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If the temperature difference DT between an object and it surroundings is not too great, the...

If the temperature difference DT between an object and it surroundings is not too great, the rate of cooling or warming obeys Newton’s Law of Cooling,

d(DT)/dt = – K DT

where K is a constant. (a) Why is there a minus sign on the right-hand side of the equation? (b) On what factors does K depend and what are its units? (c) It DTo is the temperature difference at time to, what is the temperature difference at time t later? (d) A medical examiner is called to a crime scene where a murder has occurred. Upon arriving at 1 AM the examiner measures the body temperature to be 79o F. An hour later the examiner measures the body temperature to be 77.5o F. A detective tells the examiner that the read-out on the computer controlled thermostat in the room shows that the temperature in the room has remained constant at a 70o F for the past two days. The detective asks the examiner for the time of death. What time does the examiner tell the detective?

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