Chapter 1, Problem 1.42P

(a)

Interpretation Introduction

Interpretation:

The tempertaure in Fahrenheit $\left(°\text{F}\right)$ is to be converted into degree Celcius $\left(\text{°C}\right)$ and Kelvin $\left(\text{K}\right)$.

Concept introduction:

The temperature of an object is the measure of the coldness and hotness of the object relative to another object. The S.I unit of temperature is Kelvin $\left(\text{K}\right)$. The other units of temperature are degree Celcius $\left(\text{°C}\right)$ and Fahrenheit $\left(°\text{F}\right)$.

The first is the Fahrenheit $\left(\text{°F}\right)$ scale common in the United States. On this scale, the freezing point of water is $\text{32 °F}$ and the boiling point is $\text{212 °F}$. The room temperature is around $72°\text{F}$ on this scale.

The other scale common in countries apart from the United States is the Celsius $\left(\text{°C}\right)$ scale. On this scale, the freezing point of water is $\text{0 °C}$ and the boiling point of water is $\text{100 °C}$. The room temperature is around $\text{22 °C}$.

The third scale is the Kelvin scale which is also known as Absolute scale.

The conversion factor to convert temperature from degree Celsius to Kelvin is,

$T\left(\text{K}\right)=T\left(\text{°C}\right)+273.15$ (1)

The conversion factor to convert temperature from Fahrenheit to degree Celsius is,

$T\left(°\text{C}\right)=\frac{5}{9}\left(T\left(\text{°F}\right)-32\right)$ (2)

Answer to Problem 1.42P

The tempertaure $68°\text{F}$ in degree Celcius $\left(\text{°C}\right)$ and Kelvin $\left(\text{K}\right)$ is $20°\text{C}$ and $293\text{ K}$ respectively.

Explanation of Solution

The temperature in Fahrenheit $\left(\text{°F}\right)$ is $68°\text{F}$.

Substitute $68°\text{F}$ for $T\left(\text{°F}\right)$ in equation (2) to calculate the temperature in degree Celsius.

$\begin{array}{c}T\left(°\text{C}\right)=\frac{5}{9}\left(68°\text{F}-32\right)\\ =\frac{5}{9}\left(36\right)\\ =20°\text{C}\end{array}$

Substitute $20°\text{C}$ for $T\left(°\text{C}\right)$ in equation (1) to calculate the temperature in Kelvin.

$\begin{array}{c}T\left(\text{K}\right)=20°\text{C}+273.15\\ =293.15\\ =293\text{ K}\end{array}$

Conclusion

The temperature of an object can be calculated in three different units by using the proper conversion factor. The tempertaure $68°\text{F}$ in degree Celcius $\left(\text{°C}\right)$ and Kelvin $\left(\text{K}\right)$ is $20°\text{C}$ and $293\text{ K}$ respectively.

(b)

Interpretation Introduction

Interpretation:

The boiling point of methane in Kelvin $\left(\text{K}\right)$ and Fahrenheit $\left(°\text{F}\right)$ is to be calculated.

Concept introduction:

The temperature of an object is the measure of the coldness and hotness of the object relative to another object. The S.I unit of temperature is Kelvin $\left(\text{K}\right)$. The other units of temperature are degree Celcius $\left(\text{°C}\right)$ and Fahrenheit $\left(°\text{F}\right)$.

The first is the Fahrenheit $\left(\text{°F}\right)$ scale common in the United States. On this scale, the freezing point of water is $\text{32 °F}$ and the boiling point is $\text{212 °F}$. The room temperature is around $72°\text{F}$ on this scale.

The other scale common in countries apart from the United States is the Celsius $\left(\text{°C}\right)$ scale. On this scale, the freezing point of water is $\text{0 °C}$ and the boiling point of water is $\text{100 °C}$. The room temperature is around $\text{22 °C}$.

The third scale is the Kelvin scale which is also known as Absolute scale.

The conversion factor to convert temperature from degree Celsius to Kelvin is,

$T\left(\text{K}\right)=T\left(\text{°C}\right)+273.15$ (1)

The conversion factor to convert temperature from degree Celsius to Fahrenheit is,

$T\left(\text{°F}\right)=\frac{9}{5}T\left(°\text{C}\right)+32$ (3)

Answer to Problem 1.42P

The boiling point of methane in Kelvin $\left(\text{K}\right)$ and Fahrenheit $\left(°\text{F}\right)$ is $109\text{ K}$ and $-263\text{ °F}$ respectively.

Explanation of Solution

The boiling point of methane is $-164°\text{C}$.

Substitute $-164°\text{C}$ for $T\left(\text{°C}\right)$ in equation (1) to calculate the temperature in Kelvin.

$\begin{array}{c}T\left(\text{K}\right)=-164°\text{C}+273.15\\ =109.15\\ =109\text{ K}\end{array}$

Substitute $-164°\text{C}$ for $T\left(\text{°C}\right)$ in equation (3) to calculate the temperature in Fahrenheit.

$\begin{array}{c}T\left(\text{°F}\right)=\frac{9}{5}\left(-164°\text{C}\right)+32\\ =-295.2+32\\ =-263.2\\ =-263\text{ °F}\end{array}$

Conclusion

The temperature of an object can be calculated in three different units by using the proper conversion factor. The boiling point of methane in Kelvin $\left(\text{K}\right)$ and Fahrenheit $\left(°\text{F}\right)$ is $109\text{ K}$ and $-263\text{ °F}$ respectively.

(c)

Interpretation Introduction

Interpretation:

The value of coldest possible temeperature absolute zero $\left(0\text{ K}\right)$ is to be calculated in degree Celcius $\left(\text{°C}\right)$ and Fahrenheit $\left(°\text{F}\right)$.

Concept introduction:

The temperature of an object is the measure of the coldness and hotness of the object relative to another object. The S.I unit of temperature is Kelvin $\left(\text{K}\right)$. The other units of temperature are degree Celcius $\left(\text{°C}\right)$ and Fahrenheit $\left(°\text{F}\right)$.

The first is the Fahrenheit $\left(\text{°F}\right)$ scale common in the United States. On this scale, the freezing point of water is $\text{32 °F}$ and the boiling point is $\text{212 °F}$. The room temperature is around $72°\text{F}$ on this scale.

The other scale common in countries apart from the United States is the Celsius $\left(\text{°C}\right)$ scale. On this scale, the freezing point of water is $\text{0 °C}$ and the boiling point of water is $\text{100 °C}$. The room temperature is around $\text{22 °C}$.

The third scale is the Kelvin scale which is also known as Absolute scale.

The conversion factor to convert temperature from Kelvin to degree Celsius is,

$T\left(\text{°C}\right)=T\left(\text{K}\right)-273.15$ (4)

The conversion factor to convert temperature from degree Celsius to Fahrenheit is,

$T\left(\text{°F}\right)=\frac{9}{5}T\left(°\text{C}\right)+32$ (3)

Answer to Problem 1.42P

The value of coldest possible temeperature absolute zero $\left(0\text{ K}\right)$ in degree Celcius $\left(\text{°C}\right)$ and Fahrenheit $\left(°\text{F}\right)$ is  $-273\text{ °C}$ and $-460\text{ °F}$ respectively.

Explanation of Solution

The coledest possible temeperature is $0\text{ K}$.

Substitute $0\text{ K}$ for $T\left(\text{°K}\right)$ in equation (4) to calculate the temperature in degree Celsius.

$\begin{array}{c}T\left(\text{°C}\right)=0\text{ K}-273.15\\ =-273.15\\ =-273\text{ °C}\end{array}$

Substitute $-273.15$ for $T\left(\text{°C}\right)$ in equation (3) to calculate the temperature in Fahrenheit.

$\begin{array}{c}T\left(\text{°F}\right)=\frac{9}{5}\left(-273.15\right)+32\\ =-491.67+32\\ =-459.67\\ =-460\text{ °F}\end{array}$

Conclusion

The temperature of an object can be calculated in three different units by using the proper conversion factor. The value of coldest possible temeperature absolute zero $\left(0\text{ K}\right)$ in degree Celcius $\left(\text{°C}\right)$ and Fahrenheit $\left(°\text{F}\right)$ is  $-273\text{ °C}$ and $-460\text{ °F}$ respectively.