The dead body of a cricket coach was discovered in a prominent hotel at noon on Sunday where the temperature is 700F. The temperature of the body at the time of discovery s 76 OF and one hour later the temperature is 75.30F. Newton's law of cooling says that the rate of change of temperature T(t) on an object is proportional to the difference between the time T(t) and the temperature Tm of the surrounding medium; that is = k(T - Tm) Where k is a constant of proportionality. dT dt i. By solving the differential equation, show that the temperature of the coach's body is given by T = 70 + Cekt where t is the number of hours since time of death. ii. Assuming that the coach has a normal body temperature of 98.6°F at the time of death, show that T = 70 + 28.6ekt iii. Show that k = -0.1241 and hence determine the coach's time of death.
The dead body of a cricket coach was discovered in a prominent hotel at noon on Sunday where the temperature is 700F. The temperature of the body at the time of discovery s 76 OF and one hour later the temperature is 75.30F. Newton's law of cooling says that the rate of change of temperature T(t) on an object is proportional to the difference between the time T(t) and the temperature Tm of the surrounding medium; that is = k(T - Tm) Where k is a constant of proportionality. dT dt i. By solving the differential equation, show that the temperature of the coach's body is given by T = 70 + Cekt where t is the number of hours since time of death. ii. Assuming that the coach has a normal body temperature of 98.6°F at the time of death, show that T = 70 + 28.6ekt iii. Show that k = -0.1241 and hence determine the coach's time of death.
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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Transcribed Image Text:The dead body of a cricket coach was discovered in a prominent hotel at noon on Sunday where the
temperature is 700F. The temperature of the body at the time of discovery s 76 OF and one hour
later the temperature is 75.30F. Newton's law of cooling says that the rate of change of temperature
T(t) on an object is proportional to the difference between the time T(t) and the temperature Tm of
the surrounding medium; that is = k(T - Tm) Where k is a constant of proportionality.
dT
dt
i. By solving the differential equation, show that the temperature of the coach's body is given by
T = 70 + Cekt where t is the number of hours since time of death.
ii. Assuming that the coach has a normal body temperature of 98.6°F at the time of death, show that
T = 70 + 28.6ekt
iii. Show that k = -0.1241 and hence determine the coach's time of death.
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