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Math Help - Newton's Law of Cooling/Warming

  1. #1
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    Newton's Law of Cooling/Warming

    The problem: A thermometer is taken from inside a room to the outside, where the air temperature is 5 degrees Fahrenheit. After one minute, the thermometer reads 55 degrees Fahrenheit, and after 5 minutes it reads 30 degrees Fahrenheit. What is the initial temperature in the room?

    I use: T(t)=Tm-ce^kt

    but what is my Tm? would it be 5 degrees Fahrenheit? and if so, won't I still have two unknowns: c and k?
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  2. #2
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    Quote Originally Posted by latavee View Post
    The problem: A thermometer is taken from inside a room to the outside, where the air temperature is 5 degrees Fahrenheit. After one minute, the thermometer reads 55 degrees Fahrenheit, and after 5 minutes it reads 30 degrees Fahrenheit. What is the initial temperature in the room?

    I use: T(t)=Tm-ce^kt

    but what is my Tm? would it be 5 degrees Fahrenheit? and if so, won't I still have two unknowns: c and k?
    Newton's law of cooling is:

    \frac{dT}{dt}=-k(T-T_{amb})

    Solve this and apply the given tempratures and times to solve for all the unknows in the problem.

    ( T_{amb} is the ambient tempratur and T is the temprature of the object )

    CB
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