A bucket full of hot water is kept in a room. If it cools from 75 to 70 in t₁ minutes, from 70 to 65 in t₂ minutes and 65 to 60 in t₃ minutes, then (a) t₁ t₂ > t₃ (c) t₁ = t₂ = t₃ (d) t₁ < t₂ = t₃

Answer: (a). Newton's law: rate of cooling ∝ (body temperature - room temperature). Each step is the same 5° C drop, but the average excess temperature gets smaller each time. Smaller rate means more time for the same drop. So the answer is (a) t₁ < t₂ < t₃.

A bucket full of hot water is kept in a room. If it cools from 75 to… | MHT CET 2024 (16 May, Shift 1)

Q13MHT CET 2024 · 16 MAY · SHIFT 1Medium

Newton's Law of Cooling

A bucket full of hot water is kept in a room. If it cools from $75^\circ\text{C}$ to $70^\circ\text{C}$ in $t_1$ minutes, from $70^\circ\text{C}$ to $65^\circ\text{C}$ in $t_2$ minutes and $65^\circ\text{C}$ to $60^\circ\text{C}$ in $t_3$ minutes, then

Show answer and solution

Answer: (a)

Newton's law: rate of cooling $\propto$ (body temperature $-$ room temperature).
Each step is the same $5^\circ$ C drop, but the average excess temperature gets smaller each time.
Smaller rate means more time for the same drop.
So the answer is (a) $t_1 < t_2 < t_3$ .

Report a mistake

Newton's Law of Cooling question from MHT CET 2024 (16 May, Shift 1)

More questions on Newton's Law of Cooling