Newton's Law of Cooling Math Assignment Winston Boon

8/12/2019 Newton's Law of Cooling Math Assignment Winston Boon

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Room temperature 21.8

Time (seconds) Temperature of

water (C)

Temperature

Difference

0 48.70190175 26.90

10 48.63548995 26.8420 48.56557104 26.77

30 48.49215766 26.69

40 48.42062441 26.62

50 48.29030286 26.49

60 48.18518696 26.39

70 48.08203639 26.28

80 48.01277831 26.21

90 47.95069292 26.15

100 47.83202559 26.03

110 47.7400892 25.94

120 47.66240783 25.86

130 47.57601804 25.78

140 47.48095737 25.68

150 47.35795434 25.56

160 47.32812009 25.53

170 47.28076659 25.48

180 47.15992035 25.36

190 47.08647952 25.29

200 47.01312726 25.21

210 46.90674864 25.11

220 46.81969071 25.02230 46.75187109 24.95

240 46.66850318 24.87

250 46.60084951 24.80

260 46.50729701 24.71

270 46.44154811 24.64

280 46.34650791 24.55

290 46.24816388 24.45

300 46.17407638 24.37

310 46.12760087 24.33

320 46.0364706 24.24

330 45.94890292 24.15

340 45.89402011 24.09

350 45.79466543 23.99

360 45.71426708 23.91

370 45.63738433 23.84

380 45.59641777 23.80

390 45.48900428 23.69

400 45.40898646 23.61

20.00

21.00

22.00

23.00

24.00

25.00

26.00

27.0028.00

0DifferenceinWaterandRoom

Temperature(C)

Diff


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410 45.35626273 23.56

420 45.28320048 23.48

430 45.17799871 23.38

440 45.12037912 23.32

450 45.06450252 23.26

460 44.97148009 23.17

470 44.89377998 23.09480 44.82460221 23.02

490 44.76560492 22.97

500 44.6528126 22.85

510 44.56204343 22.76

520 44.48314027 22.68

530 44.43282477 22.63

540 44.35072318 22.55

550 44.27373851 22.47

560 44.20853703 22.41

570 44.1467367 22.35

580 44.05830893 22.26

590 43.99164624 22.19

600 43.91506373 22.12


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y = 26.909e-3E-04x

R = 0.9998

100 200 300 400 500 600

Time (seconds)

rence in Temperature of Boiling Water and

oom Temperature with respect to Time


4/27

Room temperature 21.8 Add milk straight away

30mL milk


water (C)

Temperature

Difference

0 55.95914332 34.16

10 50.38807114 28.5920 50.22543817 28.43

30 50.19960922 28.40

40 50.07064629 28.27

50 49.9823888 28.18

60 49.96401957 28.16

70 49.83377308 28.03

80 49.78249228 27.98

90 49.65449673 27.85

100 49.53043872 27.73

110 49.40301829 27.60

120 49.30673457 27.51

130 49.1599006 27.36

140 49.0839141 27.28

150 49.02428164 27.22

160 48.88538153 27.09

170 48.73962907 26.94

180 48.63010856 26.83

190 48.50826481 26.71

200 48.38131868 26.58

210 48.25108498 26.45

220 48.09269873 26.29230 47.99680724 26.20

240 47.88158894 26.08

250 47.71006392 25.91

260 47.60068808 25.80

270 47.49679034 25.70

280 47.38955966 25.59

290 47.26323768 25.46

300 47.09172235 25.29

310 46.99218568 25.19

320 46.89106909 25.09

330 46.7814243 24.98

340 46.67023886 24.87

350 46.54539397 24.75

360 46.40697129 24.61

370 46.27230426 24.47

380 46.12243904 24.32

390 45.97464557 24.17

400 45.82548308 24.03

2

2

2

2

2

3

3

3

Differencebetweenwaterandroom

temperature(C)


5/27

410 45.70230149 23.90

420 45.57253265 23.77

430 45.43961991 23.64

440 45.31207576 23.51

450 45.19834714 23.40

460 45.08650884 23.29

470 45.00021848 23.20480 44.88871574 23.09

490 44.80099702 23.00

500 44.65617678 22.86

510 44.51334758 22.71

520 44.39930189 22.60

530 44.26035876 22.46

540 44.1216984 22.32

550 43.98498352 22.18

560 43.90840839 22.11

570 43.80367098 22.00

580 43.72397682 21.92

590 43.61288892 21.81

600 43.51851962 21.72


6/27


7/27

Room temperature 21.8 Add milk after 340 sec

30mL milk


water (C)

Temperature

Difference

0 55.36575719 33.57

10 55.39637532 33.6020 55.34943549 33.55

30 55.08092311 33.28

40 55.0403694 33.24

50 54.91486826 33.11

60 54.6125703 32.81

70 54.56638317 32.77

80 54.42407973 32.62

90 54.31812157 32.52

100 54.12279751 32.32

110 53.94607773 32.15

120 53.88863063 32.09

130 53.72260551 31.92

140 53.53943383 31.74

150 53.35301142 31.55

160 53.20241599 31.40

170 53.02112399 31.22

180 52.88315279 31.08

190 52.78233998 30.98

200 52.49071576 30.69

210 52.36953219 30.57

220 52.25630012 30.46230 51.98287756 30.18

240 51.80772446 30.01

250 51.72985539 29.93

260 51.55176039 29.75

270 51.41386602 29.61

280 51.21615161 29.42

290 51.10912761 29.31

300 50.92188209 29.12

310 50.69246104 28.89

320 50.55490316 28.75

330 50.36771554 28.57

340 50.31963244 28.52

350 45.60153717 23.80

360 45.25943043 23.46

370 45.18478082 23.38

380 45.12037912 23.32

390 45.04250355 23.24

400 45.02051193 23.22

Differenceinwaterandroom


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410 44.94106483 23.14

420 44.8448419 23.04

430 44.72181215 22.92

440 44.53685152 22.74

450 44.49824223 22.70

460 44.39930189 22.60

470 44.3071994 22.51480 44.20686601 22.41

490 44.0833241 22.28

500 44.02496952 22.22

510 43.93336922 22.13

520 43.8119777 22.01

530 43.72563619 21.93

540 43.62282991 21.82

550 43.55989407 21.76

560 43.48213019 21.68

570 43.38298143 21.58

580 43.29716452 21.50

590 43.18839175 21.39

600 43.1291308 21.33


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nds

y = 35.64e-9E-04x

R = 0.9237

20.00

22.00

24.00

26.00

28.00

30.00

32.00

34.00

0 100 200 300 400 500 600

temperature(C)

Time (seconds)

The Relationship between Difference in Temperatureand Time when Milk is added to Coffee after 5 minutes


10/27

Room temperature 21.8 100


water (C)

Temperature

Difference

0 68.87357047 47.07

10 68.51119946 46.7120 67.995747 46.20

30 67.3116173 45.51

40 66.64701797 44.85

50 66.14983782 44.35

60 65.53236937 43.73

70 65.00287251 43.20

80 64.56555818 42.77

90 63.98879725 42.19

100 63.49340492 41.69

110 62.95543627 41.16

120 62.54386554 40.74

130 62.03675498 40.24

140 61.60350561 39.80

150 61.05415512 39.25

160 60.68106768 38.88

170 60.21122726 38.41

180 59.80477664 38.00

190 59.34639277 37.55

200 58.93234332 37.13

210 58.63798479 36.84

220 58.21520472 36.42230 57.89745698 36.10

240 57.46013306 35.66

250 57.10731538 35.31

260 56.60401143 34.80

270 56.29711842 34.50

280 55.94468297 34.14

290 55.62561085 33.83

300 55.32088585 33.52

310 54.94520166 33.15

320 54.61056126 32.81

330 54.30414416 32.50

340 53.95004205 32.15

350 53.59451177 31.79

360 53.34517719 31.55

370 52.99194394 31.19

380 52.67206167 30.87

390 52.39643728 30.60

400 52.14140216 30.34

2

2

3

3

4

4

5

Differenceinwa

terandroom

temperature(C)


11/27

410 51.74314193 29.94

420 51.47615731 29.68

430 51.16918483 29.37

440 50.94244712 29.14

450 50.67199113 28.87

460 50.36771554 28.57

470 50.0945737 28.29480 49.80446397 28.00

490 49.55413442 27.75

500 49.34304872 27.54

510 49.10018836 27.30

520 48.80975991 27.01

530 48.57990648 26.78

540 48.31527344 26.52

550 48.05361295 26.25

560 47.81256562 26.01

570 47.56720978 25.77

580 47.28251976 25.48

590 47.05852539 25.26

600 46.88584346 25.09


12/27

y = 46.218e-0.001x

R = 0.9977

0.00

5.00

0.00

5.00

0.00

5.00

0.00

0 100 200 300 400 500 600

Time (seconds)

Rate of Cooling of Boiling Water in a 100mL

Container.


13/27

Room temperature 21.8 250mL


water (C)

Temperature

Difference

0 77.49931068 55.70

10 77.09297204 55.2920 76.72557341 54.93

30 76.30041205 54.50

40 75.80941096 54.01

50 75.4612328 53.66

60 75.04704692 53.25

70 74.67330637 52.87

80 74.35823492 52.56

90 73.88258671 52.08

100 73.62163785 51.82

110 73.34675233 51.55

120 72.880599 51.08

130 72.65121574 50.85

140 72.19659012 50.40

150 71.97434511 50.17

160 71.60580319 49.81

170 71.31829254 49.52

180 70.94714774 49.15

190 70.60005931 48.80

200 70.36942849 48.57

210 69.95543947 48.16

220 69.76298963 47.96230 69.51451161 47.71

240 69.2110783 47.41

250 68.92681493 47.13

260 68.58896554 46.79

270 68.34507556 46.55

280 68.12741227 46.33

290 67.84541942 46.05

300 67.49506167 45.70

310 67.19605179 45.40

320 66.88329512 45.08

330 66.64172439 44.84

340 66.32013167 44.52

350 65.99848949 44.20

360 65.70007133 43.90

370 65.47062367 43.67

380 65.25525032 43.46

390 64.92923848 43.13

400 64.61335929 42.81

35.00

40.00

45.00

50.00

55.00

60.00

0 100


temperature

(C)

The Rate of Cooli


14/27

410 64.33238357 42.53

420 64.05579602 42.26

430 63.84771075 42.05

440 63.61854295 41.82

450 63.39307579 41.59

460 63.16152886 41.36

470 62.91433906 41.11480 62.73110042 40.93

490 62.40995105 40.61

500 62.14101427 40.34

510 61.99417704 40.19

520 61.83606566 40.04

530 61.44216252 39.64

540 61.13518502 39.34

550 60.97327701 39.17

560 60.80737324 39.01

570 60.59172763 38.79

580 60.39764521 38.60


15/27

y = 55.225e-6E-04x

R = 0.9992

200 300 400 500 600

Time (seconds)

g of Boiling Water in a 250mL

Container


16/27

Room temperature 21.8 500mL


water (C)

Temperature

Difference

0 86.92895478 65.13

10 86.56363242 64.7620 86.08986077 64.29

30 85.79086258 63.99

40 85.52524859 63.73

50 84.86553963 63.07

60 84.29879921 62.50

70 83.68237632 61.88

80 83.40305692 61.60

90 83.30767727 61.51

100 82.79783444 61.00

110 82.42020407 60.62

120 81.80753892 60.01

130 81.85918748 60.06

140 81.31469919 59.51

150 80.84788692 59.05

160 80.3680124 58.57

170 80.07179161 58.27

180 79.27139499 57.47

190 78.53183182 56.73

200 78.48836947 56.69

210 78.24665776 56.45

220 77.68294283 55.88230 77.74672418 55.95

240 77.69002413 55.89

250 77.24656839 55.45

260 76.5535438 54.75

270 76.5329544 54.73

280 76.11339774 54.31

290 75.70863714 53.91

300 75.25521676 53.46

310 75.12951392 53.33

320 74.58859189 52.79

330 74.41650041 52.62

340 73.95610812 52.16

350 73.77416728 51.97

360 73.32472249 51.52

370 73.18654456 51.39

380 72.80915451 51.01

390 72.35876739 50.56

400 72.1477672 50.35

4

4

5

5

6

6

7

Differencebetweenw

aterandroom

temperature(C)


17/27

410 71.92883926 50.13

420 71.91065219 50.11

430 71.44381156 49.64

440 71.26760445 49.47

450 70.93533039 49.14

460 70.676267 48.88

470 70.47435447 48.67480 70.03615113 48.24

490 69.54868987 47.75

500 69.26761507 47.47

510 69.40647863 47.61

520 69.1377031 47.34

530 68.46683091 46.67

540 67.90274962 46.10

550 67.63591795 45.84

560 67.45992574 45.66

570 67.24976137 45.45

580 67.22021212 45.42

590 66.93658411 45.14

600 66.52808137 44.73


18/27

y = 64.755e-6E-04x

R = 0.998

0.00

5.00

0.00

5.00

0.00

5.00

0.00

0 100 200 300 400 500 600

Time (seconds)

Rate of Cooling of Boiling Water in a 500mL

Container


19/27


20/27

430 49.314 27.51

440 49.21605 27.42

450 49.0803 27.28

460 48.93585 27.14

470 48.82056 27.02

480 48.65523 26.86

490 48.52975 26.73500 48.40275 26.60

510 48.30457 26.50

520 48.15493 26.35

530 48.00745 26.21

540 47.83379 26.03

550 47.63948 25.84

560 47.53551 25.74

570 47.372 25.57

580 47.29655 25.50

590 47.18792 25.39

600 47.02884 25.23


21/27

y = 34.925e-5E-04x

R = 0.9994

300 400 500 600

ime (seconds)

ling Water in a Styrofoam

tainer


22/27

21.8

0 56.67948 34.88

10 56.4994 34.70

20 56.08949 34.29

30 55.77562 33.98

40 55.4168 33.6250 55.13572 33.34

60 54.79776 33.00

70 54.47614 32.68

80 54.17454 32.37

90 53.86092 32.06

100 53.61026 31.81

110 53.26299 31.46

120 52.98028 31.18

130 52.70106 30.90

140 52.43105 30.63

150 52.14905 30.35

160 51.83054 30.03

170 51.5234 29.72

180 51.22555 29.43

190 50.9836 29.18

200 50.6906 28.89

210 50.45289 28.65

220 50.19961 28.40

230 49.94749 28.15

240 49.65084 27.85

250 49.39029 27.59260 49.14904 27.35

270 48.89619 27.10

280 48.68933 26.89

290 48.42599 26.63

300 48.19587 26.40

310 47.96665 26.17

320 47.68358 25.88

330 47.44579 25.65

340 47.19842 25.40

350 46.95381 25.15

360 46.74666 24.95370 46.54539 24.75

380 46.34996 24.55

390 46.16719 24.37

400 45.9489 24.15

410 45.74847 23.95

420 45.53161 23.73

430 45.32397 23.52

440 45.13563 23.34

15.00

20.00

25.00

30.00

35.00

40.00

0 100 200


temperature(C)

T

Rate of Cooling of Boiling


23/27

450 44.94951 23.15

460 44.7336 22.93

470 44.53349 22.73

480 44.32226 22.52

490 44.14841 22.35

500 43.96666 22.17

510 43.7937 21.99520 43.63443 21.83

530 43.45237 21.65

540 43.27243 21.47

550 43.13078 21.33

560 42.92046 21.12

570 42.74839 20.95

580 42.56366 20.76

590 42.41686 20.62

600 42.24921 20.45


24/27

y = 34.689e-9E-04x

R = 0.9992

300 400 500 600

ime (seconds)

ater in a Glass Container


25/27

21.8

0 54.68093 32.88

10 54.65277 32.85

20 54.39407 32.59

30 54.06713 32.27

40 53.78974 31.9950 53.87082 32.07

60 53.58664 31.79

70 53.22976 31.43

80 52.9414 31.14

90 52.62763 30.83

100 52.40605 30.61

110 52.23138 30.43

120 52.04012 30.24

130 51.82864 30.03

140 51.38558 29.59

150 51.21427 29.41

160 50.97986 29.18

170 50.7297 28.93

180 50.32518 28.53

190 49.9732 28.17

200 49.87593 28.08

210 49.75687 27.96

220 49.41029 27.61

230 49.04054 27.24

240 48.80256 27.00

250 48.605 26.81260 48.33312 26.53

270 48.07671 26.28

280 47.67652 25.88

290 47.39132 25.59

300 47.272 25.47

310 47.18792 25.39

320 46.97474 25.17

330 46.84928 25.05

340 46.67371 24.87

350 46.49518 24.70

360 46.21197 24.41370 46.03991 24.24

380 45.84604 24.05

390 45.72623 23.93

400 45.44983 23.65

410 45.26622 23.47

420 45.03404 23.23

430 44.82798 23.03

440 44.56204 22.76

15.00

20.00

25.00

30.00

35.00

0 100 200

Differencebetweenwateran

droom

temperature(C)

Ti

The Rate of Cooling of B

Conta


26/27

450 44.41774 22.62

460 44.18181 22.38

470 44.05998 22.26

480 43.82195 22.02

490 43.64935 21.85

500 43.56652 21.77

510 43.35657 21.56520 43.10774 21.31

530 43.08965 21.29

540 43.0009 21.20

550 42.75985 20.96

560 42.56203 20.76

570 42.47392 20.67

580 42.21345 20.41

590 42.07869 20.28

600 41.91827 20.12


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Documents

Newton's Law of Cooling Math Assignment Winston Boon