The following problem is known not to be a very good physical example of Newton\
ID: 3142839 • Letter: T
Question
The following problem is known not to be a very good physical example of Newton's Law of Cooling, since the thermal conductivity of a corpse is hard to measure: in spite of this, body temperature is often used to estimate time of death. At 7 AM one morning detectives find a murder victim in a closed meat locker. The temperature of the victim measures 90 degree. Assume the meat locker is always kept at 40 degree, and at the time of death the victim's temperature was 98.6 degree. When the body is finally removed at 8 AM, its temperature is 88 degree. (a) When did the murder occur? (Round your answer to the nearest minute.) 3: 88 am (b) How big an error in the time of death would result if the live body temperature was known only to be between 98.2 degree and 101.4 degree? 1.15 hrsExplanation / Answer
dT/dt = -k(T0 -T)
dT/dt = -k(40 -T)
dt/(T-40) = k dt
ln (T - 40) = kt + c
T -40 = a *ekt
T( 7 am) = 90
90 -40 = ae7k
50 = ae7k
T(8 AM) = 88
88-40 = ae8k
48 = ae8k
ek = 48/50
k = ln (48/50) = -0.04082199
t = ? T = 98.6
98.6 -40 = a ekt
58.6 = a ekt
58.6 /50 = ek(t-7))
1.172 = ek(t-7))
ln (1.172) = k(t-7)
ln (1.172) = ln(48/50) *(t-7)
t = 3.1121 = 3am 6 min 43.56 sec
3:07 am approx
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