17. A lifeless body was found in a room whose constant temperature was 70 F. At

Question

17. A lifeless body was found in a room whose constant temperature was 70 F. At the time of discovery the body temperature was 85 F. An hour later a second reading was performed showing the body temperature at 80 ° F. Assuming that the human body temperature is about 98.6 F ¿ how many of the time it had elapsed at the death of the individual 17. A lifeless body was found in a room whose constant temperature was 70 F. At the time of discovery the body temperature was 85 F. An hour later a second reading was performed showing the body temperature at 80 ° F. Assuming that the human body temperature is about 98.6 F ¿ how many of the time it had elapsed at the death of the individual

Explanation / Answer

by newton's law of cooling ,temperatute of body at time t ,T(t)=Ta+(To-Ta)ekt

Ta=70 F, To=98.6 F

T(t)=70+(98.6-70)ekt

T(t)=70+ 28.6ekt

At the time of discovery the body temperature was 85 F

70+ 28.6ekt=85

=>ekt=15/28.6

. An hour later body temperature was 80 ° F.

70+ 28.6ek(t+1)=80

=>ekt+k=10/28.6

=>ektek=10/28.6

=>(15/28.6)ek=10/28.6

=>ek=10/15

=>k=ln(2/3)

T(t)=70+ 28.6et*ln(2/3)

At the time of discovery the body temperature was 85 F

70+ 28.6et*ln(2/3)=85

=>et*ln(2/3)=15/28.6

=>t*ln(2/3) =ln(15/28.6)

=>t =(ln(15/28.6))/(ln(2/3))

=>t =1.59 hours

death happened 1.59 hours before the body was found

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