Question

You are called to the crime scene immediately and you begin your investigation at 2 PM. The first thing you do is take the temperature of the body it is 84.4°F. You immediately walk over to the apartments thermostat and find that has been set at 68°F. The crime scene continues to be investigated wood samples taken and bagged. As everyone is finishing up, you take the temperature of the body again exactly 5 hours later and the temperature reads 79.6°F assume normal body temperature is 98.6°. What was the time of death? Use Newton’s Law if Cooling

Answer 1

As per Newton's law of cooling we know that

`(\Delta T)/(dt) = k(T_avg - T_s)`

in 5 hours the body temperature becomes 79.6 from 84.4

while the surrounding temperature is given as 68 degree F

now from above formula

`(84.4 - 79.6)/(5) = k ((84.4 + 79.6)/(2) - 68)`

`0.96 = k(14)`

now let say the person died "t" time ago

now we will have

`(98.6 - 84.4)/(t) = k ((98.6 + 84.4)/(2) - 68)`

`(14.2)/(t) = k(23.5)`

`(14.2)/(t) = (0.96)/(14)(23.5)`

`t = 8.8 hours = 9hours (approx)`

so he died at approx 5 Am in morning