The temperature of a body falls from 40∘C to 36∘C in 5 minutes when placed in a surrounding of constant temperature 16∘C. Find the time taken for the temperature of the body to become 32∘C.
As the temperature differences are small, we can use Newton's law of cooling.
Where k is a constant, θ is the temperature of the body at time t and θ0=16∘C is the temperature of the surrounding. We have,
If t be the time required for the temperature to fall from 36∘C to 32∘C then by (i),
or, ln32∘C−16∘C36∘C−16∘C=−ln(56)5 min
= 6.1 min.
The mean temperature of the body as it cools from 40∘C to 36∘C is 40∘C+36∘C2=38∘C The rate of decrease of temperature is
Newton's law of cooling is
or, -0.8∘C/min = - k(38∘C - 16∘C)=-k(22∘C)
Let the time taken for the temperature to become 32∘C be t.
During this period,.
The mean temperature is