Chapter 1.2, Problem 2PPB

Interpretation Introduction

Interpretation:  For the given temperature in Fahrenheit, it should be converted the degree Fahrenheit to degree Celsius temperature with find the range among them.

Concept Introduction:

•  Conversional formula from Celsius to Fahrenheit,

$°\text{F}\text{=}\left({}^{\text{o}}\text{C×}\frac{{\text{9}}^{\text{o}}\text{F}}{{\text{5}}^{\text{o}}\text{C}}\right)\text{+}\text{32}°\text{F}$

• Conversional formula from Celsius to Kelvin,

$\text{K}\text{=}{}^{\circ }\text{C}\text{+}\text{273}\text{.15}$

Answer to Problem 2PPB

The average surface temperatures of planets in our solar system range from

$867°F$ on Venus is ${\text{464}}^{\text{0}}\text{ C}$.

The average surface temperature of planets in our solar system range from−330°F on Neptune is ${\text{201}}^{\text{0}}\text{ C}$.

And the ${\text{Range of the celsius =464}}^{\text{0}}\text{ C}+{\text{201}}^{\text{0}}{\text{ C=665}}^{\text{0}}\text{ C}$.

Explanation of Solution

Explanation

To convert: These temperatures and the range they span to Celsius

The temperature conversion from Fahrenheit to Celsius is ( $867°F$).

Conversional formula from Fahrenheit to Celsius is

${\text{F}}^{\text{o}}\text{=}\left({}^{\text{o}}\text{C×}\frac{{\text{9}}^{\text{o}}\text{F}}{{\text{5}}^{\text{o}}\text{C}}\right)\text{+}\text{32}°\text{F}$

The given temperature in Fahrenheit can be converted to Celsius as follows;

$\text{°F}\text{=}\left({}^{\text{o}}\text{C×}\frac{{\text{9}}^{\text{o}}\text{F}}{{\text{5}}^{\text{o}}\text{C}}\right)\text{+}\text{32°F}$

$\frac{{}^{\text{o}}\text{C}}{{\text{5}}^{\text{0}}\text{ C}}\text{=}\frac{{\text{°F - 32}}^{\text{0}}\text{ F}}{{\text{9}}^{\text{0}}\text{ F}}$

${}^{\text{o}}\text{C = }\left[\frac{{\text{°F - 32}}^{\text{0}}\text{ F}}{{\text{9}}^{\text{0}}\text{ F}}\right]{\text{×5}}^{\text{0}}\text{ C}$

${}^{\text{o}}\text{C = }\left[\frac{{\text{867°F - 32}}^{\text{0}}\text{ F}}{{\text{9}}^{\text{0}}\text{ F}}\right]{\text{×5}}^{\text{0}}\text{ C=463}{\text{.889}}^{\text{0}}\text{ C}\simeq {\text{464}}^{\text{0}}\text{ C}$

To convert: The given temperature in Fahrenheit to Celsius.

The temperature conversion from Fahrenheit to Celsius is $(-330)$ F.

Conversional formula from Fahrenheit to Celsius is

${\text{F}}^{\text{o}}\text{=}\left({}^{\text{o}}\text{C×}\frac{{\text{9}}^{\text{o}}\text{F}}{{\text{5}}^{\text{o}}\text{C}}\right)\text{+}\text{32}°\text{F}$

The given temperature in Fahrenheit can be converted to Celsius as follows;

$\text{°F}\text{=}\left({}^{\text{o}}\text{C×}\frac{{\text{9}}^{\text{o}}\text{F}}{{\text{5}}^{\text{o}}\text{C}}\right)\text{+}\text{32°F}$

= $\frac{{}^{\text{o}}\text{C}}{{\text{5}}^{\text{0}}\text{ C}}\text{=}\frac{{\text{°F - 32}}^{\text{0}}\text{ F}}{{\text{9}}^{\text{0}}\text{ F}}$

= ${}^{\text{o}}\text{C = }\left[\frac{{\text{°F - 32}}^{\text{0}}\text{ F}}{{\text{9}}^{\text{0}}\text{ F}}\right]{\text{×5}}^{\text{0}}\text{ C}$

= ${}^{\text{o}}\text{C = }\left[\frac{\left(-330\right){\text{°F - 32}}^{\text{0}}\text{ F}}{{\text{9}}^{\text{0}}\text{ F}}\right]{\text{×5}}^{\text{0}}{\text{ C=201}}^{\text{0}}\text{ C}$

And the ${\text{Range of the celsius =464}}^{\text{0}}\text{ C}+{\text{201}}^{\text{0}}{\text{ C=665}}^{\text{0}}\text{ C}$

Conclusion

For the given temperature in Fahrenheit, it has been converted the degree Fahrenheit to degree Celsius temperature with finding the range between them.