Chapter 1, Problem 59E

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

1. a. the temperature of someone with a fever, 39.2°C
2. b. a cold wintery day, −25°C
3. c. the lowest possible temperature, −273°C
4. d. the melting-point temperature of sodium chloride, 801°C

Interpretation Introduction

Interpretation:

The given Celsius temperature have to be converted into Fahrenheit and Kelvin scale.

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 Celsius temperature into Fahrenheit and Kelvin scales

Answer to Problem 59E

The temperature was converted as $\text{102}\text{.56}{}^{\text{o}}\text{F}\text{and}\text{312}\text{.15}\text{K}\text{.}$

Explanation of Solution

The temperature unit conversions is given below

Given data:

$\text{39}\text{.2}{}^{\text{o}}\text{C}$

Unit conversion formula

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

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

$\begin{array}{l}{}^{\text{o}}\text{F}\text{=}\left({}^{\text{o}}\text{C}\text{×}\frac{{\text{9}}^{\text{o}}\text{F}}{{\text{5}}^{\text{o}}\text{C}}\right)\text{+}{\text{32}}^{\text{o}}\text{F}\\ \text{=}\left(\text{39}\text{.2}{}^{\text{o}}\text{C}\text{×}\frac{{\text{9}}^{\text{o}}\text{F}}{{\text{5}}^{\text{o}}\text{C}}\right)\text{+}{\text{32}}^{\text{o}}\text{F}\\ \text{=}\text{102}\text{.56}{}^{\text{o}}\text{F}\end{array}$

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

$\begin{array}{l}\text{K = °C + 273}\text{.15}\\ \text{=}\text{39}\text{.2}\text{°C}\text{+}\text{273}\text{.15}\\ \text{=}\text{312}\text{.35}\text{K}\end{array}$

Interpretation Introduction

Interpretation:

The given Celsius temperature have to be converted into Fahrenheit and Kelvin scale.

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 Celsius temperature into Fahrenheit and Kelvin scales

Answer to Problem 59E

The temperature was converted as $\text{-13}{}^{\text{o}}\text{F}\text{and}\text{248}\text{.15}\text{K}\text{.}$

Explanation of Solution

The temperature unit conversions is given below

Given data:

$\text{-25}{}^{\text{o}}\text{C}$

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

$\begin{array}{l}{}^{\text{o}}\text{F}\text{=}\left({}^{\text{o}}\text{C}\text{×}\frac{{\text{9}}^{\text{o}}\text{F}}{{\text{5}}^{\text{o}}\text{C}}\right)\text{+}{\text{32}}^{\text{o}}\text{F}\\ \text{=}\left(\text{-25}{}^{\text{o}}\text{C}\text{×}\frac{{\text{9}}^{\text{o}}\text{F}}{{\text{5}}^{\text{o}}\text{C}}\right)\text{+}{\text{32}}^{\text{o}}\text{F}\\ \text{=}\text{-13}{}^{\text{o}}\text{F}\end{array}$

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

$\begin{array}{l}\text{K = °C + 273}\text{.15}\\ \text{=}\text{-25}\text{°C}\text{+}\text{273}\text{.15}\\ \text{=}\text{248}\text{.15}\text{K}\end{array}$

Interpretation Introduction

Interpretation:

The given Celsius temperature have to be converted into Fahrenheit and Kelvin scale.

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 Celsius temperature into Fahrenheit and Kelvin scales

Answer to Problem 59E

The temperature was converted as $\text{-459}\text{.4}{}^{\text{o}}\text{F}\text{and}\text{0}\text{.15}\text{K}\text{.}$

Explanation of Solution

The temperature unit conversions is given below

Given data:

$\text{-273}{}^{\text{o}}\text{C}$

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

$\begin{array}{l}{}^{\text{o}}\text{F}\text{=}\left({}^{\text{o}}\text{C}\text{×}\frac{{\text{9}}^{\text{o}}\text{F}}{{\text{5}}^{\text{o}}\text{C}}\right)\text{+}{\text{32}}^{\text{o}}\text{F}\\ \text{=}\left(\text{-273}{}^{\text{o}}\text{C}\text{×}\frac{{\text{9}}^{\text{o}}\text{F}}{{\text{5}}^{\text{o}}\text{C}}\right)\text{+}{\text{32}}^{\text{o}}\text{F}\\ \text{=}\text{-459}\text{.4}{}^{\text{o}}\text{F}\end{array}$

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 Celsius temperature have to be converted into Fahrenheit and Kelvin scale.

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 Celsius temperature into Fahrenheit and Kelvin scales

Answer to Problem 59E

The temperature was converted as $\text{1473}\text{.8}{}^{\text{o}}\text{F}\text{and}\text{1074}\text{.15}\text{K}\text{.}$

Explanation of Solution

The temperature unit conversions is given below

Given data:

$\text{801}{}^{\text{o}}\text{C}$

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

$\begin{array}{l}{}^{\text{o}}\text{F}\text{=}\left({}^{\text{o}}\text{C}\text{×}\frac{{\text{9}}^{\text{o}}\text{F}}{{\text{5}}^{\text{o}}\text{C}}\right)\text{+}{\text{32}}^{\text{o}}\text{F}\\ \text{=}\left(\text{801}{}^{\text{o}}\text{C}\text{×}\frac{{\text{9}}^{\text{o}}\text{F}}{{\text{5}}^{\text{o}}\text{C}}\right)\text{+}{\text{32}}^{\text{o}}\text{F}\\ \text{=}\text{1473}\text{.8}{}^{\text{o}}\text{F}\end{array}$

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

$\begin{array}{l}\text{K = °C + 273}\text{.15}\\ \text{=}\text{801}\text{°C}\text{+}\text{273}\text{.15}\\ \text{=}\text{1074}\text{.15}\text{K}\end{array}$