Newton's Law Of Cooling

NCERT Class 11, Chapter 11 (Thermal Properties of Matter) states Newton's law of cooling: for small temperature differences the rate of heat loss of a body is directly proportional to the excess of its temperature over that of the surroundings, $-\frac{dT}{dt}\propto (T-T_s)$. This holds when the temperature difference is modest and the surroundings stay at constant temperature. In the example the body cools faster when it is hotter relative to the room and slows as it approaches 30°C, exactly as the law predicts. The option citing the absolute temperature alone ignores the role of the surroundings. The option invoking the fourth power describes Stefan's radiation law, valid for large differences, not Newton's approximation. The option about the mass of surrounding air is irrelevant to the cooling rate's leading dependence. It is important to remember that Newton's law is an approximation valid only for small temperature excesses and forced or natural convection, whereas radiation alone obeys the steeper fourth-power Stefan law. A consistency check confirms that the cooling rate vanishes as the body reaches surrounding temperature, so a graph of temperature against time flattens and approaches the room temperature asymptotically rather than crossing below it. Only the temperature-difference dependence correctly captures this gradual slowing as equilibrium is approached, which is why the body cools quickly at first and then more and more slowly.