Chapter 1, Problem 1.77AP

(a)

Interpretation Introduction

Interpretation:

The temperature ${\text{53}}^{\text{o}}\text{C}$ has to be converted to Fahrenheit and Kelvin.

Concept Introduction:

Temperature:  The measurement of hotness or coldness of an object is temperature.  The three temperature scales as,

1. 1) Celsius $\left({}^{\text{o}}\text{C}\right)$
2. 2) Kelvin $\left(\text{K}\right)$
3. 3) Fahrenheit $\left({}^{\text{o}}\text{F}\right)$

Celsius to Fahrenheit conversion:

Celsius can be converted to Fahrenheit using the formula,

  ${\text{T}}_{\text{F}}\text{=1}\text{.8}\left({\text{T}}_{\text{C}}\right)\text{+32}$

Celsius to Kelvin conversion:

Celsius can be converted to kelvin using the formula,

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

Answer to Problem 1.77AP

The temperature ${\text{53}}^{\text{o}}\text{C}$ in Fahrenheit is ${127}^{\text{o}}\text{F}\text{.}$

The temperature ${\text{53}}^{\text{o}}\text{C}$ in Kelvin is $\text{326}\text{K}\text{.}$

Explanation of Solution

Given,

The temperature in degree Celsius is ${\text{53}}^{\text{o}}\text{C}\text{.}$

Celsius can be converted to Fahrenheit using the formula,

  $\begin{array}{l}{\text{T}}_{\text{F}}\text{=1}\text{.8}\left({\text{T}}_{\text{C}}\right)\text{+32}\\ {\text{T}}_{\text{F}}\text{=1}\text{.8}\left({53}^{\text{o}}\text{C}\right)\text{+32}\\ {\text{T}}_{\text{F}}\text{=127}{\text{.4}}^{\text{o}}\text{F}\end{array}$

The temperature ${\text{53}}^{\text{o}}\text{C}$ in Fahrenheit is ${127}^{\text{o}}\text{F}\text{.}$

Celsius can be converted to Kelvin using the formula,

  $\begin{array}{l}{\text{T}}_{\text{K}}{\text{=T}}_{\text{C}}\text{+273}\\ {\text{T}}_{\text{K}}{\text{=53}}^{\text{o}}\text{C+273}\\ {\text{T}}_{\text{K}}\text{=326}\text{K}\end{array}$

The temperature ${\text{53}}^{\text{o}}\text{C}$ in Kelvin is $\text{326}\text{K}\text{.}$

(b)

Interpretation Introduction

Interpretation:

The temperature ${\text{350}}^{\text{o}}\text{F}$ has to be converted to Celsius and Kelvin.

Concept Introduction:

Fahrenheit to Celsius conversion:

Fahrenheit can be converted to Celsius using the formula,

  ${\text{T}}_{\text{C}}\text{=}\frac{{\text{T}}_{\text{F}}\text{-32}}{\text{1}\text{.8}}$

Fahrenheit to Kelvin conversion:

Fahrenheit can be converted to Kelvin using the formula,

  ${\text{T}}_{\text{K}}\text{=}\left({\text{T}}_{\text{F}}\text{-32}\right)\text{×}\frac{\text{5}}{\text{9}}\text{+273}\text{.15}$

Answer to Problem 1.77AP

The temperature ${\text{350}}^{\text{o}}\text{F}$ in Celsius is ${\text{177}}^{\text{o}}\text{C}\text{.}$

The temperature ${\text{350}}^{\text{o}}\text{F}$ in Kelvin is $\text{450}\text{K}\text{.}$

Explanation of Solution

Given,

The temperature in degree Fahrenheit is ${\text{350}}^{\text{o}}\text{F}\text{.}$

Fahrenheit can be converted to Celsius using the formula,

  $\begin{array}{l}{\text{T}}_{\text{C}}\text{=}\frac{{\text{T}}_{\text{F}}\text{-32}}{\text{1}\text{.8}}\\ {\text{T}}_{\text{C}}\text{=}\frac{{\text{350}}^{\text{o}}\text{F-32}}{\text{1}\text{.8}}\\ {\text{T}}_{\text{C}}\text{=176}{\text{.66}}^{\text{o}}\text{C}\\ {\text{T}}_{\text{C}}{\text{=177}}^{\text{o}}\text{C}\end{array}$

On rounding off, the temperature is Celsius is ${\text{177}}^{\text{o}}\text{C}\text{.}$

The temperature ${\text{350}}^{\text{o}}\text{F}$ in Celsius is ${\text{177}}^{\text{o}}\text{C}\text{.}$

From Kelvin:

Fahrenheit can be converted to Kelvin using the formula,

  $\begin{array}{l}{\text{T}}_{\text{K}}\text{=}\left({\text{T}}_{\text{F}}\text{-32}\right)\text{×}\frac{\text{5}}{\text{9}}\text{+273}\text{.15}\\ {\text{T}}_{\text{K}}\text{=}\left({\text{350}}^{\text{o}}\text{F-32}\right)\text{×}\frac{\text{5}}{\text{9}}\text{+273}\text{.15}\\ {\text{T}}_{\text{K}}\text{=449}\text{.64}\text{K}\end{array}$

On rounding off, the temperature in Kelvin is $\text{450}\text{K}\text{.}$

The temperature ${\text{350}}^{\text{o}}\text{F}$ in Kelvin is $\text{450}\text{K}\text{.}$

From Celsius:

The temperature in Kelvin can also be calculated from the value of calculated Celsius.

The temperature ${\text{350}}^{\text{o}}\text{F}$ in Celsius is ${\text{177}}^{\text{o}}\text{C}\text{.}$

Celsius can be converted to Kelvin using the formula,

  $\begin{array}{l}{\text{T}}_{\text{K}}{\text{=T}}_{\text{C}}\text{+273}\\ {\text{T}}_{\text{K}}{\text{=177}}^{\text{o}}\text{C+273}\\ {\text{T}}_{\text{K}}\text{=450}\text{K}\end{array}$

The temperature ${\text{350}}^{\text{o}}\text{F}$ in Kelvin is $\text{450}\text{K}\text{.}$