---
title: "The Atmosphere"
book: "Primary & Middle School Earth and Space Sciences"
subject: earth
language: en
chapter: 23
exercises: 12
source: https://one-course.com/books/earth/1/en/chapter/23-the-atmosphere
license: CC-BY-NC-SA-4.0
credit: "One Earth and Space Sciences Book, One Course (one-course.com)"
---

# Chapter 23 — The Atmosphere

At a [weather station](https://one-course.com/books/earth/1/en/chapter/7-clouds-rain-and-snow#def-g4-clouds-rain-snow-weather-station), just before the agreed hour, a meteorologist walks out onto the grass holding a balloon filled with hydrogen or helium, about $1.5\,\mathrm{m}$ across. Below it, on a long string, hang a small orange parachute and an instrument box of 60 to 80 grams: a *radiosonde*. She lets go. The balloon climbs about $300\,\mathrm{m}$ every minute, and every second the radiosonde radios down the pressure, the temperature, the humidity and its position. As it rises, the balloon swells, until it is 6 to $8\,\mathrm{m}$ across and bursts, often more than $30\,\mathrm{km}$ up, two hours after the launch. At the same hours of every day, the same scene takes place at more than 800 stations around the world.

![Launching a weather balloon in Topeka, Kansas (United States): the parachute (red) and the radiosonde hang below the balloon. Photograph by Stephen Corfidi, NOAA/National Weather Service (public domain, via Wikimedia Commons).](https://one-course.com/images/onecourse/chapters/earth-1/g8-the-atmosphere/img-285d5cf97bae.jpg)

*Launching a [weather](https://one-course.com/books/earth/1/en/chapter/1-watching-the-weather#def-g1-watching-the-weather-weather) balloon in Topeka, Kansas (United States): the parachute (red) and the radiosonde hang below the balloon. Photograph by Stephen Corfidi, NOAA/National Weather Service (public domain, via Wikimedia Commons).*

Why does the balloon swell as it rises? What does the radiosonde measure on its way up, and why does the temperature not simply keep falling? Where does the air end?

**You already know.**

The *atmosphere* is the layer of air around the Earth. Air presses on everything it touches: this is *air pressure*, measured with a barometer (the physics books). [Weather](https://one-course.com/books/earth/1/en/chapter/1-watching-the-weather#def-g1-watching-the-weather-weather) services give it in hectopascals (hPa); at [sea level](https://one-course.com/books/earth/1/en/chapter/9-the-physical-map-of-the-world#def-g4-world-physical-map-altitude) it is about $1013\,\mathrm{hPa}$. Dry air is made of about 78 % nitrogen and 21 % oxygen, with a little argon, carbon dioxide and other gases (the chemistry books). [Clouds](https://one-course.com/books/earth/1/en/chapter/7-clouds-rain-and-snow#def-g4-clouds-rain-snow-cloud) are made of tiny droplets of water or crystals of ice ([Chapter 7](https://one-course.com/books/earth/1/en/chapter/7-clouds-rain-and-snow#ch-g4-clouds-rain-snow)).

## 23.1 A thin envelope

Seen from the International Space Station, the atmosphere is a thin glowing line along the edge of the Earth. Most of the air, and almost all the [clouds](https://one-course.com/books/earth/1/en/chapter/7-clouds-rain-and-snow#def-g4-clouds-rain-snow-cloud), are in its lowest few kilometres.

![The edge of the Earth at sunset, photographed from the International Space Station above the Indian Ocean on 14 June 2010. The orange and yellow band is the lowest layer of the atmosphere, with its dark clouds; above it come paler and then blue layers, fading into the black of space. NASA photograph, ISS Expedition 23 (public domain, via Wikimedia Commons).](https://one-course.com/images/onecourse/chapters/earth-1/g8-the-atmosphere/img-3b0eebe350c9.jpg)

*The edge of the Earth at sunset, photographed from the International Space Station above the Indian [Ocean](https://one-course.com/books/earth/1/en/chapter/3-water-on-earth#def-g2-water-on-earth-ocean) on 14 June 2010. The orange and yellow band is the lowest layer of the atmosphere, with its dark [clouds](https://one-course.com/books/earth/1/en/chapter/7-clouds-rain-and-snow#def-g4-clouds-rain-snow-cloud); above it come paler and then blue layers, fading into the black of space. NASA photograph, ISS Expedition 23 (public domain, via Wikimedia Commons).*

There is no sharp top to the atmosphere: the air gets thinner and thinner with height. By convention, space begins at about $100\,\mathrm{km}$. Compared with the Earth’s radius, $6371\,\mathrm{km}$, that is very little: $100 \div
6371 \approx 0.016$, less than 2 % of the radius. On a [globe](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-globe) $30\,\mathrm{cm}$ across, the whole atmosphere would be a film about $2\,\mathrm{mm}$ thick.

![A slice of the Earth and its atmosphere drawn to scale (1\, cm for 100\, km), up to 100\, km, the edge of space (dashed). The coloured lines are the limits of the layers met later in this chapter; the lowest layer, where all the weather happens, is barely a millimetre thick.](https://one-course.com/images/onecourse/chapters/earth-1/g8-the-atmosphere/fig-d327c62065c9.svg)

*A slice of the Earth and its atmosphere drawn to scale ($1\,\mathrm{cm}$ for $100\,\mathrm{km}$), up to $100\,\mathrm{km}$, the edge of space (dashed). The coloured lines are the limits of the layers met later in this chapter; the lowest layer, where all the [weather](https://one-course.com/books/earth/1/en/chapter/1-watching-the-weather#def-g1-watching-the-weather-weather) happens, is barely a millimetre thick.*

## 23.2 Pressure falls with altitude

The air at the bottom of the atmosphere carries the weight of all the air above it. The higher one climbs, the less air is left overhead, and the lower the pressure. In the standard model of the atmosphere used by meteorologists and engineers, the pressure is $1013\,\mathrm{hPa}$ at [sea level](https://one-course.com/books/earth/1/en/chapter/9-the-physical-map-of-the-world#def-g4-world-physical-map-altitude), half of that at about $5.5\,\mathrm{km}$, and a quarter at about $10.3\,\mathrm{km}$.

Since the pressure measures the weight of the air above, the half-pressure level is also the height below which half of all the air lies: half of the atmosphere is squeezed into its lowest $5.5\,\mathrm{km}$. Below $11\,\mathrm{km}$ lies about 78 % of the air, below $30\,\mathrm{km}$ about 99 %.

![](https://one-course.com/images/onecourse/chapters/earth-1/g8-the-atmosphere/fig-77c2562a25fb.svg)

![](https://one-course.com/images/onecourse/chapters/earth-1/g8-the-atmosphere/fig-b8fdd6426256.svg)

*Pressure against [altitude](https://one-course.com/books/earth/1/en/chapter/9-the-physical-map-of-the-world#def-g4-world-physical-map-altitude). The pressure is half its sea-level value at about $5.5\,\mathrm{km}$, a quarter at about $10.3\,\mathrm{km}$.*

*The balloon swells as it climbs, because the air around it presses less and less (balloons and parachutes to scale with each other, the string shortened).*

Higher up, the pressure keeps falling, by about half again for every few kilometres, so it soon becomes tiny. Powers of ten are the best way to write it. At $30\,\mathrm{km}$, the pressure is about $12\,\mathrm{hPa}$, roughly $10^{-2}$ of its sea-level value (one hundredth); at $50\,\mathrm{km}$, about $0.8\,\mathrm{hPa}$, roughly $10^{-3}$; at $80\,\mathrm{km}$, about $0.01\,\mathrm{hPa}$, roughly $10^{-5}$ of the sea-level pressure.

![Climbers on a very high mountain carry bottles of oxygen. At 9\, km, the pressure is less than a third of its sea-level value: the air still holds 21 % oxygen, but each breath takes in far less of it (AI-generated illustration of a generic scene).](https://one-course.com/images/onecourse/chapters/earth-1/g8-the-atmosphere/img-382fb3e938cf.jpg)

*Climbers on a very high [mountain](https://one-course.com/books/earth/1/en/chapter/2-landscapes-around-us#def-g1-landscapes-around-us-landform) carry bottles of oxygen. At $9\,\mathrm{km}$, the pressure is less than a third of its sea-level value: the air still holds 21 % oxygen, but each breath takes in far less of it (AI-generated illustration of a generic scene).*

## 23.3 Temperature and the layers

Everyone who has climbed a [mountain](https://one-course.com/books/earth/1/en/chapter/2-landscapes-around-us#def-g1-landscapes-around-us-landform) knows that the air gets colder with height. The radiosondes show that this is true only in the lowest part of the atmosphere. Higher up, the temperature stops falling, then rises, then falls again, then rises once more. These changes divide the atmosphere into layers.

![The temperature of the air against altitude, from the ground to 100\, km, in the standard atmosphere (an average for the middle latitudes). The four layers are shaded; the green bar marks the height of the ozone layer.](https://one-course.com/images/onecourse/chapters/earth-1/g8-the-atmosphere/fig-4441be56471a.svg)

*The temperature of the air against [altitude](https://one-course.com/books/earth/1/en/chapter/9-the-physical-map-of-the-world#def-g4-world-physical-map-altitude), from the ground to $100\,\mathrm{km}$, in the standard atmosphere (an average for the middle [latitudes](https://one-course.com/books/earth/1/en/chapter/14-latitude-longitude-and-time-zones#def-g6-latitude-longitude-latitude)). The four layers are shaded; the green bar marks the height of the [ozone layer](#def-g8-the-atmosphere-ozone-layer).*

**Definition 23.1 (The layers of the atmosphere).**

From the ground up, the atmosphere is divided into four layers by the way its temperature changes with height:

- the *troposphere* , where the temperature falls with height and where almost all the [weather](https://one-course.com/books/earth/1/en/chapter/1-watching-the-weather#def-g1-watching-the-weather-weather) happens; its top is the *tropopause* ;
- the *stratosphere* , where the temperature rises with height, up to about $50\,\mathrm{km}$ ;
- the *mesosphere* , where the temperature falls again, up to about $85\,\mathrm{km}$ ;
- the *thermosphere* , where the very thin air gets hotter and hotter with height.

The [troposphere](#def-g8-the-atmosphere-layers) holds about 99 % of the atmosphere’s water vapour, so nearly all [clouds](https://one-course.com/books/earth/1/en/chapter/7-clouds-rain-and-snow#def-g4-clouds-rain-snow-cloud), [rain](https://one-course.com/books/earth/1/en/chapter/7-clouds-rain-and-snow#def-g4-clouds-rain-snow-precipitation) and [snow](https://one-course.com/books/earth/1/en/chapter/7-clouds-rain-and-snow#def-g4-clouds-rain-snow-precipitation) form in it. Its air is stirred all the time. The top of the [troposphere](#def-g8-the-atmosphere-layers) is not at the same height everywhere: the [tropopause](#def-g8-the-atmosphere-layers) is highest above the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator), where it can reach $20\,\mathrm{km}$, and lowest above the [poles](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles), where it can come down to $7\,\mathrm{km}$ in winter. It is also higher in summer than in winter. In the standard atmosphere, an average for the middle [latitudes](https://one-course.com/books/earth/1/en/chapter/14-latitude-longitude-and-time-zones#def-g6-latitude-longitude-latitude), it lies at $11\,\mathrm{km}$.

**Definition 23.2 (Environmental lapse rate).**

The *environmental lapse rate* is the rate at which the temperature of the air falls with height in the [troposphere](#def-g8-the-atmosphere-layers), in degrees Celsius per kilometre. It changes from day to day and from place to place; the standard atmosphere uses an average of $6.5{}^{\circ}\mathrm{C}$ per kilometre.

**Method 23.3 (Reading a temperature profile).**

1. Find the [altitude](https://one-course.com/books/earth/1/en/chapter/9-the-physical-map-of-the-world#def-g4-world-physical-map-altitude) on the vertical axis and go across to the curve; read the temperature below it.
2. Where the curve leans to the left as it goes up, the air cools with height; where it leans to the right, the air warms with height; where it is vertical, the temperature does not change.
3. The limits between layers are where the curve turns.

**Example 23.4 (An airliner at cruising height).**

An airliner cruises at $11\,\mathrm{km}$, near the [tropopause](#def-g8-the-atmosphere-layers). On the profile, the temperature there is about $-56{}^{\circ}\mathrm{C}$. With the lapse rate: from $15{}^{\circ}\mathrm{C}$ at [sea level](https://one-course.com/books/earth/1/en/chapter/9-the-physical-map-of-the-world#def-g4-world-physical-map-altitude), the air cools by $6.5 \times 11 = 71.5$ degrees, which gives $15 - 71.5 =
-56.5{}^{\circ}\mathrm{C}$. On the pressure curve, the pressure is about $227\,\mathrm{hPa}$, less than a quarter of the pressure on the ground: the cabin has to be pressurised.

Above the [tropopause](#def-g8-the-atmosphere-layers), in the [stratosphere](#def-g8-the-atmosphere-layers), airliners find a calmer ride: the air there gets warmer with height, so it is not stirred from below. In the [mesosphere](#def-g8-the-atmosphere-layers) most meteors burn up, and at its top, near $86\,\mathrm{km}$, is the coldest air of the whole atmosphere, about $-86{}^{\circ}\mathrm{C}$. In the [thermosphere](#def-g8-the-atmosphere-layers), the Sun’s X-rays and ultraviolet light heat the very thin air to hundreds, at times thousands, of degrees; yet there is so little air that it would not feel warm. Many satellites orbit the Earth there.

## 23.4 The ozone layer

The [stratosphere](#def-g8-the-atmosphere-layers) gets warmer with height because it absorbs part of the Sun’s light. The gas that does most of this is ozone, a form of oxygen (its chemistry is in the chemistry books).

**Definition 23.5 (Ozone layer).**

The *ozone layer* is the part of the [stratosphere](#def-g8-the-atmosphere-layers), between about $16\,\mathrm{km}$ and $48\,\mathrm{km}$, where about 90 % of the atmosphere’s ozone is found. It absorbs most of the Sun’s harmful ultraviolet light.

Even in the [ozone layer](#def-g8-the-atmosphere-ozone-layer), ozone is rare: only 1 to 10 molecules in a million. Yet together with oxygen, it stops between 95 % and 99.9 % of the ultraviolet light that reaches the Earth, including the most harmful kinds. The energy it absorbs is turned into heat, which is why the temperature rises through the [stratosphere](#def-g8-the-atmosphere-layers). Without the [ozone layer](#def-g8-the-atmosphere-ozone-layer), the ultraviolet light reaching the ground would harm living things.

**In the field — Following the weather balloons.**

[Weather](https://one-course.com/books/earth/1/en/chapter/1-watching-the-weather#def-g1-watching-the-weather-weather) services publish the measurements of their radiosondes, often as a chart of temperature against height for each launch. With an adult, look for the soundings of the station nearest to you, made at 00:00 or 12:00 UTC. Find the height where the temperature stops falling: that is the [tropopause](#def-g8-the-atmosphere-layers) on that day. Compare a winter sounding with a summer one.

## 23.5 Exercises

**Exercise 23.1 ★.**

Match each layer with its description: [troposphere](#def-g8-the-atmosphere-layers); [stratosphere](#def-g8-the-atmosphere-layers); [mesosphere](#def-g8-the-atmosphere-layers); [thermosphere](#def-g8-the-atmosphere-layers). (a) The temperature rises with height and the [ozone layer](#def-g8-the-atmosphere-ozone-layer) is found there. (b) Almost all the [weather](https://one-course.com/books/earth/1/en/chapter/1-watching-the-weather#def-g1-watching-the-weather-weather) happens there. (c) The coldest air of the atmosphere is at its top. (d) The very thin air is heated to hundreds of degrees; many satellites orbit there.

**Solution of Exercise 23.1.**

(a) [stratosphere](#def-g8-the-atmosphere-layers); (b) [troposphere](#def-g8-the-atmosphere-layers); (c) [mesosphere](#def-g8-the-atmosphere-layers); (d) [thermosphere](#def-g8-the-atmosphere-layers).

**Exercise 23.2 ★.**

Use the temperature profile of the standard atmosphere. (a) What is the temperature at [sea level](https://one-course.com/books/earth/1/en/chapter/9-the-physical-map-of-the-world#def-g4-world-physical-map-altitude)? (b) At $11\,\mathrm{km}$? (c) At $50\,\mathrm{km}$? (d) At $86\,\mathrm{km}$? (e) Between which [altitudes](https://one-course.com/books/earth/1/en/chapter/9-the-physical-map-of-the-world#def-g4-world-physical-map-altitude) does the temperature not change?

**Solution of Exercise 23.2.**

(a) $15{}^{\circ}\mathrm{C}$. (b) About $-56{}^{\circ}\mathrm{C}$. (c) About $-3{}^{\circ}\mathrm{C}$. (d) About $-86{}^{\circ}\mathrm{C}$. (e) From $11\,\mathrm{km}$ to about $20\,\mathrm{km}$ (and over a few kilometres near $50\,\mathrm{km}$ and just above $86\,\mathrm{km}$).

**Exercise 23.3 ★.**

True or false? Correct the false sentences. (a) The temperature of the air always falls with height. (b) Half of all the air lies below about $5.5\,\mathrm{km}$. (c) The [ozone layer](#def-g8-the-atmosphere-ozone-layer) is in the [troposphere](#def-g8-the-atmosphere-layers). (d) The [tropopause](#def-g8-the-atmosphere-layers) is higher above the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) than above the [poles](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles).

**Solution of Exercise 23.3.**

(a) False: it falls in the [troposphere](#def-g8-the-atmosphere-layers), rises in the [stratosphere](#def-g8-the-atmosphere-layers), falls in the [mesosphere](#def-g8-the-atmosphere-layers) and rises again in the [thermosphere](#def-g8-the-atmosphere-layers). (b) True. (c) False: it is in the [stratosphere](#def-g8-the-atmosphere-layers). (d) True.

**Exercise 23.4 ★.**

In which layer is each of these? (a) A [rain](https://one-course.com/books/earth/1/en/chapter/7-clouds-rain-and-snow#def-g4-clouds-rain-snow-precipitation) [cloud](https://one-course.com/books/earth/1/en/chapter/7-clouds-rain-and-snow#def-g4-clouds-rain-snow-cloud). (b) An airliner at $12\,\mathrm{km}$. (c) A [weather](https://one-course.com/books/earth/1/en/chapter/1-watching-the-weather#def-g1-watching-the-weather-weather) balloon just before it bursts, at $32\,\mathrm{km}$. (d) A meteor burning up at $75\,\mathrm{km}$.

**Solution of Exercise 23.4.**

(a) The [troposphere](#def-g8-the-atmosphere-layers). (b) The [stratosphere](#def-g8-the-atmosphere-layers) (in the standard atmosphere the [tropopause](#def-g8-the-atmosphere-layers) is at $11\,\mathrm{km}$). (c) The [stratosphere](#def-g8-the-atmosphere-layers). (d) The [mesosphere](#def-g8-the-atmosphere-layers).

**Exercise 23.5 ★★.**

On a summer day, it is $20{}^{\circ}\mathrm{C}$ at [sea level](https://one-course.com/books/earth/1/en/chapter/9-the-physical-map-of-the-world#def-g4-world-physical-map-altitude). Suppose the air cools by $6.5{}^{\circ}\mathrm{C}$ per kilometre. (a) What is the temperature at $2\,\mathrm{km}$? (b) At $3\,\mathrm{km}$? (c) At about what height does the air reach $0{}^{\circ}\mathrm{C}$? Round to one decimal.

**Solution of Exercise 23.5.**

(a) $20 - 6.5 \times 2 = 20 - 13 = 7{}^{\circ}\mathrm{C}$. (b) $20 -
6.5 \times 3 = 20 - 19.5 = 0.5{}^{\circ}\mathrm{C}$. (c) The air has to cool by 20 degrees: $20 \div 6.5 \approx 3.1$, so at about $3.1\,\mathrm{km}$.

**Exercise 23.6 ★★.**

A [mountain](https://one-course.com/books/earth/1/en/chapter/2-landscapes-around-us#def-g1-landscapes-around-us-landform) hut stands at $3000\,\mathrm{m}$. A walker leaves a village at $500\,\mathrm{m}$ where it is $18{}^{\circ}\mathrm{C}$. Using a lapse rate of $6.5{}^{\circ}\mathrm{C}$ per kilometre: (a) How many kilometres does the walker climb? (b) By how many degrees does the air cool? (c) What temperature can the walker expect at the hut?

**Solution of Exercise 23.6.**

(a) $3 - 0.5 = 2.5\,\mathrm{km}$. (b) $6.5 \times 2.5 = 16.25$: about 16 degrees. (c) $18 - 16.25 \approx 2{}^{\circ}\mathrm{C}$.

**Exercise 23.7 ★★.**

Suppose the pressure halves every $5.5\,\mathrm{km}$, starting from $1000\,\mathrm{hPa}$ at [sea level](https://one-course.com/books/earth/1/en/chapter/9-the-physical-map-of-the-world#def-g4-world-physical-map-altitude). (a) What is the pressure at $5.5\,\mathrm{km}$? At $11\,\mathrm{km}$? At $16.5\,\mathrm{km}$? (b) The standard atmosphere gives about $506\,\mathrm{hPa}$, $227\,\mathrm{hPa}$ and $96\,\mathrm{hPa}$ at these three heights (for $1013\,\mathrm{hPa}$ at [sea level](https://one-course.com/books/earth/1/en/chapter/9-the-physical-map-of-the-world#def-g4-world-physical-map-altitude)). Is the halving rule good near the ground? Higher up?

**Solution of Exercise 23.7.**

(a) $500\,\mathrm{hPa}$, $250\,\mathrm{hPa}$ and $125\,\mathrm{hPa}$. (b) Near the ground the rule is good ($500\,\mathrm{hPa}$ against $506\,\mathrm{hPa}$). Higher up it gives too much: $250\,\mathrm{hPa}$ against $227\,\mathrm{hPa}$, and $125\,\mathrm{hPa}$ against $96\,\mathrm{hPa}$. The halving rule is only a rough guide.

**Exercise 23.8 ★★.**

At [sea level](https://one-course.com/books/earth/1/en/chapter/9-the-physical-map-of-the-world#def-g4-world-physical-map-altitude) the pressure is about $1000\,\mathrm{hPa}$, that is $10^3$ hPa. (a) At $30\,\mathrm{km}$ it is about $10\,\mathrm{hPa}$. Write this as a power of ten, and say how many times smaller it is than at [sea level](https://one-course.com/books/earth/1/en/chapter/9-the-physical-map-of-the-world#def-g4-world-physical-map-altitude). (b) At $80\,\mathrm{km}$ it is about $0.01\,\mathrm{hPa}$. Write it as a power of ten. (c) How many times smaller than at [sea level](https://one-course.com/books/earth/1/en/chapter/9-the-physical-map-of-the-world#def-g4-world-physical-map-altitude) is it?

**Solution of Exercise 23.8.**

(a) $10~\text{hPa} = 10^1$ hPa; $10^3 \div 10^1 = 10^2$: a hundred times smaller. (b) $0.01~\text{hPa} = 10^{-2}$ hPa. (c) $10^3 \div 10^{-2} =
10^5$: a hundred thousand times smaller.

**Exercise 23.9 ★★.**

A [weather](https://one-course.com/books/earth/1/en/chapter/1-watching-the-weather#def-g1-watching-the-weather-weather) balloon is $1.5\,\mathrm{m}$ across at launch and $6\,\mathrm{m}$ across when it bursts. (a) How many times wider is it when it bursts? (b) Explain why it swells as it rises. (c) Why do [weather](https://one-course.com/books/earth/1/en/chapter/1-watching-the-weather#def-g1-watching-the-weather-weather) services hang a parachute below it?

**Solution of Exercise 23.9.**

(a) $6 \div 1.5 = 4$ times wider. (b) As it rises, the air around it presses less and less, so the gas inside spreads out and the balloon grows until its skin breaks. (c) After the balloon bursts, the parachute slows the fall of the radiosonde, so that it does not hurt anyone or damage anything.

**Exercise 23.10 ★★.**

The [tropopause](#def-g8-the-atmosphere-layers) can reach $20\,\mathrm{km}$ above the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) and come down to $7\,\mathrm{km}$ above the [poles](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles) in winter. (a) How many times thicker is the [troposphere](#def-g8-the-atmosphere-layers) above the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) in this case? Round to one decimal. (b) On the standard profile, the [tropopause](#def-g8-the-atmosphere-layers) is at $11\,\mathrm{km}$. Is the standard atmosphere closer to the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) or to the [poles](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles)? (c) A pilot flies from a polar region to the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) at a constant height of $10\,\mathrm{km}$. Is the plane in the [troposphere](#def-g8-the-atmosphere-layers) or the [stratosphere](#def-g8-the-atmosphere-layers) at the start (in winter)? At the end?

**Solution of Exercise 23.10.**

(a) $20 \div 7 \approx 2.9$ times thicker. (b) Closer to the [poles](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles): $11\,\mathrm{km}$ is $4\,\mathrm{km}$ above $7\,\mathrm{km}$ but $9\,\mathrm{km}$ below $20\,\mathrm{km}$ (it describes the middle [latitudes](https://one-course.com/books/earth/1/en/chapter/14-latitude-longitude-and-time-zones#def-g6-latitude-longitude-latitude), not the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator)). (c) At the start the [tropopause](#def-g8-the-atmosphere-layers) is at about $7\,\mathrm{km}$, below the plane: the plane is in the [stratosphere](#def-g8-the-atmosphere-layers). At the end the [tropopause](#def-g8-the-atmosphere-layers) is at about $20\,\mathrm{km}$: the plane is in the [troposphere](#def-g8-the-atmosphere-layers).

**Exercise 23.11 ★★★.**

The share of all the air that lies below a height is $1 - p \div
p_0$, where $p$ is the pressure at that height and $p_0 =
1013\,\mathrm{hPa}$ the pressure at [sea level](https://one-course.com/books/earth/1/en/chapter/9-the-physical-map-of-the-world#def-g4-world-physical-map-altitude). (a) At $5.5\,\mathrm{km}$, $p
\approx 506\,\mathrm{hPa}$: what share of the air lies below? (b) At $11\,\mathrm{km}$, $p \approx 227\,\mathrm{hPa}$. (c) At $30\,\mathrm{km}$, $p \approx
12\,\mathrm{hPa}$. Give the answers in per cent, to whole numbers. (d) What share of the air lies above $30\,\mathrm{km}$?

**Solution of Exercise 23.11.**

(a) $1 - 506 \div 1013 \approx 0.50$: **50 %**. (b) $1 - 227 \div
1013 \approx 0.78$: **78 %**. (c) $1 - 12 \div 1013 \approx 0.99$: **99 %**. (d) About 1 %.

**Exercise 23.12 ★★★.**

A school [globe](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-globe) is $30\,\mathrm{cm}$ across, so its radius, $15\,\mathrm{cm}$, stands for the Earth’s radius, $6371\,\mathrm{km}$. (a) How many kilometres does $1\,\mathrm{cm}$ of the [globe](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-globe) stand for? Round to the nearest kilometre. (b) How thick, in millimetres, would the atmosphere up to $100\,\mathrm{km}$ be on this [globe](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-globe)? (c) And the [troposphere](#def-g8-the-atmosphere-layers), $11\,\mathrm{km}$ thick? (d) A sheet of paper is about $0.1\,\mathrm{mm}$ thick. How many sheets would make the [troposphere](#def-g8-the-atmosphere-layers) of the [globe](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-globe)?

**Solution of Exercise 23.12.**

(a) $6371 \div 15 \approx 425$ km for each centimetre. (b) $100 \div 425
\approx 0.24$ cm, about $2.4\,\mathrm{mm}$. (c) $11 \div 425 \approx
0.026$ cm, about $0.26\,\mathrm{mm}$. (d) $0.26 \div 0.1 \approx 2.6$: two or three sheets of paper.

## 23.6 Problem: Following a weather balloon

**Problem 23.1.**

Weekend problem — a weather balloon climbs through the atmosphere; its temperatures show the layers, and its pressures show where a quarter of the sea-level pressure is left

A radiosonde is launched from a station at [sea level](https://one-course.com/books/earth/1/en/chapter/9-the-physical-map-of-the-world#def-g4-world-physical-map-altitude). Its balloon rises at about $300\,\mathrm{m}$ per minute. The table gives the pressure and the temperature it measures (the values of the standard atmosphere, rounded).

| [altitude](https://one-course.com/books/earth/1/en/chapter/9-the-physical-map-of-the-world#def-g4-world-physical-map-altitude) (km) | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| pressure (hPa) | 1013 | 795 | 617 | 472 | 357 | 265 | 194 | 142 |
| temperature ($^\circ$C) | 15 | 2 | $-11$ | $-24$ | $-37$ | $-50$ | $-56$ | $-56$ |
| [altitude](https://one-course.com/books/earth/1/en/chapter/9-the-physical-map-of-the-world#def-g4-world-physical-map-altitude) (km) | 16 | 18 | 20 | 22 | 24 | 26 | 28 | 30 |
| pressure (hPa) | 104 | 76 | 55 | 40 | 30 | 22 | 16 | 12 |
| temperature ($^\circ$C) | $-56$ | $-56$ | $-56$ | $-55$ | $-53$ | $-51$ | $-49$ | $-47$ |

**Part I — The climb.**

1. How many metres does the balloon climb in 10 minutes?
2. How long does it take to reach $6\,\mathrm{km}$ ? And $30\,\mathrm{km}$ ?
3. The balloon bursts at $30\,\mathrm{km}$ . How long has the flight lasted, in hours and minutes?
4. Name the layer the balloon is in at $8\,\mathrm{km}$ , and the layer it is in when it bursts.

**Part II — The temperature.**

5. By how many degrees does the temperature fall between the ground and $10\,\mathrm{km}$ ?
6. What is the lapse rate in degrees per kilometre in this part of the climb?
7. Between which [altitudes](https://one-course.com/books/earth/1/en/chapter/9-the-physical-map-of-the-world#def-g4-world-physical-map-altitude) does the temperature stay the same? Where is the [tropopause](#def-g8-the-atmosphere-layers) ?
8. What happens to the temperature above $20\,\mathrm{km}$ ? Which gas explains it?

**Part III — The pressure.**

9. What is half of the sea-level pressure? Between which [altitudes](https://one-course.com/books/earth/1/en/chapter/9-the-physical-map-of-the-world#def-g4-world-physical-map-altitude) is it reached?
10. What is a quarter of the sea-level pressure? Round to the nearest hectopascal.
11. Between which two [altitudes](https://one-course.com/books/earth/1/en/chapter/9-the-physical-map-of-the-world#def-g4-world-physical-map-altitude) of the table is this quarter reached?
12. The pressure falls by $71\,\mathrm{hPa}$ between $10\,\mathrm{km}$ and $12\,\mathrm{km}$ . Supposing it falls evenly, at about what [altitude](https://one-course.com/books/earth/1/en/chapter/9-the-physical-map-of-the-world#def-g4-world-physical-map-altitude) is the pressure a quarter of its sea-level value? Round to one decimal.

**Solution of Problem 23.1.**

**1.** $300 \times 10 = 3000$ m.

**2.** $6000 \div 300 = 20$ minutes; $30\,000 \div 300 = 100$ minutes.

**3.** 100 minutes, that is 1 hour and 40 minutes.

**4.** At $8\,\mathrm{km}$: the [troposphere](#def-g8-the-atmosphere-layers) (the temperature is still falling). At $30\,\mathrm{km}$: the [stratosphere](#def-g8-the-atmosphere-layers).

**5.** $15 - (-50) = 65$ degrees.

**6.** $65 \div 10 = 6.5{}^{\circ}\mathrm{C}$ per kilometre.

**7.** From $12\,\mathrm{km}$ to $20\,\mathrm{km}$ it stays at $-56{}^{\circ}\mathrm{C}$. The cooling stops between $10\,\mathrm{km}$ and $12\,\mathrm{km}$: the [tropopause](#def-g8-the-atmosphere-layers) is at about $11\,\mathrm{km}$.

**8.** It rises: $-55{}^{\circ}\mathrm{C}$ at $22\,\mathrm{km}$, $-47{}^{\circ}\mathrm{C}$ at $30\,\mathrm{km}$. The balloon is in the [stratosphere](#def-g8-the-atmosphere-layers), warmed by the ozone that absorbs the Sun’s ultraviolet light.

**9.** $1013 \div 2 \approx 507\,\mathrm{hPa}$; it is reached between $4\,\mathrm{km}$ ($617\,\mathrm{hPa}$) and $6\,\mathrm{km}$ ($472\,\mathrm{hPa}$).

**10.** $1013 \div 4 \approx 253\,\mathrm{hPa}$.

**11.** Between $10\,\mathrm{km}$ ($265\,\mathrm{hPa}$) and $12\,\mathrm{km}$ ($194\,\mathrm{hPa}$).

**12.** From $10\,\mathrm{km}$, the pressure has to fall by $265 - 253 =
12$ hPa more, out of the 71 hPa it loses over 2 km: $12 \div 71 \times 2
\approx 0.34$ km. The pressure is a quarter of its sea-level value at about **$10.3\,\mathrm{km}$**.