Chapter 8, Problem 50SGR

a

To determine

To find: the pressure for 2, 4, and 7 kilometers

Answer to Problem 50SGR

The values of the pressure are $1.33,1.77\text{ and }2.72$

Explanation of Solution

Given information:

The atmospheric pressure $P$ , in bars, of a given height on Earth is given by using the formula $P=a\cdot e^{\frac{k}{H}}$ . In the formula, a is the surface pressure on Earth, which is approximately 1 bar, $k$ is the altitude for which want to find the pressure in kilometers, and $H$ is always 7 kilometers.

Calculation:

When the altitude $k=2$ kilometer

Then,

  $\begin{array}{l}P=1\cdot e^{\frac{2}{7}}\\ P=1.33\end{array}$

When the altitude $k=4$ kilometer

Then,

  $\begin{array}{l}P=1\cdot e^{\frac{4}{7}}\\ P=1.77\end{array}$

When the altitude $k=7$ kilometer

Then,

  $\begin{array}{l}P=1\cdot e^{\frac{7}{7}}\\ P=2.72\end{array}$

Hence, the values of the pressure are $1.33,1.77\text{ and }2.72$ .

b

To determine

To explain: what do notice about the pressure as altitude increases

Answer to Problem 50SGR

The altitude increases, so the pressure increases

Explanation of Solution

Given information:

The atmospheric pressure $P$ , in bars, of a given height on Earth is given by using the formula $P=a\cdot e^{\frac{k}{H}}$ . In the formula, a is the surface pressure on Earth, which is approximately 1 bar, $k$ is the altitude for which want to find the pressure in kilometers, and $H$ is always 7 kilometers.

Explaination:

The altitude is increasing so the pressure is increasing because the value of altitude are increasing 2, 4 and 7 kilometers than the value of pressure are increasing $1.33,1.77\text{ and }2.72$

Hence, the altitude increases, so the pressure increases.