# AKA - The Horribly Failed Science Experiment

### An exercise in futility by Andy Tyminski and Lauren Wright

In this, the final exploration before the dreaded final assignment, we took on the very challenging task of boiling water, measuring its temperature, and graphing the data. You would think that for two people with a combined total of 33 years of education, that this would be a no brainer. You thought wrong!

This is not to say that we were unable to boil water. We had a cookbook, and used my mother's recipe to perfection. (Take one pot of water, put it on the stove, and heat until boiling. Feel free to use this the next time you need to create boiling water for any household usage.) But, when we took our data and matched it against the formula for Newton's Law of Cooling, we found that we had not done a good job of measuring the temperature. Let me take you back to the beginning...

It was a fine Autumn day. The temperature inside Lauren's house was balmy 74 degrees Fahrenheit. We proceeded to bring a pot of water to boil, and to measure the temperature at one minute intervals. Here is that collected data

 Minute Temperature 0 212 1 204 2 192 3 186 4 180 5 175 6 171 7 168 8 164 9 162 10 159 11 155 12 153 13 151 14 149 15 147 16 145 17 143 18 142 19 139 20 139 21 136 22 135 23 134 24 132 25 131 26 130 27 129 28 128 29 127 30 125

And, upon our return to 6680 class, we looked up the formula for Newton's Law of Cooling to help us model the actual cooling function that our data should obey. The formula for Newton's Law of Cooling is:

Where t = time in minutes, is the room temperature, is the original temperature, in this case, 212 degrees Fahrenheit, and contains k, the experimental constant. In order to find k, we first solved the equation for k given the following values of t: T(3), T(11), T(19), T(26), and T(29). Then, we averaged these values to find our value for k. We calculated k to be approximately .042901. Then, armed with this knowledge, we set up our Excel file to calculate the true cooling function or each data point based on Newton's Law.

 Minute Temperature Newton's Data 0 212 212 1 204 206.204859462488 2 192 200.653078735481 3 186 195.334438222578 4 180 190.239147486782 5 175 185.357827228474 6 171 180.681492020207 7 168 176.201533766522 8 164 171.909705858361 9 162 167.798107992885 10 159 163.859171630773 11 155 160.085646064217 12 153 156.470585069981 13 151 153.007334122942 14 149 149.68951814659 15 147 146.511029777924 16 145 143.46601812515 17 143 140.548877997494 18 142 137.754239587282 19 139 135.076958585322 20 139 132.512106711368 21 136 130.05496264225 22 135 127.701003320969 23 134 125.445895630749 24 132 123.285488418732 25 131 121.215804854627 26 130 119.233035110248 27 129 117.333529346465 28 128 115.51379099466 29 127 113.77047032032 30 125 112.10035825692

The graph of both of these data points is below.

As you can see, we didn't do a very good job of measuring the temperatures. Our perceived fears regarding this were justified when we calculated the average error of our calculations.

In order to find our average error, we took the difference between our measured temperature an the calculated one, and squared it. We then averaged the errors to find our average error.

 Minute Temperature Newton's Data Error 0 212 212 0 1 204 206.204859462488 4.86140524932501 2 192 200.653078735481 74.8757716024274 3 186 195.334438222578 87.1317369311177 4 180 190.239147486782 104.840141256067 5 175 185.357827228474 107.28458489492 6 171 180.681492020207 93.7312877373225 7 168 176.201533766522 67.265156123395 8 164 171.909705858361 62.5634467657846 9 162 167.798107992885 33.6180562971587 10 159 163.859171630773 23.6115489373111 11 155 160.085646064217 25.8637958904902 12 153 156.470585069981 12.0449607279755 13 151 153.007334122942 4.02939028112886 14 149 149.68951814659 0.475435274477404 15 147 146.511029777924 0.239091878077475 16 145 143.46601812515 2.35310039236828 17 143 140.548877997494 6.0079990711704 18 142 137.754239587282 18.0264814822011 19 139 135.076958585322 15.3902539412768 20 139 132.512106711368 42.092759324679 21 136 130.05496264225 35.3434691850422 22 135 127.701003320969 53.2753525205067 23 134 125.445895630749 73.1727015600435 24 132 123.285488418732 75.942712100058 25 131 121.215804854627 95.7304746427387 26 130 119.233035110248 115.927532937147 27 129 117.333529346465 136.106537509792 28 128 115.51379099466 155.905415325043 29 127 113.77047032032 175.020455545546 30 125 112.10035825692 166.40075709982 60.2945745962713

As you can see, our average error was over 60. Not too good. There are many possibilities as to why this happened. One major cause of error could be in the accuracy of measurement of our thermometer. Another reason of course is human error in reading the thermometer. (I was in charge of this, so you know it definitely has errors.) I guess we could repeat the experiment and try to do a better job of measuring the data, but it's the end of the semester, and I'm not really keen on spending another half-hour of my life watching water cool down. Perhaps over Winter Break...