__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__:(-dT/T) = K(T - T

_{0})

dT / K(T - T

_{0}) = -Kdt ....(i)

Where,

Temperature of the body =

*T*

Temperature of the surroundings =

*T*

_{0}= 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:

*t*

^{’}

Hence, we get:

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

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