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.

Find the rate of decay in the water temperature. Using this rate, find the water temperature after 2 hours. Find the water temperature after 3 hours. When was the water temperature 25°?

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

83.5

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

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	83.5	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