Dr. Fisanick Forensic Chemistry #7
Name:_______________________________ Period:______________ Date:__________
Your objectives in this activity are to:

Describe how one of the many factors affecting the rate a body cools works

Determine what method of heat transfer is primarily responsible for the change
Honor students will also learn how to use spreadsheets to determine time of death when ambient temperatures are varying.
Calculating time of death accurately is of primary importance in homicide investigation because it sets the time frames for alibis for suspects. Many of the methods for calculating time of death in the short time frame rely on Newton’s Law of Cooling. This says that the body temperature T(t) will exponentially approach the temperature of the environment according to
( )

T ambient

( T
0

T ambient
) e
 kt
In many cases, the body temperature at time of death (T
0
) is taken as the average, 98.6

F, the ambient temperature (the temperature of the environment) is measured, and all of the other factors affecting cooling rate appear combined in the parameter k , the temperature decay rate.
You are going to explore how various conditions change cooling rates by visiting http://www.pathguy.com/TimeDead.htm
and using the applet to find time since death given various current body temperatures.
You are to pick one of the following effects to explore:
Body weight
Location where the body was found
Covering of the body
Ambient Temperature (assume you are indoors at a constant temperature)
To do this you are going to use the applet to help you draw cooling curves for different choices of values for the effect you are exploring. For instance, you might choose to explore the effect of body weight, so you would pick 5 different values of body weight and generate a cooling curve for each one to see how they differ. You would have to select a single value for each of the other variables that might affect cooling rate and keep these constant for each of the cooling curves. These will be your controlled variables.
1.
Make a data table with columns for each of the values you choose for the effect you are exploring. All other factors should remain the same. Be sure to list your choice of other conditions in your report. Use the applet to calculate the time since death for the body temperatures in the table for each value of your chosen condition.

Dr. Fisanick Forensic Chemistry #7
Name:_______________________________ Period:______________ Date:__________
Value 1:___________________________________________________________
Value 2:___________________________________________________________
Value 3:___________________________________________________________
Value 4:___________________________________________________________
Value 5:___________________________________________________________
Settings you chose for the Controlled Variables (cross out the condition you are exploring)
Ambient Temperature:
Body Weight:
Covering:
Location:
Core Body
Temperature
Time
Since
Death for
Value 1
Time
Since
Death for
Value 2
Time
Since
Death for
Value 3
Time
Since
Death for
Value 4
Time
Since
Death for
Value 5
98.6
97
95
93
91
89
87
85
2.
Make a single plot showing the temperature decay curves for each of the values you tested as a function of time on the x-axis. Staple your plot to this handout.
3.
Analyze your set of curves and write a short paragraph describing whether you think the effect of your variable is due primarily to changes in radiative, conductive or convective heat transfer and why.

Dr. Fisanick Forensic Chemistry #7
Name:_______________________________ Period:______________ Date:__________
4.
Discuss why your curves may not look like simple exponential curves, especially at earliest times.
5.
How could you use this kind of analysis to explain to the jury why two victims who the prosecution believes died at the same time could have different core body temperatures?

Current
Time
Current time – 1 hr
Dr. Fisanick Forensic Chemistry #7
Name:_______________________________ Period:______________ Date:__________
Honors:
In addition, honors students will calculate how a body outdoors cools when there is a variation in ambient temperature. To do this you will break down the day into time blocks at constant ambient temperature, and apply Newton’s Law of Cooling to each time block working backwards in time until you reach normal body temperature. This is most easily done in an excel spreadsheet.
You can find data on how temperature varies hourly throughout the day at http://www.weather.com/outlook/health/allergies/pastweather/USNJ0543?from=36hr_top nav_allergies
You can pick your favorite city if you look up its zip code:________________________
Make the following table in excel with the data you found. The core body temperature readings in bold are what was measured by the ME at the crime scene. Given the temperature change in the core body temperature over the last hour, you can calculate a value for k once you have obtained the current ambient temperature in your city. You will assume that k doesn’t change.
You can calculate the body temperature backwards for each temperature segment using the “differential” version of Newton’s Law of Cooling:

T
 
( ( )

T ambient
( ) )  t
This just says the change in body temperature for a given time segment is equal to –k times the difference in the current body temperature and the current ambient temperature times the length of time at that ambient temperature. Adding that to the current body temperature will give you the body temperature at the beginning of the time segment.
Add a plot of the body cooling curve if you neglect the changes in ambient temperature.
Time Ambient
Temperature
(Find from website)
Core Body
Temperature at end of time segment (F)
83.7
Value of k
(calculate once and assume constant)
Change in
Body
Temperature during time segment (F)
Core Body
Temperature at beginning of time segment (F)
84.5 -0.8 83.7

Dr. Fisanick Forensic Chemistry #7
Name:_______________________________ Period:______________ Date:__________
Make a plot in excel of your two curves. Write a short paragraph in simple language describing how changes in ambient temperature affect time of death calculations suitable for a jury of non-scientists.