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# Water's heat capacity

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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 to its change in temperature.

Consider the following data that show 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 0C 420 kJ

Based on these data, please supply the following:
1. Provide a graph of the data. Is the graph sufficiently linear to allow prediction of heat supplied versus temperature in the range of 0-100 oC?
2. If so, use Microsoft Excel to 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 = (1.00 cal/g oC) * mass in grams * (final temperature - initial temperature)? Please comment.
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 the 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.

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#### Solution Summary

The solution shows how to retrieve the heat capacity of water using a linear regression of data points.
The solution includes an Excel file.

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