Chapter 11.5, Problem 45PPS

(a)

To determine

To calculate: To write an equation for the temperature $T$ at which water boils $x$ feet above sea level

Answer to Problem 45PPS

The equation for the temperature is $T=212-\frac{0.9x}{500}$

Explanation of Solution

Given information: The temperature at which water boils decreases by about ${0.9}^{\circ }F$ for every $500$ feet above sea level. The boiling point at sea level is ${212}^{\circ }F$

Calculation:

Given that the temperature at which water boils decreases by about ${0.9}^{\circ }F$ for every $500$ feet above sea level.

Let temperature be $T$ at which water boils $x$ feet above sea level

Thus, equation for temperature $T$ is given as

  $T=212-\frac{0.9x}{500}$

Conclusion:

Hence, required equation for temperature is $T=212-\frac{0.9x}{500}$

(b)

To determine

To calculate: To find at what temperature water boils on Mount Whitney

Answer to Problem 45PPS

On Mount Whitney, water boils at approximately ${186}^{\circ }F$

Explanation of Solution

Given information: The temperature at which water boils decreases by about ${0.9}^{\circ }F$ for every $500$ feet above sea level. The boiling point at sea level is ${212}^{\circ }F$

Calculation:

Given that the temperature at which water boils decreases by about ${0.9}^{\circ }F$ for every $500$ feet above sea level.

Let temperature be $T$ at which water boils $x$ feet above sea level

Thus, equation for temperature $T$ is given as

  $T=212-\frac{0.9x}{500}$

Now, given that Mount Whitney is $14494$ feet about sea level.

Thus, substituting $x=14494$ in above equation to calculate the temperature at which water boils at top of Mount Whitney is:

  $\begin{array}{l}T=212-\frac{0.9\left(14494\right)}{500}\\ T=212-26.0892\\ T=185.9108\\ T\approx {186}^{\circ }F\end{array}$

Conclusion:

Hence, water boils at approximately ${186}^{\circ }F$ on Mount Whitney