A bowl filled with very hot water cools from 98° C to 86° C in 2 minutes when the room temperature is 22° C. How long it will take to cool from 75° C to 69° C? (a) 0.5 minute (b) 1.4 minute (c) 1 minute (d) 2 minute

Answer: (b). Newton's law: (T₁ - T₂)/(t) = k((T₁ + T₂)/(2) - T₀). Case 1: (98 - 86)/(2) = k(92 - 22) ⇒ 6 = 70k Case 2: (75 - 69)/(t) = k(72 - 22) = 50k Dividing: 6/t/6 = 50/70 ⇒ t = 1.4 min So the answer is (b) 1.4 minute.

A bowl filled with very hot water cools from 98° C to 86° C in 2… | MHT CET 2026 (16 Apr, Shift 2)

Q3MHT CET 2026 · 16 APR · SHIFT 2Medium

Newton's Law of Cooling

A bowl filled with very hot water cools from $98^\circ$ C to $86^\circ$ C in 2 minutes when the room temperature is $22^\circ$ C. How long it will take to cool from $75^\circ$ C to $69^\circ$ C?

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Answer: (b)

Newton's law: $\frac{T_1 - T_2}{t} = k\left(\frac{T_1 + T_2}{2} - T_0\right)$ .
Case 1: $\frac{98 - 86}{2} = k(92 - 22) \Rightarrow 6 = 70k$
Case 2: $\frac{75 - 69}{t} = k(72 - 22) = 50k$
Dividing: $\frac{6/t}{6} = \frac{50}{70} \Rightarrow t = 1.4$ min
So the answer is (b) $1.4$ minute.

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