Newtons Law of Cooling: Practice Problem & Solution
A body cools from \(80^\circ\text{ C}\) to \(70^\circ\text{ C}\) in \(12\text{minutes}\) and from \(70^\circ\text{ C}\) to \(60^\circ\text{ C}\) in \(t \text{ minutes}\). The value of \(t\) is (temperature of surrounding is \(40^\circ\text{ C}\).
Solution Explained:
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:
According to Newton's Law of Cooling, \(\frac{T_i - T_f}{t} = K\left(\frac{T_i + T_f}{2} - T_s\right)\). For the first interval, \(\frac{80-70}{12} = K(75-40) ⇒ K = \frac{1}{42}\). For the second interval, \(\frac{70-60}{t} = K(65-40) ⇒ \frac{10}{t} = \frac{25}{42}\), which gives \(t = 16.8\text{ minutes}\).
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