Applications of First Order Differential Equations: A dead body was found within a closed room of a

Carla Murphy 2022-01-15 Answered
Applications of First Order Differential Equations: A dead body was found within a closed room of a house where the temperature was a constant 24C. At the time of discovery, the core temperature of the body was determined to be 28C. One hour later, a second measurement showed that the core temperature of the body was 26C. The core temperature of the body at the time of death is 37C. A. Determine how many hours elapsed before the body was found. B. What is the temperature of the body 5 hours from the death of the victim?
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Expert Answer

Bernard Lacey
Answered 2022-01-16 Author has 30 answers
GaceCoect5v
Answered 2022-01-17 Author has 26 answers
T=k(TTm) (Newton's Law of Cooling)
dTTTm=kdt
ln|TTm|=kt+C1T(t)=Tm+cekt
T(closed room)=21Tm=21
T(temperature at t=0)=37T(0)=37
Substitute in T(t)=Tm+cekt
37=21+ce0c=16
T=21+16ekt (1)
Where t is the time at discovery
The temperature was 27 at the time of discovery
27=21+16ekt16ekt=6 (2)
The temperature was 25 after one hour (t+1)
25=21+16ek(t+1)16ek(t+1)=4 (3)
Dividing (2) by (3)
ektek(t+1)=64=32
ektktk=32ek=32k=ln32k=0.41
Substitute in (2)
16e0.41t=6e0.41t=616=38
0.41t=ln38
t=ln38÷(0.41)
t=2.4 hours
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alenahelenash
Answered 2022-01-24 Author has 368 answers

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