Answer: Estimate Murder Time from Temp & Air: 55°F

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I'm getting 1.37984.In summary, the forensic specialist used Newton's Law of Cooling to determine the time of death for a victim whose body temperature was measured at 85.7° F at 2:10 AM and 84.8° F at 2:40 AM. Using an air temperature of 55° F and the victim's normal body temperature of 98.6° F, the specialist was able to calculate a time of death of approximately 7 hours and 26 minutes before the body was discovered.
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theintarnets
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Homework Statement


A forensic specialist took the temperature of a victim's body lying in a street at 2:10 AM and found it to be 85.7° F. At 2:40 AM, the temperature of the body was 84.8° F. When was the murder committed if the air temperature during the night was 55° F? Remember, normal body temperature is 98.6° F.

Homework Equations


I think I'm supposed to use Newton's Law of Cooling:
T = Ts + (To - Ts)e-kt

Where
T is any temperature
Ts is the surrounding temperature
To is the original temperature

The Attempt at a Solution


I know I should solve for k first, and then substitute it into the original equation to get t, but I'm not sure what to do once I get t.

84.8 = 55 + (85.7 - 84.8)e-k30 because the difference between 2:10 and 2:40 is 30 minutes.
(84.8 - 55)/(85.7 - 84.8) = e-k30
ln(2.37984) = lne-k30
ln(2.37984)/30 = -k
k = -.116662

Then
85.7 = 55 + (98.6 - 85.7)e.116662*t
(85.7 - 55)/(98.6 - 85.7) = e.116662*t
ln(2.37984) = lne.116662*t
ln(2.37984)/.116662 = t
t = 7.43203

But how do I put that into a time format?
 
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  • #2
theintarnets said:
84.8 = 55 + (85.7 - 84.8)e-k30 because the difference between 2:10 and 2:40 is 30 minutes.
You have a mistake in bold. The temperature of the surrounding medium should go there, so it's 55, not 84.8.

theintarnets said:
Then
85.7 = 55 + (98.6 - 85.7)e.116662*t
Same thing here.

theintarnets said:
(84.8 - 55)/(85.7 - 84.8) = e-k30
ln(2.37984) = lne-k30
Even though the number in bold is wrong, I'm not sure how you got 2.37984.
 
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FAQ: Answer: Estimate Murder Time from Temp & Air: 55°F

1. How accurate is the estimated murder time based on temperature and air?

The accuracy of the estimated murder time depends on various factors such as the location, time of day, and weather conditions. The estimation is based on scientific research and data, but it may not always be 100% accurate.

2. Can the estimated murder time be used as evidence in a court case?

The estimated murder time based on temperature and air is not considered as concrete evidence in a court case. It can be used as a supporting piece of evidence, but it is not the sole determining factor in a criminal investigation.

3. How does temperature and air affect the estimated murder time?

Temperature and air can greatly impact the estimated murder time. Higher temperatures and humidity levels can accelerate the decomposition of a body, making it difficult to accurately estimate the time of death. On the other hand, colder temperatures and dry air can preserve a body, making the estimation more accurate.

4. Are there any other factors that can affect the estimated murder time?

Yes, there are other factors that can affect the estimated murder time. Some of these factors include the size of the body, the type of clothing worn, and the presence of any wounds or injuries. Additionally, the presence of insects and animals can also impact the rate of decomposition and make it more challenging to estimate the time of death.

5. How do scientists determine the estimated murder time from temperature and air?

Scientists use a variety of methods and data to estimate the time of death. They may use entomology (study of insects), forensic anthropology, and forensic botany to gather information about the body and its surroundings. Additionally, they may also use mathematical models and algorithms based on temperature and air conditions to estimate the time of death.

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