Pre-Algebra
Pre-Algebra
1st Edition
ISBN: 9780618800766
Author: Ron Larson, Lee Stiff, Laurie Boswell, Timothy Kanold
Publisher: Houghton Mifflin-High School
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Chapter 1.6, Problem 34E

(a).

To determine

To Calculate: The change in temperature during various production stages of ice cream

(a).

Expert Solution
Check Mark

Answer to Problem 34E

The absolute values of changes in temperature are:

Pasteurization (Stage I) - Aging (Stage II): 85oC

Aging (Stage II) − Hardening (Stage III): 35oC

Hardening (Stage III) − Storage (Stage-IV): 25oC

Explanation of Solution

Given Information:

  • Pasteurization (Stage I) temperature is 80oC .
  • Aging (Stage II) temperature is 5oC .
  • Hardening (Stage III) temperature is 40oC .
  • Storage (Stage IV) temperature is 15oC .

Method:

  • The change in a quantity is found by subtracting the initial value of the quantity from the value after change.
  • To subtract an integer, add its opposite.

Stage I-II: The change in the temperature is 5(80) and the opposite of 80 is 80 .

Therefore, write the expression 5(80) as 5+(80) .

Further write the expression as (5+80) and 5+80 is 85 .

So, the change in temperature is 85oC and therefore, the absolute value of the change in temperature is 85oC .

Stage II-III: The change in the temperature is 40(5) and the opposite of 5 is 5 .

Therefore, write the expression 40(5) as 40+5 .

Meanwhile 40+5 is equal to 35 .

So, the change in temperature is 35oC and therefore, the absolute value of the change in temperature is 35oC .

Stage II-III: The change in the temperature is 15(40) and the opposite of 40 is 40 .

Therefore, write the expression 15(40) as 15+40 .

Meanwhile 15+40 is equal to 25 .

So, the change in temperature is 25oC and therefore, the absolute value of the change in temperature is also 25oC .

(b).

To determine

To Compare: The absolute values of changes in temperature during various stages of ice cream production and identify the greatest absolute change.

(b).

Expert Solution
Check Mark

Answer to Problem 34E

The absolute change in temperature is the maximum between Stage I(Pasteurization) and Stage II(Aging). The value of the change is 85oC .

Explanation of Solution

Given Information: The absolute values of the temperature calculated from the previous sub-part.

Stage I-II: 85oC

Stage II-III: 35oC

Stage III-IV: 25oC

Among 85, 35, and 25, the integer 85 is the highest. Therefore, the highest absolute change in temperature of 85oC is between the corresponding consecutive processes of Pasteurization (Stage I) and Aging (Stage II).

(c).

To determine

To Calculate: The difference in the temperature of mouth and the temperature of ice cream just out of freezer.

(c).

Expert Solution
Check Mark

Answer to Problem 34E

The temperature of the mouth is greater than the temperature of the ice cream, just out of freezer, by about 52oC .

Explanation of Solution

Given Information: The temperature of the mouth is 99oF . The storage temperature of ice cream is 15oC .

The formula to convert temperature form Fahrenheit scale to Celsius scale is

  C=5(F32)9

Method:

  • Put the value of the temperature of mouth given in Fahrenheit scale in the above formula to convert it to Celsius scale.
  • To find about how much warmer is the mouth compared to the stored ice cream, subtract the temperature of the stored ice cream from the temperature of mouth.

Put the given value of the mouth temperature 99oF in the formula to get

  C=5(9932)9=37oC(approximately)

The difference in temperature is then given by 37(15) .

Meanwhile, the opposite of 15 is 15 .

So, write 37(15) as 37+15 and 37+15 is in fact equal to 52 .

Therefore, the temperature of the mouth is greater than the temperature of stored ice cream by about approximately 52oC .

Chapter 1 Solutions

Pre-Algebra

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