Chapter 12, Problem 1P

Suppose you are hiking down the Grand Canyon. At the top, the temperature early in the morning is a cool $3°\text{C}\text{.}$ By late afternoon, the temperature at the bottom of the canyon has warmed to a sweltering $34°\text{C}\text{.}$ What is the difference between the higher and lower temperatures in (a) Fahrenheit degrees and (b) kelvins?

To determine

The temperature difference between higher temperature and lower temperature in Fahrenheit.

Answer to Problem 1P

  $55.8°\text{F}$

Explanation of Solution

Given:

The temperature at the top in the early morning is $3°\text{C}$ and the temperature at the bottom of the canyon by afternoon is $34°\text{C}$ .

Formula used:

The conversion of temperature from Celsius scale to Fahrenheit scale is given by formula,

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

Calculation:

The temperature difference between the higher temperature and the lower temperature is

  $\begin{array}{c}\text{Temperature}\text{difference}=34°\text{C}-3°\text{C}\\ =31°\text{C}\end{array}$

Substitute the value of temperature difference in the formula.

  $\begin{array}{c}\Delta °\text{F}=\Delta \left(\frac{9}{5}\times 31°\text{C}\right)\\ \text{=}\frac{279}{5}\\ =55.8\\ \approx 56\end{array}$

Conclusion:

The temperature difference between higher temperature and lower temperature in Fahrenheit is $56°\text{F}$ .

To determine

The temperature difference between higher temperature and lower temperature in Kelvin.

Answer to Problem 1P

  $31\text{k}$

Explanation of Solution

Given:

The temperature at the top in the early morning is $3°\text{C}$ and the temperature at the bottom of the canyon by afternoon is $34°\text{C}$ .

Formula used:

The conversion of temperature from Celsius scale to Kelvin scale is given by formula,

  ${\text{T}}_{\text{K}}={\text{T}}_{°\text{C}}+273.15$

Here, ${\text{T}}_{\text{K}}$ is the temperature in Kelvin and ${\text{T}}_{°\text{C}}$ is the temperature in degree Celsius.

Calculation:

The higher temperature in Kelvin is

  $\begin{array}{c}{\text{T}}_{\text{higher}}=34+273.15\text{K}\\ =307.15\text{K}\end{array}$

The lower temperature in Kelvin is

  $\begin{array}{c}{\text{T}}_{\text{lower}}=3+273.15\text{k}\\ =276.15\text{k}\end{array}$

The temperature difference between the higher temperature and the lower temperature is

  $\begin{array}{c}\text{Temperature}\text{difference}=307.15\text{k}-276.15\text{k}\\ =31\text{k}\end{array}$

Conclusion:

The temperature difference between higher temperature and lower temperature in Kelvin is $31\text{k}$ .