Physics - Heat & Thermo Question with Solution | TestHub

According to Newton's Law of Cooling, for small temperature differences, the rate of cooling is proportional to the average temperature difference between the body and the surroundings. For the first interval:$$\frac{60-50}{5}=K\left(\frac{60+50}{2}-20\right)$$ $$2=K(55-20)\Rightarrow 2=35K$$ For the second interval:$$\frac{50-40}{t}=K\left(\frac{50+40}{2}-20\right)$$ $$\frac{10}{t}=K(45-20)\Rightarrow \frac{10}{t}=25K$$ Dividing the two equations:$$\frac{2}{10/t}=\frac{35K}{25K}\Rightarrow \frac{2t}{10}=\frac{7}{5}\Rightarrow \frac{t}{5}=\frac{7}{5}\Rightarrow t=7\text{ minutes.}$$