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Presentation transcript:

Turn in your homework and clear your desk for the Quiz.

Homework …

Newton’s Law of Cooling C.S.I

Hiram Fentley, heir to the Fentley Feta Cheese fortune was found dead at his home at 2:30 am. The temperature in the room was a constant 70 °. His body temperature at 3:00am was 85 ° and at 4:00am was 78 °. At what time was he killed? Ever wonder how the C.S.I’s solve a crime?

Newton’s Law of Cooling states that the rate of change in the temperature of an object is proportional to the difference between the object’s temperature and the temperature of the surrounding medium. In other words… T= body temperature R = temp of the surroundings t = time C and k are both constants that we will solve for using the given information

Let’s just apply it to plain old pie… When a pie is removed from the oven it’s temperature is 200 º. After cooling in a room that had a constant temperature of 72 º for 10 minutes the temperature of the pie was 160 º. How long will it take from the time the pie was removed from the oven before it has cooled to 100 º ?

A cup of coffee cools from 150  F to 85  F in half an hour when surrounded by air whose temperature is 75  F. Use Newton’s Law of Cooling to find its temperature at the end of two hours.

At 7:00 pm, police discover a man's body in a hotel room which maintained a constant temperature of 75 º F. At the time of discovery, the temperature of the dead body was 96 º F. After four hours the temperature of the body fell to 86 º F. So, assuming the man’s initial body temperature was 98.6 º F, what time did the man die?

THE COURT CASE The dead body of Steve's Algebra 2 teacher was found behind the Media Center at 3:20pm on Monday, September 17, The cause of the death was determined to be lethal injection with a substance that causes immediate death upon entering the bloodstream. The syringe was found at the scene with Steve's fingerprints on it. Needless to say, Steve is a prime suspect. In fact, two reliable eyewitnesses saw Steve near the library at 3:20pm that same day. Steve's alibi of being in Pre-Calculus tutoring can be verified, but only from 2:15 -3:10 pm. Could Steve have committed the crime?