Chapter 1, Problem 1.43P

(a)

Interpretation Introduction

Interpretation:

The body temperature of bird in degree Celcius $\left(\text{°C}\right)$ and Kelvin $\left(\text{K}\right)$ 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 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 1.43P

The body temperature of bird in degree Celcius $\left(\text{°C}\right)$ and Kelvin $\left(\text{K}\right)$ is $\text{41 }°\text{C}$ and $314\text{ K}$ respectively.

Explanation of Solution

The body temperature of a bird is $106°\text{F}$.

Substitute $106°\text{F}$ for $T\left(\text{°F}\right)$ in equation (2) to calculate the temperature in degree Celsius.

$\begin{array}{c}T\left(°\text{C}\right)=\frac{5}{9}\left(106°\text{F}-32\right)\\ =\frac{5}{9}\left(74\right)\\ =41.111\\ =\text{41 }°\text{C}\end{array}$

Substitute $41.111°\text{C}$ for $T\left(°\text{C}\right)$ in equation (1) to calculate the temperature in Kelvin.

$\begin{array}{c}T\left(\text{K}\right)=41.111°\text{C}+273.15\\ =314.261\\ =314\text{ K}\end{array}$

Conclusion

The temperature of an object can be calculated in three different units by using the proper conversion factor. The body temperature of bird in degree Celcius $\left(\text{°C}\right)$ and Kelvin $\left(\text{K}\right)$ is $\text{41 }°\text{C}$ and $314\text{ K}$ respectively.

(b)

Interpretation Introduction

Interpretation:

The melting point of tungsten 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 1.43P

The melting point of tungsten in Kelvin $\left(\text{K}\right)$ and Fahrenheit $\left(°\text{F}\right)$ is $3683\text{ K}$ and $6170\text{ °F}$ respectively.

Explanation of Solution

The boiling point of methane is $3410°\text{C}$.

Substitute $3410°\text{C}$ for $T\left(\text{°C}\right)$ in equation (1) to calculate the temperature in Kelvin.

  $\begin{array}{c}T\left(\text{K}\right)=3410°\text{C}+273.15\\ =3683.15\\ =3683\text{ K}\end{array}$

Substitute $3410°\text{C}$ for $T\left(\text{°C}\right)$ in equation (3) to calculate the temperature in Fahrenheit.

  $\begin{array}{c}T\left(\text{°F}\right)=\frac{9}{5}\left(3410°\text{C}\right)+32\\ =6138+32\\ =6170\text{ °F}\end{array}$

Conclusion

The temperature of an object can be calculated in three different units by using the proper conversion factor. The melting point of tungsten in Kelvin $\left(\text{K}\right)$ and Fahrenheit $\left(°\text{F}\right)$ is $3683\text{ K}$ and $6170\text{ °F}$ respectively.

(c)

Interpretation Introduction

Interpretation:

The surface temperature of the sun in degree Celcius $\left(\text{°C}\right)$ 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 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 1.43P

The surface temperature of the sun in degree Celcius $\left(\text{°C}\right)$ and Fahrenheit $\left(°\text{F}\right)$ is $5.8\times {10}^3\text{ °C}$ and $1.1\times {10}^4\text{ °F}$ respectively.

Explanation of Solution

The surface temperature of the sun is $6.1\times {10}^3\text{ K}$.

Substitute $6.1\times {10}^3\text{ K}$ for $T\left(\text{°K}\right)$ in equation (4) to calculate the temperature in degree Celsius.

  $\begin{array}{c}T\left(\text{°C}\right)=6.1\times {10}^3\text{ K}-273.15\\ =5.827\times {10}^3\\ =5.8\times {10}^3\text{ °C}\end{array}$

Substitute $5827\text{ °C}$ for $T\left(\text{°C}\right)$ in equation (3) to calculate the temperature in Fahrenheit.

  $\begin{array}{c}T\left(\text{°F}\right)=\frac{9}{5}\left(5827\text{ °C}\right)+32\\ =1.0521\times {10}^4\\ =1.1\times {10}^4\text{ °F}\end{array}$

Conclusion

The temperature of an object can be calculated in three different units by using the proper conversion factor. The surface temperature of the sun in degree Celcius $\left(\text{°C}\right)$ and Fahrenheit $\left(°\text{F}\right)$ is $5.8\times {10}^3\text{ °C}$ and $1.1\times {10}^4\text{ °F}$ respectively.