Chemistry
Chemistry
9th Edition
ISBN: 9781133611097
Author: Steven S. Zumdahl
Publisher: Cengage Learning
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Chapter 1, Problem 64E

Ethylene glycol is the main component in automobile anti-freeze. To monitor the temperature of an auto cooling system, you intend to use a meter that reads from 0 to 100. You devise a new temperature scale based on the approximate melting and boiling points of a typical antifreeze solution (−45°C and 115°C). You wish these points to correspond to 0°A and 100°A, respectively.

  1. a. Derive an expression for converting between °A and °C.
  2. b. Derive an expression for converting between °F and °A.
  3. c. At what temperature would your thermometer and a Celsius thermometer give the same numerical reading?
  4. d. Your thermometer reads 86°A. What is the temperature in °C and in °F?
  5. e. What is a temperature of 45°C in °A?

(a)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

By using the given data, the answers for the given set of questions have to be given.

Concept introduction:

Conversion of temperature units in between degree Celsius, Kelvin and Fahrenheit is given by

Conversion of oFintooC:oC=(oF-32oF)×5oC9oFConversion of oCintooF:oF=(oC×9oF5oC)+32oFConversion of oCintoK:K = °C + 273.15

Answer to Problem 64E

The relationship between oCandoA is oC=1.6×oA-45

Explanation of Solution

To give: the relationship between oCandoA

The difference in degrees Celsius unit is 160oC, but in Degrees oA unit is 100oA.

The relationship between oCandoA is given below

temperatureinoC=oA×(85)-45=oA×1.6-45

The relationship between oCandoA is oC=1.6×oA-45

(b)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

By using the given data, the answers for the given set of questions have to be given.

Concept introduction:

Conversion of temperature units in between degree Celsius, Kelvin and Fahrenheit is given by

Conversion of oFintooC:oC=(oF-32oF)×5oC9oFConversion of oCintooF:oF=(oC×9oF5oC)+32oFConversion of oCintoK:K = °C + 273.15

Answer to Problem 64E

The correct expression between oFandoA units is oF=2.88oA-49.

Explanation of Solution

To give: the relationship between oFandoA

The relationship between oFandoC is given by

oC=(oF-32oF)×5oC9oF

Compare the two relationships

(oF-32)×59=85×A-45F-32 = (9/5)×(8/5)×A - (9/5)×(9x5)F-32 = 72/25 A - 81=72/25 A - 81+ 32F = 2.88 A - 49 

The relationship between oFandoA units is oF=2.88oA-49.

(c)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

By using the given data, the answers for the given set of questions have to be given.

Concept introduction:

Conversion of temperature units in between degree Celsius, Kelvin and Fahrenheit is given by

Conversion of oFintooC:oC=(oF-32oF)×5oC9oFConversion of oCintooF:oF=(oC×9oF5oC)+32oFConversion of oCintoK:K = °C + 273.15

Answer to Problem 64E

The thermometer will give same reading at oA=72=oC.

Explanation of Solution

To determine: the temperature at which the thermometer same reading in oAandoC units

Apply the relationship between oCandoA

oC=1.6×oA-45WhenA=CA=1.6×A-4545=(1/1.6)A=0.625AA=72

The thermometer will give same reading at oA=72=oC.

(d)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

By using the given data, the answers for the given set of questions have to be given.

Concept introduction:

Conversion of temperature units in between degree Celsius, Kelvin and Fahrenheit is given by

Conversion of oFintooC:oC=(oF-32oF)×5oC9oFConversion of oCintooF:oF=(oC×9oF5oC)+32oFConversion of oCintoK:K = °C + 273.15

Answer to Problem 64E

The given temperature in degrees Celsius unit is 92.6oC, in degrees Fahrenheit unit is 198.7oF.

Explanation of Solution

To determine: the given temperature in oCandoF units

Given information

86oA

Apply the relationship between oCandoA

oC=1.6×oA-45=1.6×86-45=92.6oC

Apply the relationship between oCandoF

oF=(oC×9oF5oC)+32oF=(92.6oC×9oF5oC)+32oF=198.7oF

The given temperature in degrees Celsius unit is 92.6oC, in degrees Fahrenheit unit is 198.7oF.

(e)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

By using the given data, the answers for the given set of questions have to be given.

Concept introduction:

Conversion of temperature units in between degree Celsius, Kelvin and Fahrenheit is given by

Conversion of oFintooC:oC=(oF-32oF)×5oC9oFConversion of oCintooF:oF=(oC×9oF5oC)+32oFConversion of oCintoK:K = °C + 273.15

Answer to Problem 64E

The given temperature in oA unit is 56.25oA.

Explanation of Solution

To determine: the given temperature in oA unit

Given information

45oC

Apply the relationship between oCandoA

oC=1.6×oA-4545+45=1.6oAA=90/1.6=56.25 oA

The given temperature in oA unit is 56.25oA.

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