# Water's heat capacity

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.

https://brainmass.com/math/graphs-and-functions/water-s-heat-capacity-156574

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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.