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Math Help - Temperature

  1. #1
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    Temperature

    A pan of water (46 degrees) was put into a fridge. Ten min later, its temp was 39. Ten min after that, it was 33. Use newtons law of cooling. How cold was the fridge?

    I know his law, but how do I find the rate?
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    Quote Originally Posted by Morgan82 View Post
    A pan of water (46 degrees) was put into a fridge. Ten min later, its temp was 39. Ten min after that, it was 33. Use newtons law of cooling. How cold was the fridge?

    I know his law, but how do I find the rate?
    Let T_R be the temperature inside the refridgerator (which we can assume is kept constant) and let T(t) be the temperature of the water after t minutes. "Newton's law of cooling says that heat will flow from a hotter object to a cooler at a rate proportional to the difference in temperature. Since the temperature is proportional to the amount of heat in the object, we can put the two proportions together to say \frac{dT}{dt}= k (T- T_R) where "k" is the, yet unknown, constant of proportion.

    That is a relatively simple separable differential equation which you can solve by integrating both sides of \frac{dT}{T- T_R}= k dt.

    That will, of course, depend upon three unknown constants, k, T_R, and the constant of integration. Fortunately, you have three equations, T(0)= 46, T(10)= 39, and T(20)= 33. You can solve those three equations for the three constants, in particular T_R which is what you are asked.
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