# 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.

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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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