Solution:
Given:
In this question, the initial temperature of the body is 80 degrees Celsius, and the final temperature of the body is 50 degrees Celsius.
(T1 + T2)/2 is the average temperature.
Avg Temp= (80 + 50)/2 = 65 0C
Temperature of the surrounding, T0 =20 0C
Temperature difference, ΔT= 65 0C – 20 0C = 45 0C
t=5 min
Newton’s law of cooling states that the rate of cooling is proportional to the difference in temperature between two points.
Change in temperature/ time = K ΔT
(T2 – T1)/t = KΔT
(80 – 50)/5 = K(45)
6 = K(45)
K = 6/45
K = 2/15
Average
In the second situation,
The body’s initial temperature, , is 60 degrees Celsius.
is the last temperature of the body, and it is 30 degrees Celsius.
Let t be the amount of time required for cooling.
temperature, (T1 + T2)/2 = (60 + 30)/2 = 45 0C
Temperature difference, ΔT = 45 0C – 20 0C = 25 0C
According to Newton’s law of cooling, the rate of cooling is proportional to the difference in temperature
Change in temperature/ time = K ΔT
(T2 – T1)/t = KΔT
(60 – 30)/t = (2/15) (25)
30/t = 3.33
t = 30/3.33 = 9 min
Thus, answer is 9 mins.