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MHT CET 2024 (9 May, Shift 2) · Newton's Law of Cooling

Newton's Law of Cooling question from MHT CET 2024 (9 May, Shift 2)

Q15MHT CET 2024 · 9 MAY · SHIFT 2Medium

Newton's Law of Cooling

The temperature of a liquid falls from 365 K to 359 K in 3 minutes. The time during which temperature of this liquid falls from 342 K to 338 K is [Let the room temperature be 296 K ]

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Answer: (c)

  1. Newton's law: T1−T2t=k(T1+T22−T0)\frac{T_1 - T_2}{t} = k\left(\frac{T_1 + T_2}{2} - T_0\right).
  2. Case 1: 63=k(362−296)=66k⇒k=133\frac{6}{3} = k(362 - 296) = 66k \Rightarrow k = \frac{1}{33}
  3. Case 2: 4t=133(340−296)=4433\frac{4}{t} = \frac{1}{33}(340 - 296) = \frac{44}{33}
  4. t=3t = 3 min
  5. So the answer is (c) 3 min.
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