At a crime scene, police officers find a murder victim in a tub full of warm water. A thermometer shows that the water temperature is 75 degrees F and the air temperature is 70 degrees F. It is known that most people fill a tub with water at 100 degrees F. Find Newton's Law of cooling and use it to model the temperature of the water in the tub(using a heat transfer coefficient of k=0.018). To the nearest whole minute, how long has the bathtub water been cooling?

I found the equation of T(t)=TA+(TH-TA)e^-kt

asked by Andrea

12 years ago

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1 answer

75 = 70+(100-70)e^-.018t
t = 99.54
or 100 minutes

answered by Steve

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Question

At a crime scene, police officers find a murder victim in a tub full of warm water. A thermometer shows that the water temperature is 75 degrees F and the air temperature is 70 degrees F. It is known that most people fill a tub with water at 100 degrees F. Find Newton's Law of cooling and use it to model the temperature of the water in the tub(using a heat transfer coefficient of k=0.018). To the nearest whole minute, how long has the bathtub water been cooling?
I found the equation of T(t)=TA+(TH-TA)e^-kt

Steve · Answer

75 = 70+(100-70)e^-.018t t = 99.54 or 100 minutes