Question

A body cools from 80 °C to 50 °C in 5 minutes. Calculate the time it takes to cool from 60 °C to 30 °C. The temperature of the surroundings is 20 °C.

Answer 1

According to Newton’s law of cooling, we have:

Where,

Temperature of the body = T

Temperature of the surroundings = T₀ = 20°C

K is a constant

Temperature of the body falls from 80°C to 50°C in time, t = 5 min = 300 s

Integrating equation (i), we get:

The temperature of the body falls from 60°C to 30°C in time = t^’

Hence, we get:

Equating equations (ii) and (iii), we get:

Therefore, the time taken to cool the body from 60°C to 30°C is 10 minutes.