Chapter 5.3, Problem 5RQ

(a)

Interpretation Introduction

Interpretation: Conversion of $100°\text{F}$ to Celsius degree needs to be explained.

Concept Introduction: To convert one unit into another, first a conversion factor needs to be chosen. This cancels and omits the units in the result. The relationship between Fahrenheit and Celsius scale is as follows:

  $T_{°C}=\frac{T_{°F}-32}{1.80}$

Answer to Problem 5RQ

The converted value of $100°\text{F}$ in Celsius is $37.78°\text{C}$ .

Explanation of Solution

Conversion of $100°\text{F}$ to Celsius is as follows:

  $\begin{array}{c}{T}_{°C}=\frac{T_{°F}-32}{1.80}\\ =\frac{100-32}{1.80}\\ =\frac{68}{1.80}\\ =37.78\end{array}$

Hence, the Celsius scale value of $100°\text{F}$ is $37.78°\text{C}$ .

(b)

Interpretation Introduction

Interpretation: Conversion of $-47°\text{C}$ to kelvin needs to be explained.

Concept Introduction: To convert one unit into another, first a conversion factor needs to be chosen. This cancels and omits the units in the result. The relationship between Kelvin and Celsius scale is as follows:

  $T_{°C}+273=T_{\text{K}}$

Answer to Problem 5RQ

The converted value of $-47°\text{C}$ in kelvin is $\text{226}$ K.

Explanation of Solution

Conversion of $-47°\text{C}$ to Kelvin is as follows:

  $\begin{array}{c}{T}_{\text{K}}=T_{°\text{C}}+273\\ =-47\text{+273}\\ \text{=226}\end{array}$

Hence, $-47°\text{C}$ in terms of Kelvin temperature value is $\text{226}$ K.

(c)

Interpretation Introduction

Interpretation: Conversion of $-47°\text{F}$ to kelvin needs to be explained.

Concept Introduction: To convert one unit into another, first a conversion factor needs to be chosen. This cancels and omits the units in the result. The relation between the conversion of $°\text{F}$ to Kelvin is as follows:

  $\text{K}=\left(°\text{F}-32\right)\times \frac{5}{9}+273.15$

Answer to Problem 5RQ

The converted value of $-47°\text{F}$ in Kelvin is $229.26$ K.

Explanation of Solution

Conversion of $-47°\text{F}$ to Kelvin is as follows:

  $\begin{array}{c}\text{K}=\left(°\text{F}-32\right)\times \frac{5}{9}+273.15\\ =\left(-47-32\right)\times \frac{5}{9}+273.15\\ =-79\times \frac{5}{9}+273.15\\ =-43.89+273.15\\ =229.26\end{array}$

Hence, the value of $-47°\text{F}$ in Kelvin temperature scale is $229.26$ K.

(d)

Interpretation Introduction

Interpretation: Conversion of $32°\text{C}$ to Fahrenheit degree needs to be explained.

Concept Introduction: To convert one unit into another, first a conversion factor needs to be chosen. This cancels and omits the units in the result. The relationship between Fahrenheit and Celsius scale is as follows:

  $T_{°F}=1.80\left(T_{°C}\right)+32$

Answer to Problem 5RQ

The converted value of $32°\text{C}$ in $°\text{F}$ scale is $89.6°\text{F}$ .

Explanation of Solution

Conversion of $32°\text{C}$ to $°\text{F}$ is as follows:

  $\begin{array}{c}{T}_{°F}=1.80\left(T_{°C}\right)+32\\ =1.80\left(32\right)+32\\ =57.6+32\\ =89.6\end{array}$

Hence, $32°\text{C}$ in terms of $°\text{F}$ value is $89.6°\text{F}$ .