Question

The office of the coroner is maintained at 21°C. While doing an autopsy on a murder victim, the coroner is killed and the victim's body is stolen. The coroner's assistant discovers his chief's body and finds that its temperature is 31°C. An hour later, the body temperature is down to 29°C. Assuming that the coroner's body temperature was 37°C when he died, use Newton's law of cooling to show that the coroner was killed about two hours and seven minutes before his body was found

Answer 1

t is 2.106284 hours

Explanation:

Given data

office maintained temperature (T) = 21°C

body temperature ( t) = 29°C

time = 1 hr

died body temperature (Td) = 37°C

chief's body temperature (Tc) = 31°C

to find out

show coroner was killed 2 hours and 7 minutes before his body was found

solution

we use here Newton's law of cooling that is

dT/dt = -k (t - T )

now solve this equation and we get value of k i,e

-k (t ) = ln (t-T) / (Tc - T)

we know in 1 hour body temperature change 31°C to the 29°C

so now put value of t and T , Tc to find value of k

-k(1) = ln (29-21) / (31-21)

so -k = ln (8)/(10)

and k = ln 10/8

and when temp change 37°C to 31°C we will find out time so that is

-kt = ln (31-21) / (37-21)

-ln 10/8 × t = ln (10) / (16)

so -t = ( ln 10/16) / ( ln 10/8 )

-t = −2.106284 approx two hours and seven minutes

so it is -t = −2.106284 approx two hou about two hours and seven minutes before his body was found