Cooling Time Calculation – Rankers Physics
Topic: Thermal Physics
Subtopic: Newtons Law of Cooling

Cooling Time Calculation

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 \(40^\circ\text{ C}\).
\(13.8\)
\(16.8\)
\(18.8\)
\(20.8\)

Solution:

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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