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

$\frac{\Delta T}{dt} = k(T_avg - T_s)$

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

$\frac{84.4 - 79.6}{5} = k (\frac{84.4 + 79.6}{2} - 68)$

$0.96 = k(14)$

now let say the person died "t" time ago

now we will have

$\frac{98.6 - 84.4}{t} = k (\frac{98.6 + 84.4}{2} - 68)$

$\frac{14.2}{t} = k(23.5)$

$\frac{14.2}{t} = \frac{0.96}{14}(23.5)$

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

so he died at approx 5 Am in  morning