the police discover the body of a murder victim. ... Question: The Police discov

Question

the police discover the body of a murder victim. ... Question: The Police discover the body of a murder victim. C... The Police discover the body of a murder victim. Critical to solving the crime is determining when the murder was committed. The coroner arrives at the murder scene at 12:00 p.m She immediately takes the temperature of the body and finds it to be 94.6 F. She then takes the temperature 1 hour later and finds it to be 93.4 F. The temperature of the room is 70 F. When was the murder committed? Hint normal body temperature is 98.6 F

Explanation / Answer

Answer is 9.00 AM.

Explanation: According to Newton's law of cooling, T(t) = Ts + (T0-Ts)e-kt, where Ts is the temperature of surroundings and T0 is the temperature when first recorded, k is the constant to be evaluated.

T(t) = 70 + (94.6-70) e-kt ------ Eq (1)

   = 70+ 24.6e-kt

To find the value of k, we are given that the police has tracked the temperature after 1 hour after 12.00pm and it is 93.4F

So T(1) = 70 + 24.6 e-k(1) = 93.4 where 1 is the difference between first two readings

24.6 e-k = 23.4

e-k = 0.95121

k = - ln(0.95121)

k = 0.05

So replace the value of k in eq (1)

T(t) = 70 + 24.6 e-0.05t

Assuming that the body temparature was normal at the time of death i.e 98.6F

the equation becomes

98.6 = 70 + 24.6e-0.05t

24.6e-0.05t =28.6

e-0.05t =1.1626

-0.05t = ln(1.1626)

-0.05t = 0.150

t =-3

Thus time of death was happened 3 hours before 12.00PM ie 9.00AM

So answer is 9.00AM

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