3 Atmospheric Properties

Lalu Das

TABLE OF CONTENTS

Learning outcomes

Introduction

Atmospheric properties: temperature, density, pressure and humidity

Variation of temperature

4.1. Thermodynamic properties of dry air – adiabatic temperature change

4.1.1. The equation of state – ideal gas law

4.1.2. The first law of thermodynamics and adiabatic expansion

Variation of density

Variation of pressure

Variation of humidity

7.1. Measures of water vapor in the atmosphere

Summary

Learning Outcomes

The major objective of this module is to know the physical and chemical properties of atmosphere.
After reading the module you shall be able to answer the following:
What is atmosphere?
What are the key atmospheric properties?
How temperature, pressure, density changes with several factors? What are the thermodynamic properties of atmosphere?
What are governing equations of atmosphere?

Introduction

Atmosphere is the gaseous envelope that surrounds earth. It approximately extends up to 500 km above. Our atmosphere is composed of different gases, the two most abundant of which are N2 and O2. N2 accounts for 79% of the atmosphere and O2 for 20%. Oxygen can also exist in a triatomic form (O3) called ozone, which has the significant property of absorbing ultraviolet solar radiation. Water vapor, whose abundance can vary from almost nothing in the driest of locales to about 4% of the atmosphere, is responsible for the formation of clouds (when water vapor condenses into liquid droplets or freezes into ice crystals) and precipitation as well. Additionally, water vapor is a greenhouse gas, and plays a key role in the heat budget of the Earth. Another significant greenhouse gas is carbon dioxide (CO2) that emitted as a byproduct of many industrial processes, and its increasing abundance in the atmosphere is the source of much concern regarding future climate change via global warming.

Atmospheric properties

Temperature: Temperature is the measure of thermal or internal energy of the molecules within an object or gas. We can measure temperature of an object using either direct contact or remote sensing. Temperature of air is closely related to other atmospheric properties, such as pressure, volume and density.

Density: Density measures the ‘heaviness’ of an object or how closely ‘packed’ the substance is. Density is related to both the type of material that an object is made of and how closely packed the material is.

Pressure: Pressure is the force exerted over a given area or object, either because of gravity pulling on it or other motion the object has. Molecules in the air produce pressure through both their weight and movement, and this pressure is connected to other properties of the atmosphere.

Humidity: Humidity is a measure of the amount of moisture in the air. It tells you how comfortable it is to be outside, and if there is enough moisture to create clouds and rain.

Variation of temperature

In the atmosphere, temperature is related to volume, pressure, and density. Temperature is inversely related to density but directly related to pressure and volume. This means, for example, when temperature increases, density decreases, and volume and pressure of the gas also increase. So, air that is warm and dry will tend to rise when surrounded by cooler air because warm air is less dense than the cooler air around it.

Temperature controls planting dates and the growth of plants as well as insect pests and crop diseases. As an integral part of weather, temperature also determines the type of precipitation (rain/snow/sleet) that might occur if you are in a location that is experiencing near freezing conditions.

Temperature is a measure of how much internal energy an object or gas has. For example, a gas with fast-moving molecules feels “hot” because when that gas touches something that is cooler, some of the energy of the hot gas is transferred to the cooler object and the cooler object responds by warming up. If there are two objects with different temperatures, energy always flows from the warmer object to the colder object. Atmosphere is a mixture of gases and follows the principle of fluid (liquids and gases) dynamics.

Heat energy transfer is the cause of temperature change and like any other fluid system, in atmosphere also the main mode of energy transfer is a process called convection. It works because in a fluid, “chunks” of matter (or parcels) can move up or down with respect to the rest of the fluid as they are being heated or cooled, respectively. The processes of convection are, however, governed by the laws of thermodynamics. Understanding these laws helps us quantify these processes, make predictions on the formation of clouds and fog, and explain how the vertical profile of temperature in the atmosphere is determined.

4.1.Thermodynamic properties of dry air – adiabatic temperature change

4.1.1. The equation of state – ideal gas law

If air contains no water it is called dry air. The state of a parcel of dry air is described by three properties: temperature (T, expressed in °K, where 273°K = 0°C), pressure (p, force per unit area, expressed in Newtons m-2) and density (ρ, the mass of a unit volume, in Kg m-3). In a gas these properties are related by a relatively simple physical law called the ideal gas law (ideal because it is not exact, albeit quite accurate for most applications in meteorology). This law states that:

p = ρR T

R is a coefficient, called the gas constant. It does not depend on either p, ρ, or T. The gas constant depends only on the composition of gases that make up the air (every gas has its own gas constant). Since this composition (for dry air) is roughly constant throughout most of the atmosphere R of air is constant and equal to 287 Joules kg-1 °K-1).

To understand the equation of state, it is assumed that we have a fixed mass of air enclosed in a container with rigid walls (hence with fixed volume). If we warmed the container, say by putting it over a flame, the temperature of the air (i.e. kinetic energy of the air molecules) will rise and the pressure (i.e., the force exerted by these molecules on the container walls) will increase. The density of the air will not change since we are not increasing the amount of gas in the container nor the volume of the container. The ideal gas equation states that the increase in pressure is directly proportional to the increase in temperature.

Now if we replace the rigid wall of the container with flexible ones, that are allowed to stretch freely if the pressure inside rises above that on the outside. In that case, when we raise the temperature, the pressure inside will remain constant (and equal to the outside pressure), but the container’s volume will increase. This means that the density will decrease (because the mass inside does not change). The ideal gas law states that the density decrease will be inversely proportional to the increase in temperature.

4.1.2. The first law of thermodynamics and adiabatic expansion

Let us remove the flame that heated our flexible walled container, and put it in a chamber where the pressure can be controlled from the outside, lowered or raised at will. What will happen to the density of our air parcel when we lower the pressure surrounding our container? What will happen to its temperature?

Here too the pressure on both sides of the flexible container walls will equalize – as the outside pressure drops, the container will expand and the pressure inside will drop by the same amount. The density of the air parcel in the container will decrease as well, in agreement with the ideal gas law. But what the ideal gas law cannot tell us is what will happen to the temperature. To find that out we need to consider the first law of thermodynamics – a physical law that extends the principle of conservation of energy to include the concepts of heat and work.

In thermodynamics the simplest form of energy conservation is the balance between internal energy (the kinetic energy of the body’s internal molecular motion – directly proportional to its temperature), and the amount of heat added to the body minus the work done by the body on its surroundings.

As our air parcel expands in response to the lowering of the outside pressure, the force of its internal pressure is moving the walls of the container outwards. When a force is moving an object over a given distance it does work. Thus the expanding air parcel does work on its surroundings. This work must come at the expense of internal energy (remember, heat is neither added nor taken away from the parcel in this experiment). Thus the molecular motion within the parcel will slow down, and the parcel’s temperature will drop.

The expanding parcel will experience not only lowering of its pressure and density, but also of its temperature. All three state variables: pressure, density, and temperature will remain in balance as described by the ideal gas law. The process described above is called adiabatic expansion, implying the change in parcel density without the exchange of heat with its surroundings, and its consequential cooling. The opposite will occur when the parcel is compressed. Adiabatic compression leads to warming.

Using the equation of state, the first law of thermodynamics, and the hydrostatic equation we can find that the rate of adiabatic temperature change in an ascending air parcel (also termed the adiabatic lapse rate and denoted Γd) is constant:

Γd = – ΔT / ΔZ = 9.8 °C km-1

Note that Γd is defined as the negative of the actual temperature change, so that Γd is the amount of cooling that the rising parcel experiences. Sinking air will warm at the same rate as it is being compressed by the increasing pressure.

Fig. 1: This shows that the vertical variation of the Earth’s temperature is not quite so simple to describe. There are regions where the temperature increases with height, and regions where the temperaturedecreases with height (Source:http://teachertech.rice.edu/ Participants/louviere/struct.html)

5. Variation of density

The technical definition of density is mass per unit volume. Generally, density describes how tightly packed something is. An object with a lot of material in a small space is denser than an object that has lots of air space included. In the atmosphere, gas that is less dense has a lower concentration of molecules per volume than a denser gas and will tend to rise compared to the air around it.

Why do I care? When planting crops or plants, soil density is very important. If the soil is packed too tightly, the plant or crop won’t be able to absorb any water or nutrients from the soil and will not be able to grow properly. Density in the atmosphere is also important in the formation of clouds and precipitation.

Warm air is less dense than cooler air. Air density varies with the relative humidity (amount of water vapor molecules in the air) along with temperature. Water vapor molecules (H2O in the gaseous phase) are composed of Hydrogen (H) and Oxygen (O) molecules. Hydrogen has a molecular weight of 1.01 g/mol. Dry air is composed mostly of Nitrogen (N) molecules since Earth’s atmosphere is 78% Nitrogen and 21% Oxygen. Nitrogen has a molecular weight of 14.0 g/mol. In the atmosphere, the density of air particles decreases with height, with more gas particles remaining near the surface of Earth. When only taking into account humidity, dry air is denser than moist air because of molecular weights of the gases.

A hot air balloon is a good example of how people work with density. Hot air balloons use the properties of density in order to float. In the base of the hot air balloon, there is a torch that heats up the air inside of the balloon. When the air inside the balloon becomes warmer than the surrounding air, the balloon will begin to float. The person controlling the hot air balloon can add more heat to the balloon to reach the desired height. The air inside the balloon needs to cool in order for the balloon to land.

The density of dry air can be calculated using the ideal gas law, expressed as a function of temperature and pressure:

ρ = p/RspecificT

where,

ρ = air density (kg m-3)
p = absolute pressure (Pa)
T = absolute temperature (K)
R specific = specific gas constant for dry air (J kg-1 K-1)
The specific gas constant for dry air is 287.058 J kg-1 K-1 in SI units.
This quantity may vary slightly depending on the molecular composition of air at a particular location.

Therefore:

At International Union of Pure and Applied Chemistry (IUPAC) standard temperature and pressure i.e. 0 °C and 100 kPa, respectively, dry air has a density of 1.2754 kg m-3.
At 20 °C and 101.325 kPa, dry air has a density of 1.2041 kg m-3
At 70 °F and 14.696 psi, dry air has a density of 0.074887 lb ft-3

6. Variation of pressure

Pressure is force exerted over a given area. In the atmosphere, the molecules in the air apply pressure to everything on earth, including us. For instance, individual molecules in the air push against tiny areas on the top of our head. The force that air exerts is called air pressure. The more air molecules there are above you, the greater the force they exert, so the greater the pressure.

Pressure is important because it is related to volume, density, and temperature. In the atmosphere, warm surfaces can heat the air above them, causing the air to become less dense and to rise. This can eventually result in clouds and precipitation in the areas of rising motion, such as in the center of low pressure systems. High pressure in the atmosphere causes the air to compress and sink, leading to clear skies and calm conditions.

We all live near the bottom of an ocean of air. At sea level, the weight of the air overhead presses on us with a pressure of ~105 N m-2 =14.7 lbs in-2. We are not aware of this great weight because the air presses on us from all sides, even from our insides (due to the air in our lungs).

At higher altitudes, there is less air and less weight overhead, and the pressure is less. Also, because air is readily compressible, the lower layers of air are compressed by the weight of the air above. Thus, the pressure and density of air decrease at higher altitudes. That’s why a helium balloon rises: the pressure on the underside of the balloon is greater than the pressure on the top.

Fig. 2: It shows how air pressure (in Y-axis) falls exponentially with increase in altitude (in X-axis). The mathematical form of this is given in equation 1 below. (Source:https://www.colorado.edu/physics/phys1 140/phys1140_f98/Experiments/O2/O2.html)

Where, h is the height above a level where the pressure is po, m is the average mass of an air molecule, k is the Boltzmann constant (k =1.38×10-23J K-1) and T is the temperature in oK. Note that both mgh and kT have the units of energy, so the exponent is dimensionless. It is a remarkable characteristic of the exponential function that eqn. 1 is true regardless of where we set the zero of h, so long as the pressure at h = 0 is po. This equation (derived in the Appendix A) is not quite correct, because its derivation assumes that the atmosphere is isothermal when in fact, the temperature of the air varies considerably with altitude.

Eqn. 1 can be rewritten as

Where, h0 = (kT/mg) is a characteristic height, called the scale height, of the atmosphere. The scale height is the height increase which reduces the air pressure by a factor of 1/e (= 1/2.718~0.368). If you started at sea level (p = 1 atm) and climbed a mountain with a height ho, the pressure at the peak would be (1 atm/e = 0.37 atm). At an altitude of 2ho , the pressure would be 1 atm / e2 i.e. ~ 0.135 atm.

If the pressure change p can be measured over some small height change h, then the scale height ho can be determined.

Change of pressure with temperature: According to the ideal gas law, if the volume V and number of molecules N are fixed, then the pressure p is proportional to the temperature T, and the fractional change in temperature is equal to the fractional change in pressure

7. Variation of humidity

Humidity is a measure of the amount of moisture in the air. Moist air is air that contains water in vapor form. The moisture in the air is usually referred to as humidity. The average concentration of vapor in the atmosphere is 0.48%. Another way to appreciate the amount of water in the atmosphere is to note that if all of it was condensed and made to cover the Earth uniformly, it would make a layer of liquid 1 inch thick. Air can not carry unlimited amounts of water. Even in the most humid situations the concentration of vapor in the atmosphere can not exceed a few percent. The colder the air, the less amount of vapor it can hold.

The largest source of water in the climate system is the world ocean. Water evaporates from the ocean surface to mix in the air. Wet or forest covered land surfaces are secondary sources of atmospheric water. The highest concentrations of vapor are found near the surface in the tropics. The concentration drops quite rapidly with height, and half the way up the tropical troposphere it is a fraction of what it is near the surface. Vapor concentration also falls off rapidly as we move north or south of the tropical belt, and it is generally higher over the oceans than it is over land.

7.1. Measures of water vapor in the atmosphere

There are a few ways to measure the concentration of water vapor in the atmosphere.

I. Vapor pressure (denoted e): It is the partial pressure of water vapor molecules in the atmosphere. Partial pressure is a term in thermodynamics of gas mixtures (in our case – air). We can break down the air pressure into the pressure each of its individual gas constituents would exert, had all the others been removed. The pressure in an air parcel is the sum of the partial pressures of all the constituents. The smaller the concentration of a gas in the mixture, the lower its partial pressure.However, since molecules of different constituents have different mass, the partial pressure is not directly proportional to the molecular concentration.

The concept of vapor pressure is important for understanding the processes of evaporation and saturation. If we hold a parcel of air still over flat water surface, water molecules will escape the surface and start mixing with the other gases in the air parcel. This is evaporation – it can happen even if the liquid is not at its boiling temperature. Evaporation can only go on until the maximum amount of water vapor that air can hold is reached. At this point, the pressure that the water molecules exert as they are trying to escape the liquid is equaled by the partial pressure of water in the air parcel, called the saturation vapor pressure. Saturation is a process of equilibrium where water molecules cross back and forth across the boundary between water and air, maintaining a fixed concentration in the air. The saturation vapor pressure is a function of temperature.

II. Relative humidity: It is the ratio of actual vapor pressure to saturation vapor pressure (expressed as % if multiplied by 100). This is a common way to indicate air humidity. Because perspiration plays a very important function in maintaining body temperature, relative humidity figures into consideration of the degree of comfort we have when following our daily activities.

III. Mixing ratio: It is the mass of water vapor in grams per kilogram of air. This is the most common way to indicate air humidity in scientific applications. At the Earth’s surface, mixing ratio varies from ~18 g kg-1 in the tropics to less than 2 g kg-1 near the poles.

IV. Dew point temperature: It is yet another way to express the vapor content of an air parcel. The dew point temperature gets its name from the process leading to the formation of dew. In the early morning hours before sunset, when the air is still, and the ground is cool (compared to its day time temperature) because it radiated its heat into the atmosphere and outer space, the air in immediate contact with it cools too by conduction. Since the air’s ability to hold vapor decreases with decreasing temperature, any vapor in excess of the saturation value is rejected and condenses as droplets on the ground or its cover. Following this natural process we define the dew point as the temperature at which the vapor in a cooled parcel of air begins to condense. The dew point can be either lower than (if the air is not saturated) or equal to (if the air is saturated) the actual temperature. The bigger the difference between the actual air temperature and the dew point, the drier the air is.

Summary

Atmosphere is a mixture of gases and follows the principle of fluid dynamics. Information on temperature, density, pressure and humidity properties are key to most atmospheric applications. Changes in pressure, volume and density properties are interrelated with changes in temperature of an air parcel.
Convection is the principal mode of heat transfer in atmosphere and therefore the changes in air temperature.
Atmospheric pressure decreases exponentially with height from the sea level.
Vapour pressure, relative humidity, mixing ratio and dew point are the various measures to represent atmospheric humidity i.e. water vapour.

you can view video on Atmospheric Properties