Question

Please help

Newton's Law of Cooling
H-R = Be (to the power of) -kt

When a murder is committed, the body, originally at 37 degrees, cools according to Newton's Law of Cooling. Suppose that when the body is found at 9:30 am the temp of the body is 35 degrees and that temperature of the body is 30 degrees at 4:00pm. Assuming that the temp of the surrounding air is a constant 20 degrees, when was the murder committed?

Answer 1

According Newton's law of cooling the temperature difference between body and surroundings falls exponentially - meaning, in equal intervals of time, the temperature difference fall by the same factor(and that factor is e^-kt)Example:In 10 seconds if it dropped by to 1/2 its amount, in the next 10 seconds it will again drop to 1/2 its amount.Hence it 20 seconds the initial amount will become 1/4th.

At 9:30 , the temperature difference is 35-20 = 15. At 4:00pm it is 30-20 = 10
So the temperature became 10/15th its original amount in 6.5 hours.
10/15 = e^-k(6.5).
k= 0.06.

Original temperature difference = 37-20 = 17
At 9:30 temp. difference =35-20 = 15

therefore 15/17 = e^-kt = e^-0.06*t
t= approx 2.
So the person died 2 hours before 9:30AM