chapter 4 atmospheric moisture - farmingdale state · pdf file · 2017-12-14chapter...

Chapter 4 Atmospheric Moisture

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 -20.00C

and heat it to a temperature of 1200C. 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 00C 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 1000C, 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


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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 1000C 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 00C. 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 00C, 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


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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 00C 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 1000C, 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 1000C 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 00C 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


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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

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.

(a) Bowl 1 (b) Bowl 2


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 100 0C. 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 0C 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 0C, 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 0C, 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, po + pawv. Subtracting po from po + pawv, gives the actual water

vapor pressure, pawv. As time goes on, the water vapor pressure increases as more


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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/m3 the same units as density. As

an example

Example 4.1

If 25.0 g of water vapor are added to 2000 m3 of air, what is the absolute

humidity of the air.

The absolute humidity of the air is found by its definition as

Absolute Humidity = 25 g of water vapor = 1.25 10-2 g/m3

2000 m3 of air

Thermometerpressure gauge

water

dry air

T = 20 oC

(a)

T = 20 oC

(b)

(d)

oT = 25 CT = 20 oC

(c)

Solution


4-7

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?

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


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 1.000 kg. Find the mixing ratio.

The mixings ratio of the air is found by its definition as

Solution

Solution

http://www.farmingdale.edu/faculty/peter-nolan/pdf/meteorology/PhysAtmEx4.01.xls



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Mixing Ratio = q = 12 g of water vapor = 12.0 g/kg

1.000 kg of dry air


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 0C 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 0C, 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 (0C) g/kg

-40

-30

-20

-10

0

5

10

15

20

25

30

35

40

0.1

0.3

0.75

2

3.5

5

7

10

14

20

26.5

35

47

4. 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



4-9

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 0C, 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.


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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 0C, 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 0C 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


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RH = 4.00 g (100%)

14.0 g

RH = 28.6%

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


maximum water vapor

RH = 14.00 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.

water

1 kg air

T = 20 oC

(a)

4 g water vapor

water

1 kg air

T = 20 oC

(b)

7 g water vapor

water

1 kg air

T = 20 oC

(c)

14 g water vapor


4-12

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

Figure 4.9 Changing the relative humidity of the air by changing the temperature

of the air.

temperature of 20 0C, 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


maximum water vapor

RH = 10.0 g (100%)

14.0 g

RH = 71.4%

The air in the container is now cooled to 15 0C, figure 4.9b. From Table 4.1 we see

that the air can only hold 10.0 g of water vapor at 15 0C, therefore the relative

humidity now becomes


maximum water vapor

RH = 10.0 g (100%)

10.0 g

RH = 100%

Hence by cooling the air from 20 0C to 15 0C has caused the relative humidity to

increase from 71.4% to 100 % and the air has become saturated. If the air is further

water

1 kg air

T = 20 oC

(a)

10 g water vapor

water

1 kg air

T = 15 oC

(b)

10 g water vapor

water

1 kg air

T = 10 oC

(c)

7 g water vapor


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cooled to 10 0C, 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


maximum water vapor

RH = 7.00 g (100%)

7.00 g

RH = 100%

Thus when the air was cooled from 20.0 0C to 15.0 0C 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

10.0 0C, 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


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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 0F, while a

person living in a moist climate (high relative humidity) will be very uncomfortable

at the same 85 0F.

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 0F 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 0F. 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 0F, 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 0F. 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


4-15

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 4.10. 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.


4-16

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 0C) and along the left-hand side

of the table are the values of the dry bulb temperature (in 0C). 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 0C and the wet bulb temperature was 16 0C. Using the above

values and the psychrometric table determine the relative humidity of the air.

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 0C 16 0C = 5 0C

Let us now move across the top line that shows the wet bulb depressions to the

number 5 0C that we have just determined. Now move down the left-hand side of

dry bulb temperatures to the value of 21 0C. At this 21 0C value, move across the

line until it intersects the line that comes down from the 5 0C 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%.


Example 4.5

The Dew Point Temperature. The dry bulb temperature was found to be 21 0C and

the wet bulb temperature was 16 0C. Using the above values and the psychrometric

table, table 4.2, determine the dew point temperature of the air.

We can also determine the dew point temperature with the psychrometric table. We

first determine the wet bulb depression, equation 4.4, as

Solution

Solution



4-17

Table 4.1

Psychrometric Table for Relative Humidity Dry Bulb Wet Bulb Depression

Temp. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0C

-10 67 35

-9 69 39 9

-8 71 43 15

-7 73 46 20

-6 74 49 25

-5 76 52 29 11

-4 77 55 33 12

-3 78 57 37 17

-2 79 60 40 22

-1 81 62 43 26 8

0 81 64 46 29 13

1 83 66 49 33 17

2 84 68 52 37 22 7

3 84 70 55 40 26 12

4 85 71 57 43 29 16

5 86 72 58 45 33 20 7

6 86 73 60 48 35 24 11

7 87 74 62 50 38 26 15

8 87 75 63 51 40 29 19 8

9 88 76 64 53 42 32 22 12

10 88 77 66 55 44 34 24 15 6

11 89 78 67 56 46 36 27 18 9

12 89 78 68 58 48 39 29 21 12

13 89 79 69 59 50 41 32 23 15 7

14 90 79 70 60 51 42 34 26 18 10

15 90 80 71 61 53 44 36 27 20 13 6

16 90 81 71 63 54 46 38 30 23 15 8

17 90 81 72 64 55 47 40 32 25 18 11

18 91 82 73 65 57 49 41 34 27 20 14 7

19 91 82 74 65 58 50 43 36 29 22 16 10

20 91 83 74 66 59 51 44 37 31 24 18 12 6

21 91 83 75 67 60 53 46 39 32 26 20 14 9

22 92 83 76 68 61 54 47 40 34 28 22 17 11 6

23 92 84 76 69 62 55 48 42 36 30 24 19 13 8

24 92 84 77 69 62 56 49 43 37 31 26 20 15 10 5

25 92 84 77 70 63 57 50 44 39 33 28 22 17 12 8

26 92 85 78 71 64 58 51 46 40 34 29 24 19 14 10 5

27 92 85 78 71 65 58 52 47 41 36 31 26 21 15 12 7

28 93 85 78 72 65 59 53 48 42 37 32 27 22 18 13 9 5

29 93 86 79 72 66 60 54 49 43 38 33 28 24 19 15 11 7

30 93 86 79 73 67 61 55 50 44 39 35 30 25 21 17 13 9 5

32 93 86 79 74 68 62 57 51 46 41 37 32 28 24 20 16 12 9 5

34 93 87 81 75 69 63 58 53 48 43 39 35 30 26 23 19 15 12 8 5

37 94 87 82 76 70 65 60 55 51 46 42 38 34 30 26 23 19 16 13 10 5

40 94 88 82 77 72 67 62 57 53 48 44 40 36 33 29 26 23 20 1 6 14 10 5


4-18

Table 4.2

Psychrometric Table for Dew Point Dry Bulb Temp. Wet Bulb Depression 0C 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 -10 -14 -22

- 9 -13 -20

- 8 -12 -18 -29

- 7 -11 -16 -25

- 6 -10 -14 -22

- 5 - 9 -13 -20

- 4 - 7 -11 -17 -29

- 3 - 6 -10 -15 -25

- 2 - 5 - 8 -13 -20

-1 - 4 - 7 -11 -17

0 - 3 - 6 - 9 -15 -24

1 - 2 - 5 - 8 -13 -20

2 - 1 - 3 - 6 -11 -17

3 0 - 2 - 5 - 9 -14

4 1 - 1 - 4 - 7 -11 -19

5 3 0 - 3 - 5 - 9 -15

6 4 1 - 1 - 4 - 7 -13 -21

7 5 2 0 - 3 - 6 -11 -18

8 6 3 1 - 2 - 5 - 9 -14

9 7 4 3 0 - 3 - 7 -11

10 8 6 4 1 - 2 - 5 - 9 -14 -28

11 9 7 5 2 0 - 4 - 7 -11 -22

12 10 8 6 4 1 - 2 - 5 - 9 -16

13 11 9 7 5 2 0 - 4 - 7 -13

14 12 11 9 6 4 1 - 2 - 5 -10 -17

15 13 12 10 7 5 2 0 - 3 - 8 -13

16 14 13 11 9 7 4 1 - 1 - 6 -10 -17

17 15 14 12 10 8 5 2 0 - 4 - 7 -14

18 16 15 13 11 9 7 4 2 - 2 - 5 -10 -19

19 17 16 14 12 10 8 5 3 0 - 3 - 7 -15

20 19 17 15 14 12 10 7 4 2 - 2 - 5 -10 -19

21 20 18 16 15 13 11 8 6 3 0 - 3 - 7 -15

22 21 19 17 16 14 12 10 8 5 3 - 1 - 5 -10 -19

23 22 20 18 17 15 13 11 9 6 4 0 - 3 - 7 -15

24 23 21 20 18 16 14 12 10 8 6 2 - 1 - 5 -10 -18

25 24 22 21 19 17 15 13 11 9 7 5 1 - 2 - 7 -14

26 25 23 22 20 18 17 15 13 11 9 6 3 0 - 4 - 9 -18

27 26 24 23 21 19 18 16 14 13 10 7 5 2 - 2 - 6 -13

28 27 25 24 22 21 19 17 16 14 11 9 7 4 1 - 3 -9 -18

29 28 26 25 23 22 20 18 17 15 12 10 8 6 3 - 1 - 3 -13

30 29 27 26 24 23 21 19 18 16 14 12 10 8 5 1 - 2 - 8 -15

31 30 28 27 25 24 22 20 19 17 15 13 11 9 6 3 0 - 6 -11

32 31 29 28 27 25 24 22 21 19 17 15 13 11 8 5 2 - 2 - 7 -14

33 32 30 29 28 26 25 23 22 20 18 16 14 12 10 7 4 0 - 4 -10

34 33 31 30 29 27 26 24 23 21 20 18 16 14 12 9 6 3 1 - 5 -12 -29

35 34 32 31 30 28 27 25 24 22 21 19 17 15 13 11 8 5 2 - 3 - 8 -20

36 35 33 32 31 29 28 27 26 24 22 20 19 17 15 13 10 7 4 0 - 4 -10

37 36 34 33 32 30 29 28 26 25 23 21 20 18 16 14 11 9 6 3 - 3 - 7

38 37 35 34 33 32 30 29 28 26 25 23 21 19 17 15 13 11 8 5 - 1 - 3 - 9

39 38 36 35 34 33 31 30 29 27 26 24 22 20 18 16 14 12 10 6 2 0 - 3

40 39 37 36 35 34 32 31 30 28 27 25 24 22 20 18 16 14 12 8 -6 2 - 2


4-19

Wet Bulb Depression = Tdry bulb Twet bulb (4.4)

= 21 0C 16 0C = 5 0C

Let us now move across the top line that shows the wet bulb depressions to the

number 5 0C that we have just determined. Now move down the left-hand side of

dry bulb temperatures to the value of 21 0C. At this 21 0C value, move across the

line until it intersects the line that comes down from the 5 0C 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 0C.


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.



4-20

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/m3 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.


4-21

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 -10.00C to water at

20.00C?

2. If 50.0 g of ice at 0.00C are mixed with 50.0 g of water at 80.00C what is the

final temperature of the mixture?

3. How much ice at 00C must be mixed with 50.0 g of water at 75.00C to give a

final water temperature of 200C.?

4. If 50.0 g of ice at 0.00C are mixed with 50.0 g of water at 20.00C, 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 -15.00C to steam at

1050C?

6. A 100 g iron ball is heated to 1000C and then placed in a hole in a cake of

ice at 0.000C. How much ice will melt?


4-22

7. How much steam at 1000C must be mixed with 300 g of water at 20.00C to

obtain a final water temperature of 80.00C?

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 m2). If an average

roof of a house is 60.0 m2, 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/ft3

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 F0 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 200C and is saturated with all the water vapor it can contain at that

temperature, which is 17.3 x 103 kg of water vapor per m3. The air in this

imaginary box is now lifted into the atmosphere where it is cooled to 00C. Since the

air is saturated, condensation occurs throughout the cooling process. The maximum

water vapor the air can contain at 00C is 4.847 x 103 kg of water vapor per m3 (The

heat of vaporization of water varies with temperature from 600 kcal/kg at 00C to

540 kcal/kg at 1000C. We will assume an average temperature of 10.00C 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 20.00C, (c) the mass of water vapor in this

volume at 00C, (d) the heat of vaporization of water at 10.00C, 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.

http://www.farmingdale.edu/faculty/peter-nolan/pdf/TOCPhysAtm.pdf

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