Chapter 3, Problem 17CR

Interpretation Introduction

(a)

Interpretation:

Size of the temperature unit (degree) related between the Kelvin and Celsius scale should be discussed.

Concept Introduction:

The size of each temperature unit (degree) is the same for the Celsius and Kelvin scales. This follows from the fact that the difference between the boiling point and freezing point of water is $100$ units on both of these scales.

Answer to Problem 17CR

The size of each temperature unit is same for Celsius and Kelvin scales.

Explanation of Solution

In Celsius scale, freezing point and boiling points are assigned as $0^0\text{C}$ and ${100}^0\text{C}$. On Kelvin scale, water freezes at $273\text{K}$ and boils at $373\text{K}$. So the difference between the boiling point and freezing point of water is $100$ units in both scales. Therefore the size of each temperature unit (degree) is the same for the Celsius and Kelvin scales.

Interpretation Introduction

(b)

Interpretation:

Size of the temperature unit (degree) of the Fahrenheit scale compare to the Celsius scale should be discussed.

Concept Introduction:

The Fahrenheit degree is smaller than the Celsius and Kelvin units. On Fahrenheit scale there are $180$ Fahrenheit degrees between the boiling point and freezing points of water compared with $100$ units on the other two scales.

Answer to Problem 17CR

$180$ Fahrenheit degrees = $100$ Celsius degrees

Explanation of Solution

In Celsius scale, freezing point and boiling points are assigned as $0^0\text{C}$ and ${100}^0\text{C}$. On Fahrenheit scale, water freezes at ${212}^0\text{F}$ and boils at ${32}^0\text{F}$. On Fahrenheit scale, difference between the boiling point and freezing point of water is $180$ units and on Celsius scale the difference is $100$ units. Therefore, $180$ Fahrenheit degrees = $100$ Celsius degrees.

Interpretation Introduction

(c)

Interpretation:

Normal freezing point of water on each of the three temperature scale should be stated.

Concept Introduction:

Different countries use different temperature scales, such as Fahrenheit and Celsius. In addition to that Kelvin is used as the Standard unit for temperature measurements.

Answer to Problem 17CR

Freezing point of water in Fahrenheit scale = ${32}^0\text{F}$

Freezing point of water in Celsius scale = $0^0\text{C}$

Freezing point of water in Kelvin scale = $273\text{K}$.

Explanation of Solution

Different countries use different temperature scales, such as Fahrenheit and Celsius. In addition to that Kelvin is used as the Standard unit for temperature measurements.

Freezing point of water in Fahrenheit scale = ${32}^0\text{F}$

Freezing point of water in Celsius scale = $0^0\text{C}$

Freezing point of water in Kelvin scale = $273\text{K}$.

Interpretation Introduction

(d)

Interpretation:

The given temperature measurement in Celsius scale should be converted to Kelvin and Fahrenheit scales.

Concept Introduction:

To convert Celsius into Kelvin,

${\text{T}}_{0\text{C}}+273={\text{T}}_{\text{K}}$

To convert Celsius into Fahrenheit,

${\text{T}}_{0\text{F}}=1.80\left({\text{T}}_{0\text{C}}\right)+32$.

Answer to Problem 17CR

${27.5}^0\text{C}=300.5\text{K}={81.5}^0\text{F}$.

Explanation of Solution

To convert Celsius into Kelvin,

${\text{T}}_{0\text{C}}+273={\text{T}}_{\text{K}}$

$27.5+273={\text{T}}_{\text{K}}$

${\text{T}}_{\text{K}}=300.5\text{K}$

To convert Celsius into Fahrenheit,

${\text{T}}_{0\text{F}}=1.80\left({\text{T}}_{0\text{C}}\right)+32$

$\begin{array}{l}{\text{T}}_{0\text{F}}=1.80\left(27.5\right)+32\hfill \\ {\text{T}}_{0\text{F}}=49.5+32\hfill \\ {\text{T}}_{0\text{F}}={81.5}^0\text{F}\hfill \end{array}$.

Interpretation Introduction

(e)

Interpretation:

The given temperature measurement in Kelvin scale should be converted to Celsius and Fahrenheit scales.

Concept Introduction:

To convert Celsius into Kelvin,

${\text{T}}_{0\text{C}}+273={\text{T}}_{\text{K}}$

To convert Celsius into Fahrenheit,

${\text{T}}_{0\text{F}}=1.80\left({\text{T}}_{0\text{C}}\right)+32$.

Answer to Problem 17CR

$298.1\text{K}={25.1}^0\text{C}={77.2}^0\text{F}$.

Explanation of Solution

To convert Kelvin into Celsius,

${\text{T}}_{0\text{C}}+273={\text{T}}_{\text{K}}$

$\begin{array}{l}{\text{T}}_{0\text{C}}+273=298.1\hfill \\ {\text{T}}_{0\text{C}} =298.1–273\hfill \\ {\text{T}}_{0\text{C}} ={25.1}^0\text{C}\hfill \end{array}$

To convert Celsius into Fahrenheit,

${\text{T}}_{0\text{F}}=1.80\left({\text{T}}_{0\text{C}}\right)+32$

$\begin{array}{l}{\text{T}}_{0\text{F}}=1.80\left(25.1\right)+32\hfill \\ {\text{T}}_{0\text{F}}=45.18+32\hfill \\ {\text{T}}_{0\text{F}}=\text{ 77}{\text{.18}}^0\text{F}\hfill \end{array}$

${\text{T}}_{0\text{F}}={77.2}^0\text{F}$.

Interpretation Introduction

(f)

Interpretation:

The given temperature measurement in Fahrenheit scale should be converted to Celsius and Kelvin scales.

Concept Introduction:

To convert Celsius into Kelvin,

${\text{T}}_{0\text{C}}+273={\text{T}}_{\text{K}}$

To convert Celsius into Fahrenheit,

${\text{T}}_{0\text{F}}=1.80\left({\text{T}}_{0\text{C}}\right)+32$.

Answer to Problem 17CR

98.6 ⁰ F = 37 ⁰ C = 310 K.

Explanation of Solution

To convert Fahrenheit into Celsius,

${\text{T}}_{0\text{F}}=1.80\left({\text{T}}_{0\text{C}}\right)+32$

$\begin{array}{l}98.6=1.80\left({\text{T}}_{0\text{C}}\right)+32\hfill \\ 98.6–32=1.80\left({\text{T}}_{0\text{C}}\right)\hfill \\ 1.80\left({\text{T}}_{0\text{C}}\right)=66.6\hfill \\ {\text{T}}_{0\text{C}}=66.6/1.80\hfill \\ {\text{T}}_{0\text{C}}={37}^0\text{C}\hfill \end{array}$

To convert Celsius into Kelvin,

${\text{T}}_{0\text{C}}+273={\text{T}}_{\text{K}}$

$\begin{array}{l}37+273 ={\text{T}}_{\text{K}}\hfill \\ {\text{T}}_{\text{K}} =310\text{K}\hfill \end{array}$.