Chapter 5, Problem 49A

(a)

Interpretation Introduction

Interpretation: Conversion of $-40°\text{C}$ to Fahrenheit scale needs to be explained.

Concept Introduction: To convert one unit into another then first needs to choose a conversion factor, this cancels the units 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 49A

Converted value of $-40°\text{C}$ in $°\text{F}$ scale is $-40°\text{F}$ .

Explanation of Solution

Conversion of $-40°\text{C}$ to $°\text{F}$ is as follows:

  $\begin{array}{c}{T}_{°F}=1.80\left(T_{°C}\right)+32\\ =1.80\left(-40\right)+32\\ =-72+32\\ =-40\end{array}$

Hence, $-40°\text{C}$ in terms of $°\text{F}$ scale value is $-40°\text{F}$ .

(b)

Interpretation Introduction

Interpretation: Conversion of $-40°\text{F}$ to Celsius degree needs to be explained.

Concept Introduction: To convert one unit into another then first needs to choose a conversion factor, this cancels the units 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 49A

Converted value of $-40°\text{F}$ in Celsius is $-40°\text{C}$ .

Explanation of Solution

Conversion of $-40°\text{F}$ to Celsius is as follows:

  $\begin{array}{c}{T}_{°C}=\frac{T_{°F}-32}{1.80}\\ =\frac{-40-32}{1.80}\\ =\frac{-72}{1.80}\\ =-40\end{array}$

Hence, The Celsius scale value of $-40°\text{F}$ is $-40°\text{C}$ .

(c)

Interpretation Introduction

Interpretation: Conversion of $232\text{K}$ to Celsius needs to be explained.

Concept Introduction: To convert temperature from Kelvin to Celsius scale, subtract $273$ from the Kelvin temperature. The relationship between Kelvin and Celsius scale is as follows:

  $T_{°C}=T_{\text{K}}-273$

Answer to Problem 49A

Converted value of $232\text{K}$ in Celsius is $-41°\text{C}$ .

Explanation of Solution

Conversion of $232\text{K}$ to Celsius is as follows:

  $\begin{array}{c}{T}_{°C}=T_{\text{K}}-273\\ =232-273\\ =-41\end{array}$

Hence, The Celsius scale value of $232\text{K}$ is $-41°\text{C}$ .

(d)

Interpretation Introduction

Interpretation: Conversion of $232$ K to Fahrenheit needs to be explained.

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

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

Answer to Problem 49A

Converted value of $232$ K in Fahrenheit is $-42.07°\text{F}$ .

Explanation of Solution

Conversion of $232$ K to Fahrenheit is as follows:

  $\begin{array}{c}{T}_{°\text{F}}=\left(T_{\text{K}}-273.15\right)\times \frac{9}{5}+32\\ =\left(232-273.15\right)\times \frac{9}{5}+32\\ =\frac{-370.35}{5}+32\\ =-74.07+32\end{array}$

  $T_{°\text{F}}=-42.07$

Hence, The Fahrenheit scale value of $232$ K in is $-42.07°\text{F}$ .