Thermal Properties of Matter NCERT Solutions Class 11 Physics - Solved Exercise Question 11.22

Question 11.22:

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.

Solution:

According to Newton’s law of cooling, we have:
(-dT/T) = K(T - T₀)
dT / K(T - T₀)  =  -Kdt            ....(i)
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:

∴ t' = 300 X 2 = 600 s = 10 min
Therefore, the time taken to cool the body from 60°C to 30°C is 10 minutes.