# Heating Water : Modeling with a Linear Equation

Water is the most importnt substance on Earth. One reason for its usefulness is that is exists as a liquid over a wide range of temp. In its liquid range, water absorbs or releases heat directly in proportion to its change in temp. Consider the following data that shows temp of a 1,000 g sampe of water at normal atmospheric pressure as a function of heat supplied. A kJ can simply be thought of a unit of heat.

0C 0kJ

10C 42kJ

30C 126kJ

50C 209kJ

80C 335kJ

99C 414kJ

100C 420kJ

Based on this data please supply the following

Provide a graph of the data. Is the graph sufficiently linear to allow prediction of heat supplied versus temperature in the range of 0-100C?

If so, use Microsoft Excel to provide an equation that relates heat, y, supplied to temp, x, in the range of 0-100C.

Are the results consistent with expected equation, heat =(1.00 cal/g oC) *mass in grams* (final temp-initial temp)? please comment.

Use your equation to solve for the following: Heat supplied at 60C, final temp. when 175kJ of heat has been supplied, initial temp if 200kJ of heat is added and the final temp is 50C.

Can the model supply heat/temp. data in other ranges, for example at -5 C or at 150 C? Explain why or why not.

This whole thing makes no sense to me. So if someone could please steer me in the right direction I would appreciate it. The C in this problem stands for Celsius degrees. Thank you

https://brainmass.com/math/linear-algebra/heating-water-modeling-with-a-linear-equation-154992

#### Solution Preview

1. The graph is provided in the attached Excel file. It seems to be exactly linear.

2. The linear regression equation is: y = ...

#### Solution Summary

Whether the heating of water can be modeled with a linear equation is investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.