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Math Help - Coffee Cooling Problem

  1. #1
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    Exclamation Coffee Cooling Problem

    How would you create a table that demonstrates the temperature of a cup of coffee as a function of time?

    What affect would additives like cream, sugar, or coffee syrup have on this table?

    How could you use this information to determine the best time to drink the coffee assuming that the initial temperature is 200 degrees F and the cup size is 8 ounces?
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  2. #2
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    Hello herron0009
    Quote Originally Posted by herron0009 View Post
    How would you create a table that demonstrates the temperature of a cup of coffee as a function of time?

    What affect would additives like cream, sugar, or coffee syrup have on this table?

    How could you use this information to determine the best time to drink the coffee assuming that the initial temperature is 200 degrees F and the cup size is 8 ounces?
    Set up a simple experiment. You'll need:
    A cup of the appropriate size

    A thermometer

    A clock or watch with a second hand

    Coffee, cream, sugar, etc
    Heat the coffee. Pour the hot coffee into the cup. Put the thermometer into the coffee. Note the initial temperature. Then note the temperature at regular intervals - e.g. every half-minute or every minute.

    Write your results in a table with time in the first column and temperature in the second. This table, then, shows temperature as a function of time.

    Optionally you could now plot a graph of the results, with temperature on the vertical scale, time on the horizontal scale.

    Repeat the experiment several times with various combinations of additives: cream, sugar, etc. In order to start at the same temperature as before, you may need to heat up the coffee again after adding the additive(s) (e.g. in a microwave oven), since adding cream etc will cool the coffee. Start recording the results when the temperature is the same as the initial temperature as the first experiment.

    Plotting the results on the same graph as before will allow a simple comparison to be made.

    The 'best time' to drink the coffee is a very subjective thing. Many people like their coffee scalding hot - others prefer it practically cold. If you were serious about answering this question, you would need to enlist the help of a large number of coffee-drinking volunteers. Find the average optimum temperature, and then use your tables and/or graphs to determine the time for the coffee to reach this temperature.

    Grandad
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