A forensic method for estimating the time of death of a body is based on the law of newton of cooling, given by the governing equation dT = -k(T – A(t)), dt Where k > 0 is the rate at which heat is lost from the body and A(t) is the temperature environment. The idea is to measure the body temperature at two different times, in order to to calculate the constant K, and thus "reverse extrapolate" to the temperature of the living body T = 37°C. Suppose a body was found in a room in which the ambient temperature is kept constant at 24°C. At eight in the morning the measured body temperature is 28°C, after one hour the temperature is found to have dropped to 26°C. show that integrating the measured body temperature at two different times t, and t2, will result in T(t,) = A + [T(t,) – A]e¬k(t2=t;). Calculate k and determine the time of death. Note:Newton's law of cooling
A forensic method for estimating the time of death of a body is based on the law of newton of cooling, given by the governing equation dT = -k(T – A(t)), dt Where k > 0 is the rate at which heat is lost from the body and A(t) is the temperature environment. The idea is to measure the body temperature at two different times, in order to to calculate the constant K, and thus "reverse extrapolate" to the temperature of the living body T = 37°C. Suppose a body was found in a room in which the ambient temperature is kept constant at 24°C. At eight in the morning the measured body temperature is 28°C, after one hour the temperature is found to have dropped to 26°C. show that integrating the measured body temperature at two different times t, and t2, will result in T(t,) = A + [T(t,) – A]e¬k(t2=t;). Calculate k and determine the time of death. Note:Newton's law of cooling
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![A forensic method for estimating the time of death of a body is based on the law of
newton of cooling, given by the governing equation
dT
= -k(T – A(t)),
dt
Where k > 0 is the rate at which heat is lost from the body and A(t) is the temperature
environment. The idea is to measure the body temperature at two different times, in order to
to calculate the constant K, and thus "reverse extrapolate" to the temperature of the
living body T = 37°C.
Suppose a body was found in a room in which the ambient temperature is
kept constant at 24°C. At eight in the morning the measured body temperature is 28°C,
after one hour the temperature is found to have dropped to 26°C. show that
integrating the measured body temperature at two different times t, and t2, will result
in
T(t,) = A + [T(t,) – A]e¬k(t2=t;).
Calculate k and determine the time of death.
Note:Newton's law of cooling](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc493cc63-e1a4-4cf5-83d1-25d30c380d01%2F17db4b1b-6f96-4944-9e3e-12f8502f6549%2Fc9yo6s_processed.png&w=3840&q=75)
Transcribed Image Text:A forensic method for estimating the time of death of a body is based on the law of
newton of cooling, given by the governing equation
dT
= -k(T – A(t)),
dt
Where k > 0 is the rate at which heat is lost from the body and A(t) is the temperature
environment. The idea is to measure the body temperature at two different times, in order to
to calculate the constant K, and thus "reverse extrapolate" to the temperature of the
living body T = 37°C.
Suppose a body was found in a room in which the ambient temperature is
kept constant at 24°C. At eight in the morning the measured body temperature is 28°C,
after one hour the temperature is found to have dropped to 26°C. show that
integrating the measured body temperature at two different times t, and t2, will result
in
T(t,) = A + [T(t,) – A]e¬k(t2=t;).
Calculate k and determine the time of death.
Note:Newton's law of cooling
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