Chapter 1, Problem 62P

Interpretation Introduction

(a)

Interpretation:

The given temperature $0\text{K}$ , $0°\text{F}$ and $0°\text{C}$ is to be ranked from lowest to highest.

Concept introduction:

Kelvin $\left(\text{K}\right)$ is the S.I unit of temperature. One unit can be converted into another by the use of proper conversion factors.

The formula to convert temperature from degree Celsius to Kelvin is,

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

The formula to convert temperature from degree Celsius to Fahrenheit is,

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

Answer to Problem 62P

The temperatures are ranked from lowest to highest.

  $\begin{array}{cc}\text{Temperature}& \text{Rank}\\ \text{0 K}& 3\\ \text{0 }°\text{F}& 2\\ \text{0 }°\text{C}& 1\end{array}$

Explanation of Solution

To compare the temperature value, first, convert the temperature in a particular scale and then compare which would have a higher value.

All the given temperature should be converted into Celsius.

Rearrange equation (2) for $T\left(°\text{C}\right)$ as follows:

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

The value of $T\left(°\text{F}\right)$ is $0°\text{F}$.

Substitute $T\left(°C\right)$ in the above expression.

  $\begin{array}{c}T\left(°\text{C}\right)=\frac{5}{9}\left(T\left(\text{°F}\right)-32\right)\\ =\frac{5}{9}\left(0-32\right)\\ =-17.77°\text{C}\end{array}$

Rearrange equation (1) for $T\left(\text{K}\right)$ as follows:

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

The value of $T\left(\text{K}\right)$ is $0\text{K}$.

Substitute $T\left(\text{K}\right)$ in the above expression.

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

As compared to the temperature value among $\text{0 }°\text{C}$ , $0\text{K}$ and $\text{0 }°\text{F}$ , the temperature at $\text{0 }°\text{C}$ would have a higher value as compared to the other temperature and the temperature at $\text{0 }°\text{F}$ has a higher value than the temperature at $0\text{K}$.

The temperatures are ranked from lowest to highest here, one is assigned to the highest temperature and three is assigned to the lowest temperature.

  $\begin{array}{cc}\text{Temperature}& \text{Rank}\\ \text{0 K}& 3\\ \text{0 }°\text{F}& 2\\ \text{0 }°\text{C}& 1\end{array}$

Interpretation Introduction

(b)

Interpretation:

The given temperature $100\text{K}$ , $100°\text{F}$ and $100°\text{C}$ is to be ranked from lowest to highest.

Concept introduction:

Kelvin $\left(\text{K}\right)$ is the S.I unit of temperature. One unit can be converted into another by the use of proper conversion factors.

The formula to convert temperature from degree Celsius to Kelvin is,

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

The formula to convert temperature from degree Celsius to Fahrenheit is,

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

Answer to Problem 62P

The temperatures are ranked from lowest to highest.

  $\begin{array}{cc}\text{Temperature}& \text{Rank}\\ \text{100 K}& 3\\ \text{100 }°\text{F}& 2\\ \text{100 }°\text{C}& 1\end{array}$

Explanation of Solution

To compare the temperature value, first, convert the temperature in a particular scale and then compare which would have a higher value.

All the given temperature should be converted into Celsius.

Rearrange equation (2) for $T\left(°\text{C}\right)$ as follows:

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

The value of $T\left(°\text{F}\right)$ is $100°\text{F}$.

Substitute $T\left(°\text{C}\right)$ in the above expression.

  $\begin{array}{c}T\left(°\text{C}\right)=\frac{5}{9}\left(T\left(\text{°F}\right)-32\right)\\ =\frac{5}{9}\left(100-32\right)\\ =37.77°\text{C}\end{array}$

Rearrange equation (1) for $T\left(\text{K}\right)$ as follows:

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

The value of $T\left(\text{K}\right)$ is $100\text{K}$.

Substitute $T\left(\text{K}\right)$ in the above expression.

  $\begin{array}{c}T\left(\text{°C}\right)=T\left(\text{K}\right)-273.15\\ =100-273.15\\ =-173.15\text{°C}\end{array}$

As compared to the temperature value among $\text{100 }°\text{C}$ , $\text{100 K}$ and $\text{100 }°\text{F}$ , the temperature at $\text{100 }°\text{C}$ would have a higher value as compared to the other temperature and the temperature at $\text{100 }°\text{F}$ has a higher value than the temperature at $\text{100 K}$.

The temperatures are ranked from lowest to highest here, 1 is assigned to the highest temperature and 3 is assigned to the lowest temperature.

  $\begin{array}{cc}\text{Temperature}& \text{Rank}\\ \text{100 K}& 3\\ \text{100 }°\text{F}& 2\\ \text{100 }°\text{C}& 1\end{array}$