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# Using a Linear Equation for Heat

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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.

##### Solution Summary

An Excel file plus detailed step-by-step explanations are provided.

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Hi!

The Excel file is attached. Here are the answers. Feel free to put these in your own words.

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 Excel file that I have attached. The graph is very linear (because it looks like it's close to a straight line).

2. If so, use Microsoft Excel to provide an equation that relates heat, y. Supplied to Temperature, x, in the range of 0-100*c?

Excel determined that the ...

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