You find a dead body at 3PM Its temperature is 886 F An hour

You find a dead body at 3PM. Its temperature is 88.6 F. An hour later its temperature is 78.6 F. The ambient air temperature at 3PM was 68.6 F. At 4PM it is 63.6 F. Assuming that the ambient air temperature decreased linearly with time from the time of death and that the corpses temperature at the time of death was 98.6 F, find the time of death.

Let t = 0 be the time of death and t = t_d is the time of discovery (measured in hours after time of death).

Let T(t) be temperature in farenheit at time t hours.

Solution

Given Data,

Dead Body Find at time = 3pm

At Temp = 88.6F

Hour = 78.6F

Ambient air Temp = 68.6F at 3 PM

                              =63.6F at 4 PM

Ambient air temp graudually decreases .

Generally , Body cools 1.4F/hour

After 12 hours ,the body loses =0.7F

NORMAL Body temp = 98.6F

Corpse Temperature at time of death = 98.6F

Formulae for calucating time of death is,

Hours since death = 98.6 - corpse Temp/1.5

                               =98.6 - 98.6/1.5

                               =32.86 Hours

As in general,Calucate the Time of death

Step1 :    Temp = Normal Body Temp - Given Temp

                    T = 98.6F - 68.6F=30.0F

Step2: Calculate the time first 12 hours , when body cools at 1.4 F/hours

              = 12 hours * 1.4F/hour = 16.8 F lost in first 12 hours

Step3: Calcuate the time after 12 hours

             = 30.0F-16.8F =13.2F lost after 12 hours

Step 4: Caluate time after 12 hours ,the body loses =0.7F

                       = 13.2F * 1 hr/0.7F

                        =18.8F

Step 5: Determine the total time of death caluclation

               td = 18.8+12

                td    = 30.8 hours per death