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IB MATH METHODS

IB MATH METHODS

MATHEMATICAL MODELING PROJECT

"THE COOLING LIQUID"

 

Task: Carry out an experiment to find a mathematical model "Function" that indicates how fast hot water cools down when left alone.

Materials Needed: Thermometer, stop watch, bunsen burner, cups/containers

Procedure:

1. Record the room temperature before beginning the experiment

2. Heat a liquid and pour it in to a cup.

3. Insert a thermometer into the cup and ensure that the cup is covered to prevent the

release of steam. Do not remove the thermometer from the cup.

4. Record the liquid’s initial temperature and the temperature every 2 minutes for a

period of 20 minutes

Instructions:

  1. Graph the data obtained from the experiment. Include room temperature. (Total 2 graphs)
  2. Use the graph and the table to find a good mathematical model (function) that best fits the data.
  3. At each time (t), find the difference between the liquid temperature (Tl) and the room temperature (Tr). Are the differences decreasing exponentially? Are there any values that don’t fit the same patterns as the rest. If so, What could the variations be due to?
  4. Based on the graph, what temperature will the liquid reach if left alone long enough?
  5. What do you predict the temperature of the liquid would be if left to cool down for 24 minutes?
  6. Calculate the % error for your predicted temperature.

Email: altaji@isp.edu.pa