Question

A body cools according to Newton’s law from 100°C to 60°C in 20 minutes. The temperature of the surroundings is 20°C. How long will it take to cool down to 30°C?

Answer 1

Let θ°C be the temperature of the body at time t.

The temperature of the surrounding is given to be 20°C.

According to Newton’s law of cooling

On integrating, we get

Now, when t = 20, \(\theta\) = 60

∴ the body will cool down to 30°C in 60 minutes, i.e. in 1 hour.