Newton's Law Of Cooling

Newton's law of cooling states that the rate at which a body loses heat is proportional to the excess of its temperature over the surroundings, $\frac{dT}{dt}=-k(T-T_s)$. The larger this excess temperature, the faster the body cools; as the body approaches the surroundings the cooling rate slows markedly. For each successive 10-degree drop the average excess over the $30^{\circ }\text{C}$ room becomes smaller, so the cooling slows and each step takes longer than the previous one. Among the listed intervals, $50^{\circ }\text{C}$ to $40^{\circ }\text{C}$ has the smallest average excess temperature, roughly 15 degrees, so it is traversed most slowly and takes the longest time. The interval $80^{\circ }\text{C}$ to $70^{\circ }\text{C}$ has the largest excess and is actually the quickest, which is why the question's given 5 minutes is the shortest of the four. The intermediate intervals fall in between. This monotonic slowing is the central NCERT consequence of Newton's law of cooling. As a plausibility check, everyday experience confirms that tea cools rapidly at first and then lingers near room temperature, matching the chosen slowest final interval.