Chapter 4 Atmospheric Moisture

Transcription

1 4.1 Introduction We said in the first chapter that the three main topics that will be studied to describe weather and meteorology in general are heat, moisture, and air motion. As we saw in the last chapters, the heat supplies the energy that drives the atmosphere while the moisture in the atmosphere is responsible for humidity, dew, fog, visibility, clouds, and precipitation. Also through the process of evaporation water vapor becomes an important medium for conveying latent heat into the air, thus giving it a function in the heat exchange as well as in the moisture exchange between the earth and the atmosphere. It is interesting that of all the water on the planet only a minute fraction of the earth s water is stored as clouds and vapor in the atmosphere at any one time. 4.2 Change of State Matter is usually said to exist in three states or phases: solid, liquid, and gas. Solids are hard bodies that resist deformations, whereas liquids and gases have the characteristic of being able to flow. A liquid flows and takes the shape of whatever container in which it is placed. A gas also flows into a container and spreads out until it occupies the entire volume of the container. Water is the only substance that exists in all these three states or phases in the pressures and temperatures normally found in the atmosphere. When matter is in the solid state it has its least energy and when it is in the gaseous state it has the greatest energy. Let us examine the behavior of matter when it is heated over a relatively large range of temperatures. In particular let us consider a piece of ice at C and heat it to a temperature of C. The ice is placed inside a strong, tightly sealed, windowed enclosure containing a thermometer. Heat is then applied as shown in figure 4.1. The temperature is observed as a function of time and is plotted in figure 4.2. As the heat is applied to the solid ice, the temperature of the block increases with time until 0 0 C is reached. At this point the temperature remains constant, even though heat is being continuously applied. Looking at the block of ice, through the window in the container, we observe small drops of liquid water forming on the block of ice. The ice is starting to melt. It is observed that the temperature remains constant until every bit of the solid ice is converted into the liquid water. A change of phase is being observed. That is, the ice is changing from the solid phase into the liquid phase. As soon as all the ice is melted, an increase in temperature of the liquid water is again observed. The temperature increases up to C, and then levels off. Thermal energy is being applied, but the temperature is not changing. Looking through the window into the container, we see that there are bubbles forming throughout the liquid. The water is boiling. The liquid water is being

2 Figure 4.1 Converting ice to water to steam. Figure 4.2 Graph of phase changes. converted to steam, the gaseous state of water. The temperature remains at this constant value of C until every drop of the liquid water has been converted to the gaseous steam. After that, as heat is continuously supplied, an increase in the temperature of the steam is observed. Superheated steam is being made. (Note, one should not try to do this experiment on his or her own, because enormous pressures can be built up by the steam, causing the closed container to explode.) Let us go back and analyze this experiment more carefully. As the thermal energy was supplied to the below freezing ice, its temperature increased to 0 0 C. At this point the temperature remained constant even though heat was being continuously applied. Where did this thermal energy go if the temperature never changed? The thermal energy went into the melting of the ice, changing its phase from the solid to the liquid phase. If the solid is observed in terms of its lattice structure, figure 4.3, it can be seen that each molecule is vibrating about its Figure 4.3 The lattice structure. equilibrium position. As heat is applied, the vibration increases, until at 0 0 C, the vibrations of the molecules become so intense that the molecules literally pull apart from one another changing the entire structure of the material. This is the melting process. The amount of heat necessary to tear these molecules apart is a constant and is called the latent heat of fusion of that material. The latent heat of fusion is 4-2

3 the amount of heat necessary to convert 1 kg of the solid to 1 kg of the liquid. For water, it is found experimentally that it takes 80 kcal or 334,000 J of thermal energy to melt 1 kg of ice. Hence we take the latent heat of fusion of water to be Lf = 80 kcal/kg = 334,000 J/kg If we must supply 80 kcal/kg to melt ice, then we must take away 80 kcal/kg to freeze water. That is, the heat of fusion is equal to the heat of melting. The word latent means hidden or invisible, and not detectable as a temperature change. Heat supplied that does change the temperature is called sensible heat, because the heat supplied is sensed as a change in temperature. In the liquid state there are still molecular forces holding the molecules together, but because of the energy and motion of the molecules, these forces cannot hold the molecules in the relatively rigid position they had in the solid state. This is why the liquid is able to flow and take the shape of any container in which it is placed. As the water at 0 0 C is further heated, the molecules absorb more and more energy, increasing their mean velocity within the liquid. This appears as a rise in temperature of the liquid. At C, so much energy has been imparted to the water molecules, that the molecular speeds have increased to the point that the molecules are ready to pull away from the molecular forces holding the liquid together. As further thermal energy is applied, the molecules fly away into space as steam. The temperature of the water does not rise above C because all the applied heat is supplying the molecules with the necessary energy to escape from the liquid. The heat that is necessary to convert 1 kg of the liquid to 1 kg of the gas is called the latent heat of vaporization. For water, it is found experimentally that it takes 540 kcal or 2,260,000 J of thermal energy to boil 1 kg of liquid water. Hence we take the latent heat of vaporization of water to be Lv = 540 kcal/kg = 2,260,000 J/kg Because this amount of thermal energy must be given to water to convert it to steam, then this same quantity of thermal energy will be given up to the environment when steam condenses back into the liquid state. Therefore, the heat of vaporization is equal to the heat of condensation. Liquid water can also be converted to the gaseous state at any temperature, a process called evaporation. Thus, water left in an open saucer overnight will be gone by morning. Even though the temperature of the water remained at the room temperature, the liquid was converted to a gas. It evaporated into the air. The gaseous state of water is then usually referred to as water vapor rather than steam. At 0 0 C the latent heat of vaporization is 600 kcal/kg = 2,510,000 J/kg. It is also possible for the solid ice to go directly into the gaseous water vapor state without ever going through the liquid state. This process is called sublimation. Sublimation frequently removes snow from the ground in cold dry winter weather, even though the temperature is below freezing and the particular 4-3

4 area may be in shadow, that is, no sun is shining directly on the ground. It is also possible for the gaseous water vapor to go directly into the solid ice state without passing through the liquid state. This process is sometimes called deposition. This process is often noticed when you go out of your house on a very cold morning in the winter time and you observe ice on the car windows and on the grass. The ice is called frost. The water vapor did not condense into water and then the water froze into ice. Rather, the water vapor went directly from the gaseous state into the solid state. It is interesting to note here that there is no essential difference in the water molecule when it is either a solid, a liquid, or a gas. The molecule consists of the same two hydrogen atoms bonded to one oxygen atom. The difference in the state is related to the different energy, and hence speed of the molecule in the different states. A summary of the changes of state of water and the heat absorbed or liberated in these processes is shown in figure 4.4. Figure 4.4 Changes of State for Water. 4.3 Humidity To understand the concept of humidity, we must first understand the concept of evaporation. Consider the two bowls shown in figure 4.5. Both are filled with (a) Bowl 1 (b) Bowl 2 Figure 4.5 The process of evaporation. water. Bowl 1 is open to the environment, while a glass plate is placed over bowl 2. If we leave the two bowls overnight, upon returning the next day we would find bowl 1 empty while bowl 2 would still be filled with water. What happened to the water in bowl 1? The water in bowl 1 has evaporated into the air and is gone. 4-4

5 Evaporation is the process by which water goes from the liquid state to the gaseous state at any temperature. Boiling, as you recall, is the process by which water goes from the liquid state to the gaseous state at the boiling point of C. Whereas in the process of evaporation, it is possible for liquid water to go to the gaseous state at any temperature. Evaporation occurs from bodies of water, water droplets in clouds, fog or soils. Just as there is a latent heat of vaporization for boiling water (Lv = 540 kcal/kg), the latent heat of vaporization of water at 0 0 C is Lv = 600 kcal/kg. The latent heat at any in between temperature can be found by interpolation. Thus, in order to evaporate 1 kg of water into the air at 0 0 C, you would have to supply 600 kcal of thermal energy to the water. The molecules in the water in bowl 1 are moving about in a random order. But their attractive molecular forces still keep them together. These molecules can now absorb heat from the surroundings. This absorbed energy shows up as an increase in the kinetic energy of the molecule, and hence an increase in the velocity of the molecule. When the liquid molecule has absorbed enough energy it moves right out of the liquid water into the air above as a molecule of water vapor. (Remember the water molecule is the same whether it is a solid, liquid, or gas, namely H2O, two atoms of hydrogen and one atom of oxygen. The difference is only in the energy of the molecule.) Since the most energetic of the water molecules escape from the liquid, the molecules left behind have lower energy, hence the temperature of the remaining liquid decreases. Hence, evaporation is a cooling process. The water molecule that evaporated took the thermal energy with it, and the water left behind is just that much cooler. The remaining water in bowl 1 again absorbs energy from the environment, thereby increasing the temperature of the water in the bowl. This increased thermal energy is used by more liquid water molecules to escape into the air as more water vapor. The process continues until all the water in bowl 1 is evaporated. Now when we look at bowl 2, the water is still there. Why didn t all that water evaporate into the air? To explain what happens in bowl 2 let us do the following experiment. Water is placed in a container and a plate is then placed over the water. Dry air, air that does not contain water vapor, is then allowed to fill the top portion of the closed container, figure 4.6a. A thermometer is used to measure the temperature of the air, T = 20 0 C, and a pressure gauge is used to measure the pressure of the air, po, in the container. The plate separating the dry air from the water is now removed by sliding it out of the closed container. As time goes by, the pressure recorded by the pressure gauge is observed to increase, figure 4.6b. This occurs because some of the liquid water molecules evaporate into the air as water vapor. Water vapor is a gas like any other gas and it exerts a pressure. It is this water vapor pressure that is being recorded as the increased pressure on the gauge. The gauge is reading the air pressure of the dry air plus the actual water vapor pressure of the gas, p o + p awv. Subtracting p o from p o + p awv, gives the actual water vapor pressure, pawv. As time goes on, the water vapor pressure increases as more 4-5

6 Thermometer T = 20 o C dry air pressure gauge T = 20 o C water (a) T = 20 o C (b) T = 25 oc (c) (d) Figure 4.6 Water vapor in the air. and more water molecules evaporate into the air. However, after a while, the pressure indicated by the gauge, becomes a constant. At this point the air contains the maximum amount of water vapor that it can hold at that temperature. As new molecules evaporate into the air, some of the water vapor molecules condense back into the liquid, figure 4.6c. An equilibrium condition is established, whereby just as many water vapor molecules are condensing as liquid water molecules are evaporating. At this point, the air is said to be saturated. That is, the air contains the maximum amount of water vapor that it can hold at that temperature. The vapor pressure read by the gauge is now called the saturation vapor pressure, pswv. The amount of water vapor in the air is called humidity. There are many different ways to measure humidity, some of them are as follows: 1. Absolute Humidity - Absolute humidity is the ratio of the mass of water vapor to a unit volume of air, and is measured in g/m 3 the same units as density. As an example Example 4.1 If 25.0 g of water vapor are added to 2000 m 3 of air, what is the absolute humidity of the air. Solution The absolute humidity of the air is found by its definition as Absolute Humidity = 25 g of water vapor = g/m m 3 of air 4-6

7 To go to this Interactive Example click on this sentence. Absolute Humidity is used often in air conditioning but not in meteorology, because as the volume of air increases as air ascends into the atmosphere, the absolute humidity decreases. When air descends and the volume decreases, the absolute humidity would increase. We prefer a unit for humidity that does not change with volume. 2. Specific Humidity (m) - Specific Humidity is defined as the ratio of the mass of water vapor in the air to a unit mass of air including the water vapor. As an example Example 4.2 If 12.0 g of water vapor are added to 1000 g of air, what is the specific humidity of the air? Solution The specific humidity of the air is found by its definition as S.H. = m = 12 g of water vapor = 11.9 g/kg 1012 g of air To go to this Interactive Example click on this sentence. 3. Mixing Ratio (q) - The Mixing Ratio is defined as the ratio of the mass of the water vapor in the air to a unit mass of dry air. As an example Example 4.3 If we mix 12 g of water vapor into 1000 g of dry air, the total amount of dry air is kg. Find the mixing ratio. Solution The mixings ratio of the air is found by its definition as 4-7

8 Mixing Ratio = q = 12 g of water vapor = 12.0 g/kg kg of dry air To go to this Interactive Example click on this sentence. In most cases considered the specific humidity m is approximately equal to the mixing ratio q. Notice that the mixing ratio is a ratio of masses and does not depend on pressure or volume of the air. If the air is saturated, the mixing ratio is called the saturated mixing ratio and is shown in table 4.1. As an example of the information available in table 4.1, notice that if the air temperature is 25 0 C the air is capable of holding a maximum of 20 g of water vapor for each kilogram of dry air. If the air temperature drops to 20 0 C, the air is now only capable of holding 14 g of water vapor per kilogram of dry air. Notice that as the temperature continues to decrease, the air is capable of holding smaller and smaller quantities of water vapor. Table 4.1 Saturation Mixing Ratio (at sea-level pressure) Temperature ( 0 C) g/kg Relative Humidity - RH is defined as the ratio of the amount of water vapor actually present in the air to the maximum amount of water vapor that the air can hold at a given temperature and pressure, times 100%. That is, RH = actual water vapor (100%) (4.1) maximum water vapor 4-8

9 Since the amount of water vapor in the air is directly proportional to the water vapor pressure, the water content in the air can also be measured in terms of the pressure exerted by the water vapor in the air. The partial pressure exerted by the water vapor in the air is called the vapor pressure. It is expressed in millibars or inches of Hg. When air contains all the water vapor it can hold at that temperature it is said to be saturated and its vapor pressure then equals its saturation vapor pressure. The air is then at its dew point temperature. Therefore, the relative humidity (RH) of the air can also be written as RH = actual vapor pressure (100%) (4.2) saturation vapor pressure RH = pawv (100%) (4.3) pswv When the air is saturated, the actual vapor pressure recorded by the gauge is equal to the saturation vapor pressure and hence, the relative humidity is 100%. If the air in the container of figure 4.6 is now heated, we will notice that the pressure indicated by the pressure gauge increases, figure 4.6d. Part of the increased pressure is caused by the increase of the pressure of the air. This increase can be calculated by the ideal gas equation and subtracted from the gauge reading, so that we can determine any increase in pressure that would come from an increase in the actual water vapor pressure. We notice that by increasing the air temperature to 25 0 C, the water vapor pressure also increases. After a while, however, the water vapor pressure again becomes a constant. The air is again saturated. We see from this experiment that the maximum amount of water vapor that the air can hold is a function of temperature. At low temperatures the air can only hold a little water vapor, while at high temperatures, the air can hold much more water vapor. We can now see why the water in bowl 2, figure 4.5, did not disappear. Water evaporated from the liquid into the air above, increasing the relative humidity of the air. However, once the air became saturated, the relative humidity was equal to 100%, and no more water vapor could evaporate into it. This is why you can still see the water in bowl 2, there is no place for it to go. In general, the amount of evaporation depends upon the following factors: 1) The vapor pressure. Whenever the actual vapor pressure of the air is less than the maximum vapor pressure allowable at that temperature, the saturation vapor pressure, then evaporation will readily occur. Greater evaporation occurs whenever the air is dry, that is, at low relative humidities. Less evaporation occurs when the air is moist, that is at high relative humidities. 2) Temperature. When the temperature of the air is high, the air is able to hold more moisture, and hence greater evaporation will occur. 3) Wind movement and turbulence. Air movement and turbulence replaces air near the water surface with less moist air and hence increases the rate of evaporation. 4-9

10 Because of the temperature dependence of water vapor in the air, when the temperature of the air is increased, the capacity of the air to hold water increases. Therefore, if no additional water is added to the air, the relative humidity will decrease because the capacity of the air to hold water vapor has increased. Conversely, when the air temperature is decreased, its capacity to hold water vapor decreases, and therefore the relative humidity of the air increases. This temperature dependence causes a decrease in the relative humidity during the day light hours, and an increase in the relative humidity during the night time hours, with the maximum relative humidity occurring in the early morning hours just before sunrise. This can be seen in figure 4.7. Figure 4.7 The daily variation of relative humidity. The relative humidity is greater over land in the winter because the temperature is lower. The relative humidity has a slight maximum over the oceans in the summer. In general, the water vapor pressure is greatest over the equator and decreases towards the poles. Whereas the relative humidity is greatest over the equator, decreases as you go north or south of the equator, but then starts to increase again because of the lower temperatures toward the poles. From what we have seen, we can change the relative humidity by (1) changing the amount of water vapor in the air or by (2) changing the temperature of the air. As an example of the changing of the relative humidity by changing the water vapor content of the air consider the container shown in figure 4.8a. The container contains air at the constant temperature of 20 0 C, and some liquid water at the bottom of the container. At the instant considered there are 4.00 g of water vapor in the air above the water. If we look at table 4.1 we see that at 20 0 C the air is capable of holding 14.0 g of water vapor. Therefore the relative humidity, equation 4.1, becomes RH = actual water vapor (100%) (4.1) maximum water vapor 4-10

11 RH = 4.00 g (100%) 14.0 g RH = 28.6% T = 20 o C 1 kg air 4 g water vapor T = 20 o C 1 kg air 7 g water vapor water (a) water (b) T = 20 o C 1 kg air 14 g water vapor water (c) Figure 4.8 Changing the relative humidity of the air by adding water to it. As time goes by, more water evaporates into the air in the container until there are now 7.00 g of water vapor in the container, figure 4.8b. The relative humidity now becomes RH = actual water vapor (100%) maximum water vapor RH = 7.00 g (100%) 14.0 g RH = 50.0% Finally after a longer period of time and more evaporation, figure 4.8c, there are 14.0 g of water vapor in the container and the relative humidity becomes RH = actual water vapor (100%) maximum water vapor RH = g (100%) 14.0 g RH = 100% Hence, by adding water vapor to the air by the process of evaporation, the relative humidity increased until it reached 100% and the air became completely saturated. Finally we should note that if we were to remove some of the air in the container and replace it by some dry air, we could reverse the process and lower the amount of water vapor in the air, and thus would lower the relative humidity. 4-11

12 Now let us see what happens when we keep the amount of water vapor in the air a constant, but change the temperature of the air. As an example of the changing of the relative humidity by changing the temperature of the air let us now consider the container shown in figure 4.9a. The container contains air at the T = 20 o C 1 kg air 10 g water vapor T = 15 o C 1 kg air 10 g water vapor water (a) water (b) T = 10 o C 1 kg air 7 g water vapor water (c) Figure 4.9 Changing the relative humidity of the air by changing the temperature of the air. temperature of 20 0 C, and some liquid water at the bottom of the container. The air contains some 10 g of water vapor. The maximum amount of water vapor that the air can hold at that temperature is 14 g. Therefore, the relative humidity of the air in the container is found as RH = actual water vapor (100%) maximum water vapor RH = 10.0 g (100%) 14.0 g RH = 71.4% The air in the container is now cooled to 15 0 C, figure 4.9b. From Table 4.1 we see that the air can only hold 10.0 g of water vapor at 15 0 C, therefore the relative humidity now becomes RH = actual water vapor (100%) maximum water vapor RH = 10.0 g (100%) 10.0 g RH = 100% Hence by cooling the air from 20 0 C to 15 0 C has caused the relative humidity to increase from 71.4% to 100 % and the air has become saturated. If the air is further 4-12

13 cooled to 10 0 C, figure 4.9c, the air will now only be able to hold 7.00 g of water vapor. Thus 3.00 g of water will condense out of the air into the water below. The relative humidity will be RH = actual water vapor (100%) maximum water vapor RH = 7.00 g (100%) 7.00 g RH = 100% Thus when the air was cooled from C to C the relative humidity increased from 71.4% to 100% and the air became saturated. Further cooling caused water vapor in the air to condense out of the air into the water below such that the relative humidity remained at 100%. Conversely if the air started out saturated at C, heating it up would cause the relative humidity to decrease. We have shown that the relative humidity of the air can be increased by adding more water vapor to the air or by lowering the temperature of the air. And the relative humidity can be decreased by taking water vapor out of the air or by raising the temperature of the air. A practical application of the concepts of relative humidity in our daily lives is in how the body cools itself. Through the process of perspiration, the body secretes microscopic droplets of water onto the surface of the skin of the body. As these tiny droplets of water evaporate into the air, they cool the body. As long as the relative humidity of the air is low, evaporation occurs readily, and the body cools itself. However whenever the relative humidity becomes high, it is more difficult for the microscopic droplets of water to evaporate into the air. The body cannot cool itself, and the person will feel very uncomfortable. We are all aware of the discomfort caused by the hot and humid days of August. The high relative humidity prevents the normal evaporation and cooling of the body. As some evaporation occurs from the body, the air next to the skin will become saturated, and no further cooling can occur. If a fan is used, you will feel more comfortable because the fan will blow the saturated air next to your skin away and replace it with air that is slightly less saturated. Hence, the evaporation process can continue while the fan is in operation and the body cools itself. Another way to cool the human body in the summer is to use an air conditioner. The air conditioner not only cools the air to a lower temperature, but it also removes a great deal of water vapor from the air, thereby decreasing the relative humidity of the air and permitting the normal evaporation of moisture from the skin. (Note that if the air conditioner did not remove water vapor from the air, cooling the air would increase the relative humidity making you even more uncomfortable.) In the hot summertime, people enjoy swimming as a cooling experience. Not only the immersion of the body in the cool water is so satisfying, but when the person comes out of the water, evaporation of the sea or pool water from the person adds to the cooling of the person. It is also customary to wear loose clothing in the summertime. The reason for this is to facilitate the flow of air over the body and 4-13

14 hence assist in the evaporation process. Tight fitting clothing will prevent this evaporation process and the person will feel hotter. If you happen to live in a dry climate (low relative humidity), then you can feel quite comfortable at 85 0 F, while a person living in a moist climate (high relative humidity) will be very uncomfortable at the same 85 0 F. What many people do not realize, is that you can also feel quite uncomfortable even in the wintertime, because of the humidity of the air. If the relative humidity is very low in your home then evaporation will occur very rapidly, cooling the body perhaps more than is desirable. As an example, the air temperature might be 70 0 F but if the relative humidity is low, say 30%, then evaporation will readily occur from the skin of the body, and the person will feel cold even though the air temperature is 70 0 F. In this case the person can feel more comfortable if he or she uses a humidifier. A humidifier is a device that adds water vapor to the air. By increasing the water vapor in the air, and hence increasing the relative humidity, the rate of evaporation from the body will decrease. The person will no longer feel cold at 70 0 F, but will feel quite comfortable. If too much water vapor is added to the air, increasing the relative humidity to near a 100%, then evaporation from the body will be hampered, the body will not be able to cool itself, and the person will feel too hot even though the temperature is only 70 0 F. Thus too high or two low a relative humidity will make the human body uncomfortable. 4.4 Dew We have seen that condensation is the change of state from water vapor to liquid water. When moist air comes in contact with cool surfaces such as the ground or the leaves of grass, it may be cooled to the point where its relative humidity is 100%. The air thus becomes saturated. As further cooling continues some of the water vapor condenses out of the air onto the colder surfaces producing dew. Heat of condensation is given off to the air as the water vapor condenses, thereby warming the air and hence slowing down the cooling process. The temperature of the air at which the air becomes saturated and condensation begins is called the dew point temperature. Just as water condenses on the ground, it can also condense in the free air if it has something to condense on. What it has to condense on are particles of smoke, salt, and dust in the air. These particles are called condensation nuclei because the water vapor will condense on them. These condensation nuclei are also called hygroscopic particles. Condensation of water vapor onto hygroscopic particles in the free air occurs in the formation of fog and clouds and we will discuss this further in the next chapter. 4.5 Humidity Measurements Although we define the relative humidity of the air as the ratio of the actual vapor pressure in the air to the saturation vapor pressure, it is not very convenient 4-14

15 to measure these vapor pressures. Therefore other approaches are used to measure the humidity in the air. Of the many ways to measure humidity probably the one most used utilizes the device called the sling psychrometer. The sling psychrometer consists of two liquid in a glass thermometers mounted on a narrow board that is free to rotate as shown in figure One of the thermometers has a wick that covers the mercury bulb, and water is placed over the wick. This thermometer is called the wet bulb thermometer. The other thermometer is not covered with a wick and is called the dry bulb thermometer. There is a handle on the psychrometer and the psychrometer is swung freely in the air by this handle for a couple of minutes. As the thermometers are rotated the water on the wick of the wet bulb evaporates, thereby cooling the wet bulb thermometer and thus lowering its temperature. The temperature of the wet bulb thermometer is observed and recorded as the wet bulb temperature. The temperature of the dry bulb Figure 4.10 Sling psychrometer thermometer is recorded as the dry bulb temperature. If the air is very dry (low relative humidity) a great deal of evaporation will occur from the wet bulb and the wet bulb temperature will be low. If, on the other hand, the air is very humid (high relative humidity), there is already a great deal of water vapor in the air and there is not much room for too much more. Hence very little evaporation of water from the wet bulb can take place and the wet bulb temperature does not decrease very much. In either case the temperature of the dry bulb does not change because no evaporation occurs from the dry bulb. The dry bulb temperature is essentially the same as the air temperature. The difference between the wet bulb temperature and the dry bulb temperature is called the wet bulb depression and is given by Wet Bulb Depression = Tdry bulb Twet bulb (4.4) The wet bulb depression is a measure of how saturated the air is. If the depression is equal to zero, then Tdry bulb = Twet bulb, the air is saturated and the relative humidity is 100%. (When Tdry bulb = Twet bulb no water can evaporate from the wick of the wet bulb because the air is already saturated and there is no room for more water vapor molecules.) If the wet bulb depression is very large, this means that the air is very dry (low relative humidity) and a great deal of water was evaporated from the wick of the wet bulb thereby lowering the temperature of the wet bulb considerably. 4-15

16 To get more precise information on the relative humidity in the air a psychrometric table is used, see table 4.1 below. Notice that across the top of the table are the values of the wet bulb depression (in 0 C) and along the left-hand side of the table are the values of the dry bulb temperature (in 0 C). An example of the use of the psychrometric table is given in example 4.4. Thus by using the sling psychrometer and the psychrometric table, table 4.1, the relative humidity can be easily determined. The sling psychrometer is also used to determine the dew point temperature but now table 4.2 is used. An example is shown in example 4.5. Example 4.4 Relative Humidity. After using the sling psychrometer, the dry bulb temperature was found to be 21 0 C and the wet bulb temperature was 16 0 C. Using the above values and the psychrometric table determine the relative humidity of the air. Solution We determine the relative humidity with the psychrometric table. We first determine the wet bulb depression, equation 4.4, as Wet Bulb Depression = Tdry bulb - Twet bulb (4.4) = 21 0 C 16 0 C = 5 0 C Let us now move across the top line that shows the wet bulb depressions to the number 5 0 C that we have just determined. Now move down the left-hand side of dry bulb temperatures to the value of 21 0 C. At this 21 0 C value, move across the line until it intersects the line that comes down from the 5 0 C wet bulb depression value and observe that these two lines intersect at the value 60. This value, 60 is the relative humidity of the air. That is, the relative humidity of the air is 60%. To go to this Interactive Example click on this sentence. Example 4.5 The Dew Point Temperature. The dry bulb temperature was found to be 21 0 C and the wet bulb temperature was 16 0 C. Using the above values and the psychrometric table, table 4.2, determine the dew point temperature of the air. Solution We can also determine the dew point temperature with the psychrometric table. We first determine the wet bulb depression, equation 4.4, as 4-16

17 Table 4.1 Psychrometric Table for Relative Humidity Dry Bulb Wet Bulb Depression Temp C

18 Table 4.2 Psychrometric Table for Dew Point Dry Bulb Temp. Wet Bulb Depression 0 C

19 Wet Bulb Depression = Tdry bulb Twet bulb (4.4) = 21 0 C 16 0 C = 5 0 C Let us now move across the top line that shows the wet bulb depressions to the number 5 0 C that we have just determined. Now move down the left-hand side of dry bulb temperatures to the value of 21 0 C. At this 21 0 C value, move across the line until it intersects the line that comes down from the 5 0 C wet bulb depression value and observe that these two lines intersect at the value 13. This value, 13 is the dew point temperature of the air. That is, the dew point temperature of the air is 13 0 C. To go to this Interactive Example click on this sentence. Another standard device that is used to measure humidity is the hair hygrometer. A characteristic effect of human hair is that human hair lengthens as the relative humidity increases and shortens as the relative humidity decreases. Several strands of hair are placed together forming a cord of hair. The hair is placed under tension through a series of linkages to an indicator that reads the relative humidity directly between 0 and 100%. This is the mechanism inside the circular hygrometer that is usually found in homes. The hygrometer is a convenient device to measure relative humidity but it is not as accurate as the sling psychrometer and must be recalibrated often. A hygrograph is a recording hygrometer that measures the relative humidity by a hair hygrometer but then records this information in the same form as the thermograph. Thus a graph of the relative humidity is obtained with the hygrograph. Since the measuring device is the hair hygrometer it is not as accurate as desired. Another device to measure moisture in the air is the Dew Point Hygrometer. The dew point hygrometer consists of a highly polished, hollow, metallic container that contains a highly volatile liquid such as ether. A thermometer is placed in the liquid to measure the temperature of the liquid. On the top of the hygrometer is a device, similar to the soft bulb syringe on top of a vaporizer that upon squeezing causes ether to be evaporated. As the ether is allowed to evaporate, the liquid and the metal container are cooled. More and more ether is allowed to evaporate until water condenses on the metallic surface of the hygrometer. At this point the temperature is recorded. At this point the metallic surface is cooled to the point where the air in contact with the metal surface is cooled to saturation. The water vapor in the air then condenses on the metal surface. This condensing water on the metal surface is the same as dew and the temperature recorded on the thermometer is thus called the dew point temperature. In this way the dew point temperature of the air can be determined. 4-19

20 Most people have observed this effect on a hot moist day in the summertime. As an example, suppose you were having a cool drink that is being cooled by the ice placed in the drink. If it is a very humid day, condensation will occur on the outside of the glass because the cold glass surface has cooled the water vapor in the air, which is in contact with the glass, down to the condensation point. If you were to place a thermometer into the drink when this condensation begins, you would record the dew point temperature. The Language of Meteorology Phases of matter - Matter exists in three phases, the solid phase, the liquid phase, and the gaseous phase. Change of phase - The change in a body from one phase of matter to another. As an example, melting is a change from the solid state of a body to the liquid state. Boiling is a change in state from the liquid state to the gaseous state. Sublimation is the change in state from a gas directly to a solid without ever going through the liquid state. Latent heat of fusion - The amount of heat necessary to convert one kilogram of the solid to one kilogram of the liquid. Latent heat of vaporization - The amount of heat necessary to convert one kilogram of the liquid to one kilogram of the gas. Humidity - the amount of water vapor in the air. Absolute Humidity - is the ratio of the mass of water vapor to a unit volume of air, and is measured in g/m 3 the same units as density. Specific Humidity (m) is the ratio of the mass of water vapor in the air to a unit mass of air including the water vapor. Mixing Ratio (q) - is the ratio of the mass of the water vapor in the air to a unit mass of dry air. Relative Humidity - is the ratio of the amount of water vapor actually present in the air to the maximum amount of water vapor that the air can hold at a given temperature and pressure, times 100%. Dew - When moist air comes in contact with cool surfaces such as the ground or the leaves of grass, it may be cooled to the point where its relative humidity is 100%. The air thus becomes saturated. As further cooling continues some of the water vapor condenses out of the air onto the colder surfaces producing dew. 4-20

21 Dew point temperature - The temperature of the air at which the air becomes saturated and condensation begins. Sling psychrometer - a device used to measure humidity. Psychrometric Table - A table used with the Sling thermometer to measure Relative Humidity and the Dew Point temperature. Hair hygrometer. Since human hair lengthens as the relative humidity increases and shortens as the relative humidity decreases, it is used as a means to measure humidity. A hygrograph is a recording hygrometer that measures the relative humidity by a hair hygrometer but then records this information in the same form as the thermograph. Questions for Chapter 4 1. Discuss how the human body uses the latent heat of vaporization to cool the body through the process of evaporation. 2. Discuss how the relative humidity affects the process of evaporation in general and how it affects the human body in particular. 3. It is possible for a gas to go directly to the solid state without going through the liquid state, and vice versa. The process is called sublimation. An example of such a process is the formation of frost. Discuss the entire process of sublimation, the latent heat involved, and give some more examples of the process. 4. Why does ice melt when an object is placed upon it? Describe the process of ice-skating from the pressure of the skate on the ice. Problems for Chapter 4 1. How many joules are needed to change 50.0 g of ice at C to water at C? 2. If 50.0 g of ice at C are mixed with 50.0 g of water at C what is the final temperature of the mixture? 3. How much ice at 0 0 C must be mixed with 50.0 g of water at C to give a final water temperature of 20 0 C.? 4. If 50.0 g of ice at C are mixed with 50.0 g of water at C, what is the final temperature of the mixture? How much ice is left in the mixture? 5. How much heat is required to convert 10.0 g of ice at C to steam at C? 6. A 100 g iron ball is heated to C and then placed in a hole in a cake of ice at C. How much ice will melt? 4-21

22 7. How much steam at C must be mixed with 300 g of water at C to obtain a final water temperature of C? 8. The solar constant is the amount of energy from the sun falling on the earth per second, per unit area and is given as S.C. = 1350 J/(s m 2 ). If an average roof of a house is 60.0 m 2, how much energy impinges on the house in an 8-hour period? Express the answer in Joules, kwhr, Btu and kcal. Assuming you could convert all of this heat at 100% efficiency, how much fuel could you save if # 2 fuel oil supplies 140,000 Btu/gal Natural gas supplies 1,000 Btu/ft 3 Electricity supplies 3,415 Btu/kWhr? 9. How much thermal energy can you store in a 2000 gal tank of water if the water has been subjected to a temperature change of 70.0 F 0 in a solar collector? 10. The energy that fuels thunderstorms and hurricanes comes from the heat of condensation released when saturated water vapor condenses to form the droplets of water which become the clouds that we see in the sky. Consider the amount of air contained in an imaginary box 5.00 km long, 10.0 km wide and 30.0 m high that covers the ground at the surface of the earth at a particular time. The air temperature is 20 0 C and is saturated with all the water vapor it can contain at that temperature, which is 17.3 x 10 3 kg of water vapor per m 3. The air in this imaginary box is now lifted into the atmosphere where it is cooled to 0 0 C. Since the air is saturated, condensation occurs throughout the cooling process. The maximum water vapor the air can contain at 0 0 C is x 10 3 kg of water vapor per m 3 (The heat of vaporization of water varies with temperature from 600 kcal/kg at 0 0 C to 540 kcal/kg at C. We will assume an average temperature of C for the cooling process.) Find: (a) the volume of saturated air in the imaginary box, (b) the mass of water vapor in this volume at C, (c) the mass of water vapor in this volume at 0 0 C, (d) the heat of vaporization of water at C, and (e) the thermal energy given off in the condensation process. (f) Discuss this quantity of energy in terms of the energy that powers thunderstorms and hurricanes. Diagram for problem 10. To go to another chapter, return to the table of contents by clicking on this sentence. 4-22