# Heat Transfer from Water Bottles

Heat Transfer from Water Bottles Daniel Carlson Daniel Ricks Introduction Cyclists want their water to stay cold What water bottle will keep ice water cold the longest? Is it worth spending the extra money for a fancy water bottle? Introduction 5 Bottles Tested

Traditional Bottle Aquafina Bottle Thermos Insulated Bottle Nalgene Bottle Heat Transfer Problem Pour equal amounts of ice water in the bottles Measure the temperatures for 2 hours Assumptions Assume the bottles are cylinders Neglect heat transfer through lids Assume all the bottles are roughly the same size

Heat Transfer Problem Rconv1 1 h1 2r1 L Rconv2 T TH 2O q Rtotal 1 h2 2r2 L Rcond r2 ln r1

2kL T TH 2O r2 ln r1 1 1 h1 2r1 L h2 2r2 L 2kL Bottles with small k values results in a small rate of heat transfer Results The thermos performed the best The insulated bottle also performed well Traditional bottles are similar in results Temperature Change of Ice Water k values for bottles

k normal .160 kinsulated .126 k aquafina .173 k na lg ene .147 16 14 Temperature (degC) kthermos .092 18 12 Thermos 10 Insulated Nalgene

8 Normal 6 Aquafin 4 2 0 0 20 40 60 Time (minutes) 80

100 120 Conclusion Buying an expensive bottle is worth it (if you like cold water) Using a thermos traditionally used for hot beverages is even better than an insulated water bottle A thermos keeps water cold twice as long as a plastic water bottle Appendix T TH 2 O q Rtotal T TH 2O r2

ln r1 1 1 h1 2r1 L h2 2r2 L 2kL h1 1138 r1 .060 qnormal 25.9 h2 7.4 r2 .065 qthermos 15.8 T 17.4

L .1 qinsulated 21.1 TH 2O 5.1 qaquafina 27.7 qna lg ene 24.0 Solving the equation for k gives: k normal .160 kthermos .092 kinsulated .126 k aquafina .173 k na lg ene .147

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