Chapter 1, Problem 1.34P

Perfrom the following conversions:

1. ${106}^{\text{o}}\text{F}$ (the body temperature of many birds) to K and ${}^{\text{o}}\text{C}$ ${3410}^{\text{o}}\text{C}$ (the melting point of tungsten, the highest for any metallic element) to ${\text{K and }}^{\text{o}}\text{F}$ $\text{6}\text{.1}\times {\text{10}}^{\text{3}}\text{ K}$ (the surface temperature of the Sun) to ${}^{\text{o}}{\text{F and }}^{\text{o}}\text{C}$

Interpretation Introduction

Interpretation: The conversion of $106°\text{F}$ to $°\text{C}$ and $\text{K}$ should be performed.

Concept introduction:Temperature is used to determine hotness or coldness of any object or body. Thermometer is used to record temperature of any substance. Three different temperature scales are usually used for temperature measurement and these are Fahrenheit, Celsius, and Kelvin.

Conversion factor is ratio that is widely used to describe relation between two different units. In order to convert one unit into another, original unit is multiplied with proper conversion factor to yield new unit. This is done as mentioned below.

  $\text{Final unit}=\left(\cancel{\text{Original unit}}\right)\left(\frac{\text{Final unit}}{\cancel{\text{Original unit}}}\right)$

Explanation of Solution

The conversion factor to convert temperature from Fahrenheit to degree Celsius is as follows:

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

Therefore $106°\text{F}$ can be converted to $°\text{C}$ as follows:

  $\begin{array}{c}T\left(°\text{C}\right)=\frac{5}{9}\left(T\left(\text{°F}\right)-32\right)\\ =\frac{5}{9}\left(106-32\right)\\ =41.11°\text{C}\end{array}$

The conversion factor to convert temperature from Celsius to Kelvin is as follows:

  $0°\text{C}=273.15\text{ K}$

Therefore $41.11°\text{C}$ can be converted to $\text{K}$ as follows:

  $\begin{array}{c}T\left(\text{K}\right)=\left(41.11+273.15\right)\text{ K}\\ =\text{314}\text{.26 K}\end{array}$

Interpretation Introduction

Interpretation: The conversion of $3410°\text{C}$ to $\text{K}$ and $°\text{F}$ should be performed.

Concept introduction:Temperature is used to determine hotness or coldness of any object or body. Thermometer is used to record temperature of any substance. Three different temperature scales are usually used for temperature measurement and these are Fahrenheit, Celsius, and Kelvin.

Conversion factor is ratio that is widely used to describe relation between two different units. In order to convert one unit into another, original unit is multiplied with proper conversion factor to yield new unit. This is done as mentioned below.

  $\text{Final unit}=\left(\cancel{\text{Original unit}}\right)\left(\frac{\text{Final unit}}{\cancel{\text{Original unit}}}\right)$

Explanation of Solution

The conversion factor to convert temperature from degree Celsius to degree Fahrenheit is as follows:

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

Therefore $3410°\text{C}$ can be converted to $°\text{C}$ as follows:

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

The conversion factor to convert temperature from Celsius to Kelvin is as follows:

  $0°\text{C}=273.15\text{ K}$

Therefore $3410°\text{C}$ can be converted to $\text{K}$ as follows:

  $\begin{array}{c}T\left(\text{K}\right)=\left(3410+273.15\right)\text{ K}\\ =\text{3683}\text{.15 K}\end{array}$

Interpretation Introduction

Interpretation: The conversion of $6.1\times {10}^3\text{ K}$ to $°\text{C}$ and $°\text{F}$ should be performed.

Concept introduction:Temperature is used to determine hotness or coldness of any object or body. Thermometer is used to record temperature of any substance. Three different temperature scales are usually used for temperature measurement and these are Fahrenheit, Celsius and Kelvin.

Conversion factor is ratio that is widely used to describe relation between two different units. In order to convert one unit into another, original unit is multiplied with proper conversion factor to yield new unit. This is done as mentioned below.

  $\text{Final unit}=\left(\cancel{\text{Original unit}}\right)\left(\frac{\text{Final unit}}{\cancel{\text{Original unit}}}\right)$

Explanation of Solution

The conversion factor to convert temperature from Celsius to Kelvin is as follows:

  $0°\text{C}=273.15\text{ K}$

Therefore $0\text{ K}$ can be converted to $°\text{C}$ as follows:

  $\begin{array}{c}T\left(°\text{C}\right)=\left(6.1\times {10}^3-273.15\right)°\text{C}\\ =5826.85°\text{C}\end{array}$

The conversion factor to convert temperature from degree Celsius to degree Fahrenheit is as follows:

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

Therefore $\text{5826}\text{.85 }°\text{C}$ can be converted to $°\text{F}$ as follows:

  $\begin{array}{c}T\left(°\text{F}\right)=\frac{9}{5}\left(T\left(\text{°C}\right)\right)+32\\ =\frac{9}{5}\left(\text{5826}\text{.85}\right)+32\\ =\text{10520}\text{.33 }°\text{F}\end{array}$