Newton's Law of Cooling Math Assignment Winston Boon

Time (seconds) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400

21.8 Temperature of Temperature water (°C) Difference 48.70190175 26.90 48.63548995 26.84 48.56557104 26.77 48.49215766 26.69 48.42062441 26.62 48.29030286 26.49 48.18518696 26.39 48.08203639 26.28 48.01277831 26.21 47.95069292 26.15 47.83202559 26.03 47.7400892 25.94 47.66240783 25.86 47.57601804 25.78 47.48095737 25.68 47.35795434 25.56 47.32812009 25.53 47.28076659 25.48 47.15992035 25.36 47.08647952 25.29 47.01312726 25.21 46.90674864 25.11 46.81969071 25.02 46.75187109 24.95 46.66850318 24.87 46.60084951 24.80 46.50729701 24.71 46.44154811 24.64 46.34650791 24.55 46.24816388 24.45 46.17407638 24.37 46.12760087 24.33 46.0364706 24.24 45.94890292 24.15 45.89402011 24.09 45.79466543 23.99 45.71426708 23.91 45.63738433 23.84 45.59641777 23.80 45.48900428 23.69 45.40898646 23.61

Difference in Tem Room Tempera Difference in Water and Room Temperature (°C)

Room temperature

28.00 27.00 26.00 25.00 24.00 23.00 22.00 21.00 20.00 0

410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600

45.35626273 45.28320048 45.17799871 45.12037912 45.06450252 44.97148009 44.89377998 44.82460221 44.76560492 44.6528126 44.56204343 44.48314027 44.43282477 44.35072318 44.27373851 44.20853703 44.1467367 44.05830893 43.99164624 43.91506373

23.56 23.48 23.38 23.32 23.26 23.17 23.09 23.02 22.97 22.85 22.76 22.68 22.63 22.55 22.47 22.41 22.35 22.26 22.19 22.12

Difference in Temperature of Boiling Water and Room Temperature with respect to Time

y = 26.909e-3E-04x R² = 0.9998 100

200

300

400

Time (seconds)

500

600

Time (seconds) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400

21.8 Temperature of Temperature water (°C) Difference 55.95914332 34.16 50.38807114 28.59 50.22543817 28.43 50.19960922 28.40 50.07064629 28.27 49.9823888 28.18 49.96401957 28.16 49.83377308 28.03 49.78249228 27.98 49.65449673 27.85 49.53043872 27.73 49.40301829 27.60 49.30673457 27.51 49.1599006 27.36 49.0839141 27.28 49.02428164 27.22 48.88538153 27.09 48.73962907 26.94 48.63010856 26.83 48.50826481 26.71 48.38131868 26.58 48.25108498 26.45 48.09269873 26.29 47.99680724 26.20 47.88158894 26.08 47.71006392 25.91 47.60068808 25.80 47.49679034 25.70 47.38955966 25.59 47.26323768 25.46 47.09172235 25.29 46.99218568 25.19 46.89106909 25.09 46.7814243 24.98 46.67023886 24.87 46.54539397 24.75 46.40697129 24.61 46.27230426 24.47 46.12243904 24.32 45.97464557 24.17 45.82548308 24.03

Add milk straight away 30mL milk

Difference between water and room temperature (°C)

Room temperature

34.00 32.00 30.00 28.00 26.00 24.00 22.00 20.00

410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600

45.70230149 45.57253265 45.43961991 45.31207576 45.19834714 45.08650884 45.00021848 44.88871574 44.80099702 44.65617678 44.51334758 44.39930189 44.26035876 44.1216984 43.98498352 43.90840839 43.80367098 43.72397682 43.61288892 43.51851962

23.90 23.77 23.64 23.51 23.40 23.29 23.20 23.09 23.00 22.86 22.71 22.60 22.46 22.32 22.18 22.11 22.00 21.92 21.81 21.72

raight away

The Relationship between Difference in Temperature and Time when Milk is Immediately added to Coffee 34.00 32.00 y = 29.414e-5E-04x R² = 0.9502

temperature (°C)

30.00 28.00 26.00 24.00 22.00 20.00 0

100

200

300

Time (seconds)

400

500

600

21.8

Time (seconds) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400

Temperature of Temperature water (°C) Difference 55.36575719 33.57 55.39637532 33.60 55.34943549 33.55 55.08092311 33.28 55.0403694 33.24 54.91486826 33.11 54.6125703 32.81 54.56638317 32.77 54.42407973 32.62 54.31812157 32.52 54.12279751 32.32 53.94607773 32.15 53.88863063 32.09 53.72260551 31.92 53.53943383 31.74 53.35301142 31.55 53.20241599 31.40 53.02112399 31.22 52.88315279 31.08 52.78233998 30.98 52.49071576 30.69 52.36953219 30.57 52.25630012 30.46 51.98287756 30.18 51.80772446 30.01 51.72985539 29.93 51.55176039 29.75 51.41386602 29.61 51.21615161 29.42 51.10912761 29.31 50.92188209 29.12 50.69246104 28.89 50.55490316 28.75 50.36771554 28.57 50.31963244 28.52 45.60153717 23.80 45.25943043 23.46 45.18478082 23.38 45.12037912 23.32 45.04250355 23.24 45.02051193 23.22

Add milk after 340 seconds 30mL milk

Difference in water and room temperature (°C)

Room temperature

34.00 32.00 30.00 28.00 26.00 24.00 22.00 20.00

410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600

44.94106483 44.8448419 44.72181215 44.53685152 44.49824223 44.39930189 44.3071994 44.20686601 44.0833241 44.02496952 43.93336922 43.8119777 43.72563619 43.62282991 43.55989407 43.48213019 43.38298143 43.29716452 43.18839175 43.1291308

23.14 23.04 22.92 22.74 22.70 22.60 22.51 22.41 22.28 22.22 22.13 22.01 21.93 21.82 21.76 21.68 21.58 21.50 21.39 21.33

fter 340 seconds

The Relationship between Difference in Temperature and Time when Milk is added to Coffee after 5 minutes temperature (°C)

34.00 32.00 30.00 28.00

y = 35.64e-9E-04x R² = 0.9237

26.00 24.00 22.00 20.00 0

100

200

300

400

Time (seconds)

500

600

Time (seconds) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400

21.8 Temperature of Temperature water (°C) Difference 68.87357047 47.07 68.51119946 46.71 67.995747 46.20 67.3116173 45.51 66.64701797 44.85 66.14983782 44.35 65.53236937 43.73 65.00287251 43.20 64.56555818 42.77 63.98879725 42.19 63.49340492 41.69 62.95543627 41.16 62.54386554 40.74 62.03675498 40.24 61.60350561 39.80 61.05415512 39.25 60.68106768 38.88 60.21122726 38.41 59.80477664 38.00 59.34639277 37.55 58.93234332 37.13 58.63798479 36.84 58.21520472 36.42 57.89745698 36.10 57.46013306 35.66 57.10731538 35.31 56.60401143 34.80 56.29711842 34.50 55.94468297 34.14 55.62561085 33.83 55.32088585 33.52 54.94520166 33.15 54.61056126 32.81 54.30414416 32.50 53.95004205 32.15 53.59451177 31.79 53.34517719 31.55 52.99194394 31.19 52.67206167 30.87 52.39643728 30.60 52.14140216 30.34

100

Difference in water and room temperature (°C)

Room temperature

50.00 45.00 40.00 35.00 30.00 25.00 20.00

410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600

51.74314193 51.47615731 51.16918483 50.94244712 50.67199113 50.36771554 50.0945737 49.80446397 49.55413442 49.34304872 49.10018836 48.80975991 48.57990648 48.31527344 48.05361295 47.81256562 47.56720978 47.28251976 47.05852539 46.88584346

29.94 29.68 29.37 29.14 28.87 28.57 28.29 28.00 27.75 27.54 27.30 27.01 26.78 26.52 26.25 26.01 25.77 25.48 25.26 25.09

Rate of Cooling of Boiling Water in a 100mL Container. 50.00 45.00 40.00 y = 46.218e-0.001x R² = 0.9977

35.00 30.00 25.00 20.00 0

100

200

300

400

Time (seconds)

500

600

Time (seconds) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400

21.8 Temperature of Temperature water (°C) Difference 77.49931068 55.70 77.09297204 55.29 76.72557341 54.93 76.30041205 54.50 75.80941096 54.01 75.4612328 53.66 75.04704692 53.25 74.67330637 52.87 74.35823492 52.56 73.88258671 52.08 73.62163785 51.82 73.34675233 51.55 72.880599 51.08 72.65121574 50.85 72.19659012 50.40 71.97434511 50.17 71.60580319 49.81 71.31829254 49.52 70.94714774 49.15 70.60005931 48.80 70.36942849 48.57 69.95543947 48.16 69.76298963 47.96 69.51451161 47.71 69.2110783 47.41 68.92681493 47.13 68.58896554 46.79 68.34507556 46.55 68.12741227 46.33 67.84541942 46.05 67.49506167 45.70 67.19605179 45.40 66.88329512 45.08 66.64172439 44.84 66.32013167 44.52 65.99848949 44.20 65.70007133 43.90 65.47062367 43.67 65.25525032 43.46 64.92923848 43.13 64.61335929 42.81

250mL

Difference between water and room temperature (°C)

Room temperature

The Rate of Cooling of Boiling W Container 60.00 55.00 50.00 45.00 40.00 35.00 0

100

200

410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580

64.33238357 64.05579602 63.84771075 63.61854295 63.39307579 63.16152886 62.91433906 62.73110042 62.40995105 62.14101427 61.99417704 61.83606566 61.44216252 61.13518502 60.97327701 60.80737324 60.59172763 60.39764521

42.53 42.26 42.05 41.82 41.59 41.36 41.11 40.93 40.61 40.34 40.19 40.04 39.64 39.34 39.17 39.01 38.79 38.60

e of Cooling of Boiling Water in a 250mL Container

y = 55.225e-6E-04x R² = 0.9992

200

300

Time (seconds)

400

500

600

Time (seconds) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400

21.8 Temperature of Temperature water (°C) Difference 86.92895478 65.13 86.56363242 64.76 86.08986077 64.29 85.79086258 63.99 85.52524859 63.73 84.86553963 63.07 84.29879921 62.50 83.68237632 61.88 83.40305692 61.60 83.30767727 61.51 82.79783444 61.00 82.42020407 60.62 81.80753892 60.01 81.85918748 60.06 81.31469919 59.51 80.84788692 59.05 80.3680124 58.57 80.07179161 58.27 79.27139499 57.47 78.53183182 56.73 78.48836947 56.69 78.24665776 56.45 77.68294283 55.88 77.74672418 55.95 77.69002413 55.89 77.24656839 55.45 76.5535438 54.75 76.5329544 54.73 76.11339774 54.31 75.70863714 53.91 75.25521676 53.46 75.12951392 53.33 74.58859189 52.79 74.41650041 52.62 73.95610812 52.16 73.77416728 51.97 73.32472249 51.52 73.18654456 51.39 72.80915451 51.01 72.35876739 50.56 72.1477672 50.35

500mL

Difference between water and room temperature (°C)

Room temperature

70.00 65.00 60.00 55.00 50.00 45.00 40.00

410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600

71.92883926 71.91065219 71.44381156 71.26760445 70.93533039 70.676267 70.47435447 70.03615113 69.54868987 69.26761507 69.40647863 69.1377031 68.46683091 67.90274962 67.63591795 67.45992574 67.24976137 67.22021212 66.93658411 66.52808137

50.13 50.11 49.64 49.47 49.14 48.88 48.67 48.24 47.75 47.47 47.61 47.34 46.67 46.10 45.84 45.66 45.45 45.42 45.14 44.73

Rate of Cooling of Boiling Water in a 500mL Container 70.00

temperature (°C)

65.00 60.00

y = 64.755e-6E-04x R² = 0.998

55.00 50.00 45.00 40.00 0

100

200

300

400

Time (seconds)

500

600

Styrofoam Time 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420

Temperature 56.47851 34.67851 56.42214 34.62 56.37834 34.58 56.20565 34.41 56.04393 34.24 55.87245 34.07 55.71391 33.91 55.47198 33.67 55.28217 33.48 55.1276 33.33 54.97151 33.17 54.75744 32.96 54.55434 32.75 54.41007 32.61 54.2383 32.44 54.04528 32.25 53.81939 32.02 53.62207 31.82 53.49424 31.69 53.30798 31.51 53.11071 31.31 52.95112 31.15 52.75523 30.96 52.59867 30.80 52.41374 30.61 52.19882 30.40 52.00577 30.21 51.91427 30.11 51.67674 29.88 51.49883 29.70 51.34976 29.55 51.22743 29.43 51.04164 29.24 50.83037 29.03 50.69432 28.89 50.58276 28.78 50.41954 28.62 50.24205 28.44 50.04673 28.25 49.99525 28.20 49.81545 28.02 49.68738 27.89 49.48126 27.68

Difference between water and room temperature (°C)

21.8

Rate of Cooling of Boiling Water in a Sty Container 36 34 32 30 28 26 24 22 20 0

100

200

Time (seconds)

430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600

49.314 49.21605 49.0803 48.93585 48.82056 48.65523 48.52975 48.40275 48.30457 48.15493 48.00745 47.83379 47.63948 47.53551 47.372 47.29655 47.18792 47.02884

27.51 27.42 27.28 27.14 27.02 26.86 26.73 26.60 26.50 26.35 26.21 26.03 25.84 25.74 25.57 25.50 25.39 25.23

ng of Boiling Water in a Styrofoam Container y = 34.925e-5E-04x R² = 0.9994

300

400

Time (seconds)

500

600

21.8 56.67948 56.4994 56.08949 55.77562 55.4168 55.13572 54.79776 54.47614 54.17454 53.86092 53.61026 53.26299 52.98028 52.70106 52.43105 52.14905 51.83054 51.5234 51.22555 50.9836 50.6906 50.45289 50.19961 49.94749 49.65084 49.39029 49.14904 48.89619 48.68933 48.42599 48.19587 47.96665 47.68358 47.44579 47.19842 46.95381 46.74666 46.54539 46.34996 46.16719 45.9489 45.74847 45.53161 45.32397 45.13563

34.88 34.70 34.29 33.98 33.62 33.34 33.00 32.68 32.37 32.06 31.81 31.46 31.18 30.90 30.63 30.35 30.03 29.72 29.43 29.18 28.89 28.65 28.40 28.15 27.85 27.59 27.35 27.10 26.89 26.63 26.40 26.17 25.88 25.65 25.40 25.15 24.95 24.75 24.55 24.37 24.15 23.95 23.73 23.52 23.34

Rate of Cooling of Boiling Water in a Glass C Difference between water and room temperature (°C)

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440

40.00 35.00 30.00 25.00 20.00 15.00 0

100

200

Time (seconds)

450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600

44.94951 44.7336 44.53349 44.32226 44.14841 43.96666 43.7937 43.63443 43.45237 43.27243 43.13078 42.92046 42.74839 42.56366 42.41686 42.24921

23.15 22.93 22.73 22.52 22.35 22.17 21.99 21.83 21.65 21.47 21.33 21.12 20.95 20.76 20.62 20.45

of Boiling Water in a Glass Container

y = 34.689e-9E-04x R² = 0.9992

300

400

Time (seconds)

500

600

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440

54.68093 54.65277 54.39407 54.06713 53.78974 53.87082 53.58664 53.22976 52.9414 52.62763 52.40605 52.23138 52.04012 51.82864 51.38558 51.21427 50.97986 50.7297 50.32518 49.9732 49.87593 49.75687 49.41029 49.04054 48.80256 48.605 48.33312 48.07671 47.67652 47.39132 47.272 47.18792 46.97474 46.84928 46.67371 46.49518 46.21197 46.03991 45.84604 45.72623 45.44983 45.26622 45.03404 44.82798 44.56204

32.88 32.85 32.59 32.27 31.99 32.07 31.79 31.43 31.14 30.83 30.61 30.43 30.24 30.03 29.59 29.41 29.18 28.93 28.53 28.17 28.08 27.96 27.61 27.24 27.00 26.81 26.53 26.28 25.88 25.59 25.47 25.39 25.17 25.05 24.87 24.70 24.41 24.24 24.05 23.93 23.65 23.47 23.23 23.03 22.76

Difference between water and room temperature (°C)

21.8

The Rate of Cooling of Boiling Water in a P Container 35.00 30.00 25.00 20.00 15.00 0

100

200

300

Time (Seconds)

450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600

44.41774 44.18181 44.05998 43.82195 43.64935 43.56652 43.35657 43.10774 43.08965 43.0009 42.75985 42.56203 42.47392 42.21345 42.07869 41.91827

22.62 22.38 22.26 22.02 21.85 21.77 21.56 21.31 21.29 21.20 20.96 20.76 20.67 20.41 20.28 20.12

oling of Boiling Water in a Plastic Container

y = 33.202e-8E-04x R² = 0.9987

300

400

Time (Seconds)

500

600