Physical Properties Of

Some important numbers for Earth's atmosphere are given in Table 1.3. Global mean surface pressure is 1.013 x 105Pa = 1013 h Pa. (The hecto Pascal is now the official unit of atmospheric pressure [1 h Pa = 102 Pa], although the terminology "millibar" [1 mbar = 1 h Pa] is still in common use and will also be used here.)

The global mean density of air at the surface is 1.235 kgm-3. At this average density we require a column of air of about 7-8 km high to exert pressure equivalent to 1 atmosphere.

Throughout the region of our focus (the lowest 50 km of the atmosphere), the mean free path of atmospheric molecules is so short and molecular collisions so frequent that the atmosphere can be regarded as a continuum fluid in local thermodynamic equilibrium (LTE), and so the "blackbody" ideas to be developed in Chapter 2 are applicable. (These statements break down at sufficiently high altitude, > 80 km, where the density becomes very low.)

If in LTE, the atmosphere accurately obeys the perfect gas law,1 then

where p is pressure, p, density, T, absolute temperature (measured in Kelvin), Rg, the universal gas constant

Rg = 8.3143 J K-1mol-1, the gas constant for dry air

R = R = 287J kg-1K-1, ma and the mean molecular weight of dry air (see Table 1.2, last entry), ma = 28.97 (x10-3 kg mol-1).

Robert Boyle (1627-1691) made important contributions to physics and chemistry and is best known for Boyle's law, describing an ideal gas. With the help of Robert Hooke, he showed among other things that sound did not travel in a vacuum, proved that flame required air, and investigated the elastic properties of air.

TABLE 1.3. Some atmospheric numbers.

Atmospheric mass Ma 5.26 x 1018 kg

Global mean surface pressure ps 1.013 x 105 Pa

Global mean surface temperature Ts 288 K

Global mean surface density ps 1.235kgm-3

TABLE 1.4. Properties of dry air at STP.

Specific heat at constant pressure Specific heat at constant volume Ratio of specific heats Density at 273K, 1013mbar Viscosity at STP Kinematic viscosity at STP Thermal conductivity at STP Gas constant for dry air cp 1005 J kg-1 K-1

cv 718Jkg-1K-1

From Eq. 1-1 we see that it is only necessary to know any two of p, T, and p to specify the thermodynamic state of dry air completely. Thus at STP, Eq. 1-1 yields a density p0 = 1.293kgm-3, as entered in Table 1.4, where some of the important physical parameters for dry air are listed.

Note that air, as distinct from liquids, is compressible (if p increases at constant T, p increases) and has a relatively large coefficient of thermal expansion (if T increases at constant p, p decreases). As we shall see, these properties have important consequences.

Air is a mixture of gases, and the ideal gas law can be applied to the individual components. Thus if pv and pd are, respectively, the masses of water vapor and of dry air per unit volume (i.e., the partial densities) then the equations for the partial pressures (that is the pressure each component would exert at the same temperature as the mixture, if it alone occupied the volume that the mixture occupies) are:

where e is the partial pressure of water vapor, pd is the partial pressure of dry air, Rv is the gas constant for water vapor, and Rd is the gas constant for dry air. By Dalton's law of partial pressures, the pressure of the mixture, p, is given by:

In practice, because the amount of water vapor in the air is so small (see Table 1.2), we can assume that pd >> e, and so p ~ pd.

Now imagine that the air is in a box at temperature T, and suppose that the floor of the box is covered with water, as shown in Fig. 1.4. At equilibrium, the rate of evaporation will equal the rate of condensation, and the air is said to be saturated with water vapor. If we looked into the box, we would see a mist.2 At this point, e has reached

2 This is true provided there are plenty of condensation nuclei—tiny particles—around to ensure condensation takes place (see GFD Lab I).

FIGURE 1.4. Air over water in a box at temperature T. At equilibrium the rate of evaporation equals the rate of condensation. The air is saturated with water vapor, and the pressure exerted by the vapor is es, the saturated vapor pressure. On the right we show the mixture comprising dry 'd' and vapor V components.

FIGURE 1.4. Air over water in a box at temperature T. At equilibrium the rate of evaporation equals the rate of condensation. The air is saturated with water vapor, and the pressure exerted by the vapor is es, the saturated vapor pressure. On the right we show the mixture comprising dry 'd' and vapor V components.

FIGURE 1.5. Saturation vapor pressure es (in mbar) as a function of T in °C (solid curve). From Wallace & Hobbs, (2006).

the saturated vapor pressure, es. In fact, saturation occurs whenever the partial pressure of water exceeds the saturation vapor pressure es. As shown in Fig. 1.5, es is a function only of temperature and increases very rapidly with T. To a good approximation at typical atmospheric temperatures, es(T) is given by:

where A = 6.11 hPa and p = 0.067°C-1 are constants and T is in °C, a simplified statement of the Clausius-Clapeyron relationship. The saturated vapor pressure increases exponentially with temperature, a property which is enormously important for the climate of the planet.

From Eq. 1-4 (see also Fig. 1.5) we note that es = 16.7hPa at T = 15°C. From Table 1.2 we deduce that Rv = Rg/mv = 461.39 J kg-1 K-1 and so, using Eq. 1-2, at saturation pv = 0.0126kgm-3. This is the maximum amount of water vapor per unit volume that can be held by the atmosphere at this temperature.

The es (T) curve shown in Fig. 1.5 has the following very important climatic consequences:

• The moisture content of the atmosphere decays rapidly with height, because T decreases with height, from the Earth's surface up to 10 km or so. In Chapter 3 we will see that at the surface the mean temperature is about 15°C, but falls to about -50°C at a height of 10 km (see Fig. 3.1). We see from Fig. 1.5 that es —> 0 at this temperature. Thus most of the atmosphere's water vapor is located in the lowest few km. Moreover, its horizontal distribution is very inhomo-geneous, with much more vapor in the warm tropics than in cooler higher latitudes. As will be discussed in Chapter 2, this is crucially important in the transfer of radiation through the atmosphere.

• Air in the tropics tends to be much more moist than air over the poles, simply because it is warmer in the tropics than in polar latitudes; see Section 5.3.

• Precipitation occurs when moist air is cooled by convection, and causes H2O concentrations to be driven back to their value at saturation at a given T; see Section 4.5.

• In cold periods of Earth's history, such as the last glacial maximum 20,000 years ago, the atmosphere was probably much more arid than in warmer periods. Conversely, warm climates tend to be much more moist; see Section 12.3.

1.3.3. GFD Lab I: Cloud formation on adiabatic expansion

The sensitive dependence of saturation vapor pressure on temperature can be readily demonstrated by taking a carboy and pouring warm water into it to a depth of a few cm, as shown in Fig. 1.6. We leave it for a few minutes to allow the air above the warm water to become saturated with water vapor. We rapidly reduce the pressure in the bottle by sucking at the top of the carboy. You can use your lungs to suck the air out, or a vacuum cleaner. One might expect that the rapid adiabatic expansion of the air would reduce its temperature and hence lower the saturated vapor pressure sufficiently that the vapor would condense to form water droplets, a ''cloud in the jar.'' To one's disappointment, this does not happen.

The process of condensation of vapor to form a water droplet requires condensation

FIGURE 1.6. Warm water is poured into a carboy to a depth of 10 cm or so, as shown on the left. We leave it for a few minutes and throw in a lighted match to provide condensation nuclei. We rapidly reduce the pressure in the bottle by sucking at the top. The adiabatic expansion of the air reduces its temperature and hence the saturated vapor pressure, causing the vapor to consense and form water droplets, as shown on the right.

FIGURE 1.6. Warm water is poured into a carboy to a depth of 10 cm or so, as shown on the left. We leave it for a few minutes and throw in a lighted match to provide condensation nuclei. We rapidly reduce the pressure in the bottle by sucking at the top. The adiabatic expansion of the air reduces its temperature and hence the saturated vapor pressure, causing the vapor to consense and form water droplets, as shown on the right.

nuclei, which are small particles on which the vapor can condense. We can introduce such particles into the carboy by dropping in a lighted match and repeating the experiment. Now on decompression we do indeed observe a thick cloud forming which disappears again when the pressure returns to normal, as shown in Fig. 1.6 (right).

In the bottom kilometer or so of the atmosphere there are almost always abundant condensation nuclei, because of the presence of sulfate aerosols, dust, smoke from fires, and ocean salt. Clouds consist of liquid water droplets (or ice particles) that are formed by condensation of water vapor onto these particles when T falls below the dew point, which is the temperature to which air must be cooled (at constant pressure and constant water vapor content) to reach saturation.

A common atmospheric example of the phenomenon studied in our bottle is the formation of fog due to radiational cooling of a shallow, moist layer of air near the surface. On clear, calm nights, cooling due to radiation can drop the temperature to the dew point and cause fog formation, as shown in the photograph of early morning mist on a New England lake (Fig. 1.7).

The sonic boom pictured in Fig. 1.8 is a particularly spectacular consequence of the sensitive dependence of es on T: just as in our bottle, condensation of water is caused by the rapid expansion and subsequent adi-abatic cooling of air parcels induced by the shock waves resulting from the jet going through the sound barrier.

Solar Power Sensation V2

Solar Power Sensation V2

This is a product all about solar power. Within this product you will get 24 videos, 5 guides, reviews and much more. This product is great for affiliate marketers who is trying to market products all about alternative energy.

Get My Free Ebook


Post a comment