Chapter 1, Problem 57E

Convert the following Fahrenheit temperatures to the Celsius and Kelvin scales.

1. a. −459°F, an extremely low temperature
2. b. −40,°F, the answer to a trivia question
3. c. 68°F, room temperature
4. d. 7 × 10⁷ °F, temperature required to initiate fusion reactions in the sun

Interpretation Introduction

Interpretation:

The given temperature unit conversions has to be given.

Concept introduction:

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

$\begin{array}{l}{\text{Conversion of }}^{\text{o}}\text{F}\text{into}{}^{\text{o}}\text{C:}\\ {}^{\text{o}}\text{C}\text{=}\left({}^{\text{o}}\text{F}\text{-}{\text{32}}^{\text{o}}\text{F}\right)\text{×}\frac{{\text{5}}^{\text{o}}\text{C}}{{\text{9}}^{\text{o}}\text{F}}\\ {\text{Conversion of }}^{\text{o}}\text{C}\text{into}{}^{\text{o}}\text{F:}\\ {}^{\text{o}}\text{F}\text{=}\left({}^{\text{o}}\text{C}\text{×}\frac{{\text{9}}^{\text{o}}\text{F}}{{\text{5}}^{\text{o}}\text{C}}\right)\text{+}{\text{32}}^{\text{o}}\text{F}\\ {\text{Conversion of }}^{\text{o}}\text{C}\text{into}\text{K:}\\ \text{K = °C + 273}\text{.15}\end{array}$

To convert: The given Fahrenheit temperature into Celsius and Kelvin scales

Answer to Problem 57E

The temperature conversion was $\text{-273}{}^{\text{o}}\text{C}\text{and}\text{0}\text{.15}\text{K}\text{.}$

Explanation of Solution

The temperature unit conversions is given below

Given data:

$\text{-}\text{459}{}^{\text{o}}\text{F}$

Unit conversion formula

$\begin{array}{l}{\text{Conversion of }}^{\text{o}}\text{F}\text{into}{}^{\text{o}}\text{C:}\\ {}^{\text{o}}\text{C}\text{=}\left({}^{\text{o}}\text{F}\text{-}{\text{32}}^{\text{o}}\text{F}\right)\text{×}\frac{{\text{5}}^{\text{o}}\text{C}}{{\text{9}}^{\text{o}}\text{F}}\\ {\text{Conversion of }}^{\text{o}}\text{C}\text{into}\text{K:}\\ \text{K = °C + 273}\text{.15}\end{array}$

Apply the unit conversion to calculate the given temperature in ${}^{\text{o}}\text{C}\text{unit}$

$\begin{array}{l}{}^{\text{o}}\text{C}\text{=}\left({}^{\text{o}}\text{F}\text{-}{\text{32}}^{\text{o}}\text{F}\right)\text{×}\frac{{\text{5}}^{\text{o}}\text{C}}{{\text{9}}^{\text{o}}\text{F}}\\ \text{=}\left(\text{-459}{}^{\text{o}}\text{F-32}{}^{\text{o}}\text{F}\right)\text{×}\frac{{\text{5}}^{\text{o}}\text{C}}{{\text{9}}^{\text{o}}\text{F}}\\ \text{=}\text{-273}{}^{\text{o}}\text{C}\end{array}$

Apply the unit conversion to calculate the given temperature in $\text{K}\text{unit}$

$\begin{array}{l}\text{K = °C + 273}\text{.15}\\ \text{=}\text{-273}\text{°C}\text{+}\text{273}\text{.15}\\ \text{=}\text{0}\text{.15}\text{K}\end{array}$

Interpretation Introduction

Interpretation:

The given temperature unit conversions has to be given.

Concept introduction:

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

$\begin{array}{l}{\text{Conversion of }}^{\text{o}}\text{F}\text{into}{}^{\text{o}}\text{C:}\\ {}^{\text{o}}\text{C}\text{=}\left({}^{\text{o}}\text{F}\text{-}{\text{32}}^{\text{o}}\text{F}\right)\text{×}\frac{{\text{5}}^{\text{o}}\text{C}}{{\text{9}}^{\text{o}}\text{F}}\\ {\text{Conversion of }}^{\text{o}}\text{C}\text{into}{}^{\text{o}}\text{F:}\\ {}^{\text{o}}\text{F}\text{=}\left({}^{\text{o}}\text{C}\text{×}\frac{{\text{9}}^{\text{o}}\text{F}}{{\text{5}}^{\text{o}}\text{C}}\right)\text{+}{\text{32}}^{\text{o}}\text{F}\\ {\text{Conversion of }}^{\text{o}}\text{C}\text{into}\text{K:}\\ \text{K = °C + 273}\text{.15}\end{array}$

To convert: The given Fahrenheit temperature into Celsius and Kelvin scales

Answer to Problem 57E

The temperature conversion was $\text{-40}{}^{\text{o}}\text{C}\text{and}\text{233}\text{.15}\text{K}\text{.}$

Explanation of Solution

The temperature unit conversions is given below

Given data:

$\text{-}\text{40}{}^{\text{o}}\text{F}$

Apply the unit conversion to calculate the given temperature in ${}^{\text{o}}\text{C}\text{unit}$

$\begin{array}{l}{}^{\text{o}}\text{C}\text{=}\left({}^{\text{o}}\text{F}\text{-}{\text{32}}^{\text{o}}\text{F}\right)\text{×}\frac{{\text{5}}^{\text{o}}\text{C}}{{\text{9}}^{\text{o}}\text{F}}\\ \text{=}\left(\text{-40}{}^{\text{o}}\text{F-32}{}^{\text{o}}\text{F}\right)\text{×}\frac{{\text{5}}^{\text{o}}\text{C}}{{\text{9}}^{\text{o}}\text{F}}\\ \text{=}\text{-40}{}^{\text{o}}\text{C}\end{array}$

Apply the unit conversion to calculate the given temperature in $\text{K}\text{unit}$

$\begin{array}{l}\text{K = °C + 273}\text{.15}\\ \text{=}\text{-40}\text{°C}\text{+}\text{273}\text{.15}\\ \text{=}\text{233}\text{.15}\text{K}\end{array}$

Interpretation Introduction

Interpretation:

The given temperature unit conversions has to be given.

Concept introduction:

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

$\begin{array}{l}{\text{Conversion of }}^{\text{o}}\text{F}\text{into}{}^{\text{o}}\text{C:}\\ {}^{\text{o}}\text{C}\text{=}\left({}^{\text{o}}\text{F}\text{-}{\text{32}}^{\text{o}}\text{F}\right)\text{×}\frac{{\text{5}}^{\text{o}}\text{C}}{{\text{9}}^{\text{o}}\text{F}}\\ {\text{Conversion of }}^{\text{o}}\text{C}\text{into}{}^{\text{o}}\text{F:}\\ {}^{\text{o}}\text{F}\text{=}\left({}^{\text{o}}\text{C}\text{×}\frac{{\text{9}}^{\text{o}}\text{F}}{{\text{5}}^{\text{o}}\text{C}}\right)\text{+}{\text{32}}^{\text{o}}\text{F}\\ {\text{Conversion of }}^{\text{o}}\text{C}\text{into}\text{K:}\\ \text{K = °C + 273}\text{.15}\end{array}$

To convert: The given Fahrenheit temperature into Celsius and Kelvin scales

Answer to Problem 57E

The temperature conversion was $\text{20}{}^{\text{o}}\text{C}\text{and}\text{293}\text{.15}\text{K}\text{.}$

Explanation of Solution

The temperature unit conversions is given below

Given data:

$\text{68}{}^{\text{o}}\text{F}$

Apply the unit conversion to calculate the given temperature in ${}^{\text{o}}\text{C}\text{unit}$

$\begin{array}{l}{}^{\text{o}}\text{C}\text{=}\left({}^{\text{o}}\text{F}\text{-}{\text{32}}^{\text{o}}\text{F}\right)\text{×}\frac{{\text{5}}^{\text{o}}\text{C}}{{\text{9}}^{\text{o}}\text{F}}\\ \text{=}\left(\text{68}{}^{\text{o}}\text{F-32}{}^{\text{o}}\text{F}\right)\text{×}\frac{{\text{5}}^{\text{o}}\text{C}}{{\text{9}}^{\text{o}}\text{F}}\\ \text{=}\text{20}{}^{\text{o}}\text{C}\end{array}$

Apply the unit conversion to calculate the given temperature in $\text{K}\text{unit}$

$\begin{array}{l}\text{K = °C + 273}\text{.15}\\ \text{=}\text{20}\text{°C}\text{+}\text{273}\text{.15}\\ \text{=}\text{293}\text{.15}\text{K}\end{array}$

Interpretation Introduction

Interpretation:

The given temperature unit conversions has to be given.

Concept introduction:

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

$\begin{array}{l}{\text{Conversion of }}^{\text{o}}\text{F}\text{into}{}^{\text{o}}\text{C:}\\ {}^{\text{o}}\text{C}\text{=}\left({}^{\text{o}}\text{F}\text{-}{\text{32}}^{\text{o}}\text{F}\right)\text{×}\frac{{\text{5}}^{\text{o}}\text{C}}{{\text{9}}^{\text{o}}\text{F}}\\ {\text{Conversion of }}^{\text{o}}\text{C}\text{into}{}^{\text{o}}\text{F:}\\ {}^{\text{o}}\text{F}\text{=}\left({}^{\text{o}}\text{C}\text{×}\frac{{\text{9}}^{\text{o}}\text{F}}{{\text{5}}^{\text{o}}\text{C}}\right)\text{+}{\text{32}}^{\text{o}}\text{F}\\ {\text{Conversion of }}^{\text{o}}\text{C}\text{into}\text{K:}\\ \text{K = °C + 273}\text{.15}\end{array}$

To convert: The given Fahrenheit temperature into Celsius and Kelvin scales

Answer to Problem 57E

The temperature conversion was $\text{38888871}\text{.11}{}^{\text{o}}\text{C}\text{and}\text{38889144}\text{.26}\text{K}\text{.}$

Explanation of Solution

The temperature unit conversions is given below

Given data:

$\text{7}\text{×}{\text{10}}^{\text{7}}{}^{\text{o}}\text{F}$

Apply the unit conversion to calculate the given temperature in ${}^{\text{o}}\text{C}\text{unit}$

$\begin{array}{l}{}^{\text{o}}\text{C}\text{=}\left({}^{\text{o}}\text{F}\text{-}{\text{32}}^{\text{o}}\text{F}\right)\text{×}\frac{{\text{5}}^{\text{o}}\text{C}}{{\text{9}}^{\text{o}}\text{F}}\\ \text{=}\left(\text{70000000}{}^{\text{o}}\text{F-32}{}^{\text{o}}\text{F}\right)\text{×}\frac{{\text{5}}^{\text{o}}\text{C}}{{\text{9}}^{\text{o}}\text{F}}\\ \text{=}\text{38888871}\text{.11}{}^{\text{o}}\text{C}\end{array}$

Apply the unit conversion to calculate the given temperature in $\text{K}\text{unit}$

$\begin{array}{l}\text{K = °C + 273}\text{.15}\\ \text{=}\text{38888871}\text{.11}\text{+}\text{273}\text{.15}\\ \text{=}\text{38889144}\text{.26}\text{K}\end{array}$