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

Accepted Solution

Answer:t is 2.106284 hours Step-by-step explanation:Given data office maintained temperature (T) = 21°Cbody temperature ( t) = 29°Ctime = 1 hrdied body temperature (Td) = 37°C chief's body  temperature (Tc) = 31°Cto find out show coroner was killed 2 hours and 7 minutes before his body was foundsolutionwe 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°Cso 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 10/8and 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 minutesso it is -t = −2.106284 approx  two hou about two hours and seven minutes before his body was found