Question

2. According to Newton’s Law of Cooling, the rate of change of the temperature of an object can be modeled using the following differential equation:

dT/dt = k(T-T_R)

where T is the temperature of the object (in ◦F), TR is the room temperature (in ◦F), and κ is the constant of proportionality.
On a crime show, the detective discovers a dead body in a hotel room.
(a) Write the differential equation to describe the change in temperature of the body if κ = −0.405 and thermostat in the hotel room is set at 70◦F.
(b) Solve the differential equation using an appropriate method. State the method you used and show your work.
(c) Assuming the victim was a healthy 98.6◦F at the time of the murder, we have the initial condition that T(0) = 98.6. Find the particular solution to the IVP.
(d) If the body temperature is 85◦F when the crime scene is discovered, how long has the victim been dead? (Assume t is measured in hours.)

Answer 1

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