   Chapter 12.5, Problem 58E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Newton’s law of cooling Newton’s law of cooling can be used to estimate time of death. (Actually the estimate may be quite rough because cooling does not begin until metabolic processes have ceased.) Suppose a corpse is discovered at noon in a 70°F room and at that time the body temperature is 96 .1°F . If at 1 p.m. the body temperature is 94 .6°F , use Newton’s law of cooling to estimate the time of death.

To determine

To calculate: The time of death of a corpse with the help of Newton’s law of cooling when the temperature of the room and corpse at noon are 70° F and 96.1° F respectively while at 1 P.M. the temperature of the corpse become 94.6° F.

Explanation

Given information:

A dead body is found at noon and the temperature of the room and corpse at noon are 70° F and 96.1° F respectively while at 1 P.M. the temperature of the corpse become 94.6° F.

Formula used:

The newton law of cooling is, u=T+Aekt

Where T is the temperature of the surroundings, k is any constant and t is any instantaneous time.

The logarithmic rule of integrals, 1xdx=ln|x|+C where x0.

The natural logarithm property,

logab=yb=ay.

Calculation:

Consider the Newton law of cooling is, u=T+Aekt.

Now, the room temperature at noon is 70° F.

Substitute 70 for T in u=T+Aekt.

u=70+Aekt

Consider at noon as initial time, t=0 and the temperature of the corpse is 96.1° F.

Substitute 0 for t and 96.1 for u in u=70+Aekt.

96.1=70+Aek(0)26.1=A

Substitute 26.1 for A in u=70+Aekt.

u=70+26.1ekt

Now, after 1 P.M., the temperature of the corpse decreases to 94.6° F. So total time between noon to 1 P.M. is 1 hour.

Substitute 1 for t and 94.6 for u in u=70+26.1ekt

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