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# Model the Data for Temperature of Water and the Heat Supplied

Water is the most important substance on Earth. One reason for its usefulness is that it exists as a liquid over a wide range of temperatures. In its liquid range water absorbs or releases heat directly in proportion ot its change in temperature.
Consider the following data that shows temperature of a 1,000 g sample of water at normal atmospheric pressure as a function of heat supplied. A kj can simply be thought of a unit of heat.
Temperature Heat Supplied
0 oC 0 kj
10 oC 42 kj
30 oC 126 kj
50 oC 209 kj
80 oC 335 kj
99 oC 414 kj
100 oC 420 kj
Based on these data, please supply the following:
1. Provide a graph of the data. Is the graph sufficiently to allow prediction of heat supplied versus temperature in the range of 0-100 oC?
2. If so, provide an equation that relates heat, y, supplied to temperature, x, in the range of 0-100 oC.
3. Are the results consistent with the expected equation, heat = (1.00cak/g oC) * mass in grams*
4. Use your equation to solve for the following:
*heat supplied at 60 oC
*final temperature when 175 kj of heat has been supplied
*initial temperature if 200 kj of heat is added and final temperature is 50 oC
5. Can the model supply heat/temperature data in other ranges, for example at -5 oC or at 150 oC? Explain why or why not.

#### Solution Preview

1. Provide a graph of the data Is the graph sufficient linear to allow prediction of heat supplied versus Temperature in the range of 0-100*c?

See the graph in the attached Excel file. Yes, the graph is extremely linear (it looks line a straight line). It will allow prediction for temperature in the range of 0-100 degrees C.

2. If so, use Microsoft Excel to provide an equation that relates heat, y. Supplied to Temperature, x, in the range of o-100*c?

Excel has determined that the ...

#### Solution Summary

This is a series of questions regarding modeling temperature with a linear equation. The data plot and equation of the line are provided in an attached Excel file. The solutions for the heat supplied, final temperature and initial temperature under different conditions are also provided. It also briefly identifies why the model will not work outside of the specified range.

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