The project is about a murder of a person named Joe D. wood which took place at the Mayfair Dinner. Detective Daphne Marlow was the person responsible for investigating the murder. They body was found hidden in the fridge suggesting that it was a cold murder. The police identified the body at 5.30 am, but the coroner arrived at the crime scene at 6.00 am. He then determined the temperature of the body in which he found out that it was 85 degrees Fahrenheit. After thirty minutes he measured the body temperature, and he found out that it was 84 degrees Fahrenheit, meaning that the temperature of the dead body was reducing. The coroner also noted that the refrigerator temperature was reading 50 degrees Fahrenheit.
With these details, the Detective wanted to establish the time at which the deceased was murdered. His first approach, he utilized Newton’s law of cooling that states the rate at which an object cools is proportional to the difference between the body temperatures at a specified time and the temperature of the environment that the body inhabits. Using Newton’s equation the detective was able to estimate the time of the murder, as follows (Cooper p.67);
dT ⁄dt = k (T- Tm), t>0
Where k is a constant of proportionality
T is the body temperature
Tm is the temperature of the surrounding that is the refrigerator.
In this case, the detective used t =-1/2, so as to get the time behind the scheduled.
Therefore, using linear differentiation, the following equation will be obtained, in order to find the value of k, with a known t:
K= (t1 –t2) = -ln {T (t1) – Tm/ T ( t2 ) – Tm) , ln= natural logarithm; representing loge
K -1/2= ln {84-50 / 85- 50}
k = 2 ln 0.971
=2 x 0.0294
= 0.0588
Time of death =- 1/k ln (98.6 – 50 / 85 – 60)
= 1/0.0588 ln 1.389
= - 5.59hrsRounded of, is – 6hrs
Therefore time of death is: - 6(hrs)
Actual time is: ( 6.00 am – 6(hrs)
= 12 a.m that is 12 midnight.
The detective estimated the victim was murdered at 12am.
The detective went to take another cup of coffee and wondered what if the body was moved to the fridge in a weak attempt to hide the body. He realized this assumption would change his previous estimate. He went back to the crime scene to observe the temperature of fridge thermostat, where it read; 700F
Assuming the time the body was moved to be h=6. She wanted to obtain the fall of body temperature that was caused by the move. She used the unit step function µ (Cooper P. 70)
Tm (t) = 50 + 20µ (t-h)
If t was 6 am and h was 6, then µ 6
50 + 20(1)
700 F
Using Laplace transformation, and the value of K in equation 1, which is ‘0.0588, time of death can be estimated
The equation: dT/ dt = k (T-Tm (t))
While transformed:
Time of death =- 1/k ln (98.6 – 70 / 85 – 70)
Time is= -6hrs
Actual time is 12 midnight
After a while, her partner Marie called her and identified three suspects, one is the victim's ex-wife, the second suspect was the cook. Each suspect was with the victim at different time, making the detective draw a table of estimating different times the body was moved (Seddon P.55).
Detective Daphne estimates seem to point out at the cook called Shorty. She then decided to question the cook because he was the suspect identified to be with the victim within the time frame that Joe died. He was with him from 10.30 pm to 2 pm whereas Joe seems to have been killed at around 12 midnight.
Still being curious, the detective used Algor mortis law clearly to estimate the time the victim was killed. This is because; in real life the cooling of the body is not only determined by the Newton’s law, but also this other law that considers another possible factor. This factor is the fact that chemical body process still continue to generate heat even after death (Seddon P 56).
The equation used was:
T= 98.6 – To/1.5
Where the time estimated was still around midnight. Therefore, the detective concluded that the cook must know something about the murder or he is the guilty one.
Reference
Cooper, Christopher. Forensic science. London: Dk Pub, 2008. Print. P. 67-70
Seddon, Ayn. Forensic science. Pasadena, Calif.: Salem Press, 2009. Print. P. 55-56
