Newton's Law of Cooling

Newton's Law of Cooling

Newton's law of cooling describes the cooling rate of a body relative to the temperatures of the object and the surroundings. The following data was collected for a container of water at an initial temperature of 100°C placed inside a freezer compartment at 0°C. The time is measured in minutes and the temperature is measured in degrees Celsius.

Time

Temp

Time

Temp

Time

Temp

0 100 40 67 80 45

2 98 42 66 82 44

4 96 44 64 84 43

6 94.5 46 63 86 42

8 92.5 48 62 88 41.5

10 90.5 50 61 90 40.5

12 88 52 59 92 40

14 87 54 58 94 39

16 85 56 57 96 38.5

18 93.5 58 56 98 37.5

20 82 60 55 100 36.5

22 80 62 53.5 102 36

24 78.5 64 53 104 35.5

26 77 66 52 106 34.5

28 75 68 50.5 108 34

30 74 70 49.5 110 33

32 73 72 48.5 112 32.5

34 71 74 47.5 114 32

Using a statistical package or a graphing calculator, make a scatterplot with time as the independent variable and temperature as the dependent variable. With a statistical package or a graphing calculator fit a quadratic equation to this data. Use this equation to predict the water temperature after 2 hours, 3 hours, and 4 hours.

With a statistical package or a graphing calculator fit an equation of the form ln y = . . . . Rewrite this equation using properties of exponents so it is of the form y = . . . . Use this equation to predict the water temperature after 2 hours, 3 hours, and 4 hours.

Compare your quadratic predictions with your exponential predictions. Which equation do you think gives the better prediction, the quadratic or exponential? Explain.

Time	Temp	Time	Temp	Time	Temp
0	100	40	67	80	45
2	98	42	66	82	44
4	96	44	64	84	43
6	94.5	46	63	86	42
8	92.5	48	62	88	41.5
10	90.5	50	61	90	40.5
12	88	52	59	92	40
14	87	54	58	94	39
16	85	56	57	96	38.5
18	93.5	58	56	98	37.5
20	82	60	55	100	36.5
22	80	62	53.5	102	36
24	78.5	64	53	104	35.5
26	77	66	52	106	34.5
28	75	68	50.5	108	34
30	74	70	49.5	110	33
32	73	72	48.5	112	32.5
34	71	74	47.5	114	32