Question

A body was found at midnight in a warehouse where the temperature was 55. The medical examiner found the temperature of the body to be 66. What was the approximate time of death?

Answer 1

5 p.m.

Explanation:

Newton's law of cooling-

`T(t)=t_a+(t_0-t_a)e^(-kt)`

where,

`t_0` = the initial temp. = 98.6 F (human body temp.)

k = 0.1947,

T(t) = 66 F,

`t_a` = 55 F,

Putting the values,

`\Rightarrow 66=55+(98.6-55)e^(-0.1947\cdot t)\\\\\Rightarrow 66=55+(43.6)e^(-0.1947\cdot t)\\\Rightarrow (43.6)e^(-0.1947\cdot t)=11\\\Rightarrow e^(-0.1947\cdot t)=(11)/(43.6)=0.2523\Rightarrow \ln e^(-0.1947\cdot t)=\ln 0.2523\\\Rightarrow -0.1947\cdot t* \ln e=\ln 0.2523\\\Rightarrow -0.1947\cdot t* 1=\ln 0.2523\\\Rightarrow t=(\ln 0.2523)/(-0.1947)\\\Rightarrow t=7\ h`

Therefore, the time of death was 7 hours before midnight i.e at 5 pm.