts the law.
the straight line rising from a point on the θ axis option is correct.
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