Question

Cooling:

The body of an apparent victim of a crime is discovered by detectives at 9 AM, at which time the body temperature was measured to be 88°. Two hours later the temperature was 82°. Using Newton’s Law of Cooling, determine the time of death if the room temperature was a constant 75°.

Answer 1

where:

k: the constant of proportionality

T: the temperature of the surrounding enviroment (constant)

Ts: the temperature of the object at time t

T(0)= 88

T(1)=82

to determine C and, we substitute the initial conditions to arrive at the system of equations

the first equation tells us , so the second equation becomes:

thus,

the solution is:

assuming the boby temperature was last 98.6

that is, the ime of death was approximately 58 minutes before 9:00, or 8:02