Newtons Law of Cooling: Practice Problem & Solution
A body cools from \(80^\circ\text{C}\) to \(50^\circ\text{C}\) in 6 minutes. The time it takes to cool from \(60^\circ\text{C}\) to \(40^\circ\text{C}\) is (The temperature of surrounding is \(20^\circ\text{C}\))
Short Solution (Best for NEET):
To solve this problem, we apply the core principles of Newtons Law of Cooling. Understanding the underlying formula is key to arriving at the correct answer below:
Using Newton's law of cooling: \(\frac{T_1 - T_2}{t} = K \left[ \frac{T_1 + T_2}{2} - T_0 \right]\). For the first case, \(\frac{30}{6} = K[65 - 20] ⇒ 5 = 45K ⇒ K = \frac{1}{9}\). For the second case, \(\frac{20}{t} = \frac{1}{9}[50 - 20] = \frac{30}{9} = \frac{10}{3} ⇒ t = 6 \text{ minutes}\).
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