Question

At 10:30 AM, detectives discover a dead body in a room and measure its temperature at 27°C. One hour later, the body's temperature had dropped to 24.8°C. Determine the time of death (when the body temperature was a normal 37°C), assuming that the temperature in the room was held constant at 22°C. (Round your answer to two decimal places.)
:The time of death was approximately_______ hours before 10:30 AM.

Answer 1

Answer:

The time of death was approximately 4 hours before 10:30 AM.

Explanation:

Temperature of the body when discovered by detective at 10:30 AM= 27°C

After discovery, Temperature of the body at 11.30 AM= 24.8°C

Change in time = ΔT = 1 hour

Rate of change of body temperature with respect to time :

$R=\frac{24.8^oC-27^oC}{1 hour}=-2.2^oC/hour$

Normal body temperature = 37°C

Change in time since death = ΔT'

$R=\frac{27^oC-37^oC}{\Delta T'}$

$-2.2^oC/hour=\frac{27^oC-37^oC}{\Delta T'}$

$\Delta T'=\frac{27^oC-37^oC}{-2.2^oC/Hour}=4.54 hour\approx 4 hours$

The time of death was approximately 4 hours before 10:30 AM.