Introduction to Weather: Moisture in the Air Vapor Pressure and Dew Point

Transcription

1 IDS 102 Winter 2008 Introduction to Weather: Moisture in the Air Vapor Pressure and Dew Point During fall quarter we covered the topic of pressure and it has been a while since the, so let s review a couple of concepts before applying this concept to moisture in the air. Describe what pressure is and how pressure differs from force: When we discussed the pressure due to the atmosphere, we used the units of pounds per square inch. Explain how this is a unit of pressure in the atmosphere. Why is it that we feel pressure on our ears if we stand on the bottom of a swimming pool? (Why does it feel like the pressure is pushing horizontally on our ears?) The person to the right is blowing up a balloon. When we stop blowing on the balloon, the air rushes back out, so this means that the air pressure must have been (greater or lesser) inside the balloon. In the space below, imagine that the line is a side view of a very small part of the balloon. Page 1 of 12

2 Draw the number of molecules of gas inside the balloon vs. outside the balloon. Use small circles to represent the molecules. (Note: Molecules actually have odd shapes because nitrogen, for example, almost always runs around was a molecule of two nitrogen atoms. However, our model will represent molecules as circular because that s much easier to draw). Outside the balloon Inside the balloon The air around you is a mixture of nitrogen, oxygen, carbon dioxide, water vapor, and other gases. This means that if there were 100 molecules of gas outside the balloon, about 78 would be nitrogen, 20 would be oxygen, and the other two might be any number of different gases including water and carbon dioxide. Inside the balloon, there must have been (more/ less) gas molecules than outside the balloon for a given volume of space. What would happen to the number of gas molecules inside the balloon and overall the volume of the balloon if we increased the temperature of gases inside the balloon? Explain your answer. What would happen to the temperature of the gas inside the balloon if we made the balloon s volume larger? (Like putting the same amount of gas in a larger space?) Page 2 of 12

3 The amount of any one of the gases (nitrogen, oxygen, water, etc.) that is in the air is often measured in terms of partial pressure. Partial pressure = the specific contribution of one gas to the overall pressure of all gasses combined. Vapor pressure is directly related to the abundance of a specific gas (water vapor) in the atmosphere. In other words, vapor pressure = the partial pressure of water vapor. The vapor pressure of water is measured using called either bars, millibars (which is abbreviated as mbar ), or units called pascals (which is abbreviated as Pa ). These are units of pressure, which is force per unit area. Pressure may seem like a strange concept to use to measure the amount of a certain kind of gas around you, but the following exercise is to help you understand why and how that is done. First, the numbers How big is a pascal? A millibar? A bar? A pascal (1 Pa) is a small unit of pressure. Set a smooth sheet of notebook paper on a smooth tabletop and a pascal turns out to be about the same as the pressure that the paper exerts on the surface of the table underneath it (not much). A millibar (1 mbar) is another unit of pressure. If you set a penny on the table, the average pressure that the penny exerts on the table underneath it is about one millibar (it is almost exactly one millibar if the penny was minted before 1982). One bar equals one thousand millibars (mbar), and it is very close to the pressure of the atmosphere pressing in around us. 1 bar = 1,000 millibars (mbar) = 100,000 pascals (Pa) How many millibars (mbars) are there in 100 bars? How many pascals (Pa) are there in 100 bars? How many pascals (pa) are there in one millibars (mbar)? The Latin prefix for 100 is hecto, so one hectopascal (hpa) is one hundred pascals. How many hpa are there in one mbar? How many hpa are there in one Bar? Page 3 of 12

4 Atmospheric pressure varies due to the weather, but it is typically within a few percent of one bar. If the atmospheric pressure is bar (this is a low pressure ), what is the atmospheric pressure in hpa? Air pressure is caused by molecules bouncing around and bouncing off of things. The more often they bounce, and the harder they bounce, the more pressure there will be. We can make the molecules in a sealed container bounce more often by adding more molecules. We could make them bounce more often and harder by increasing the temperature (which makes them move around faster). Imagine that the air pressure in the room where you are sitting is caused by 500 balls bouncing off of the sides of the room. In reality the air pressure is caused by an uncountable huge number 1 of molecules, some shaped like balls and some not. The pressure gauge on the wall says that the pressure created by all of these balls is 1000 mbar. You quickly look around the room and notice that 270 of the balls are red, 155 of the balls are blue, 65 of the balls are green, and the rest are white. The red balls make up what fraction of the total? The partial pressure is the amount of pressure due to one kind of ball. What is the partial pressure of the red balls in the room? What is the partial pressure of the green balls? What is the partial pressure of the white balls? 1 At ordinary temperatures and pressures, in a room that is 5 meters long by 3 meters wide by 2.5 meters high (about 16 feet by 10 feet by 8 feet), the number of molecules in the room would be about 10 27, which is a one followed by 27 zeroes. If you had one billion warehouses, and each warehouse contained one billion boxes, and each box contained one billion grains of sand, you would have grains of sand. You would also have more sand than there is on this planet. Page 4 of 12

5 Your friend calls on the cell phone (which you aren t supposed to have on during class) and tells you that she is bringing some more white balls into the room. She promises she will take out an equal number of colored balls so that the total pressure won t increase. Checking the thermometer you see that the temperature is 22 C, and your handy dandy white ball pressure chart says the maximum partial pressure for white balls (saturation point for white balls) at 22 C is a partial pressure of 25 mbar. What would happen if your friend removed two red balls and added two white balls? Then what would happen if your friend removed two more red balls and added two more white balls? In actual dry air (this either means that there is no water or that we are ignoring the water for the time being), 79% of the molecules are nitrogen (N 2 ), a fifth of the molecules are oxygen (O 2 ), one molecule out of 107 is argon (Ar), and one molecule out of 3000 is carbon dioxide (CO 2 ). Calculate the following in a room that where the atmosphere has the composition listed above and a total pressure is 1000 mbar What is the partial pressure of oxygen? What is the partial pressure of CO 2? Page 5 of 12

6 For a sample of real air (perhaps in another room), one molecule out of 100 is water vapor. The pressure is still 1000 mbar, so the number of molecules in a given amount of volume is the same. This means there must be fewer of the other kinds of molecules (such as only 78.2% nitrogen and 19.8% oxygen). What is the partial pressure of water in this sample? Suddenly the temperature in the room drops to 5 C. The vapor pressure of water at 5 C is 8.7 mbar. This is the maximum possible partial pressure of water vapor in the air. What would happen as the temperature dropped to 5 C? When we talk about moisture in the atmosphere we are talking about the presence of water molecules. The water may be present as a solid (snow or ice) as a liquid (rain) or as a gas (water vapor). When water is in its gaseous state, we can t detect its presence with our senses. The properties that we associate with water (ex. wetness) are only noticeable when water is a liquid. So how can we be sure that there is actually water present in the atmosphere? Think of all the evidence you have for the fact that there is water vapor in the air. You should be thinking of physical evidence or observations not something like because I read it in the paper. List as many as you can in the space below. Page 6 of 12

7 This is a photo of Castle Geyser in Yellowstone National Park. Is the column of steam above the geyser water vapor? Well, yes and no. There is probably some water vapor there, but we cannot see water vapor in the air. We can only see it when it is in a liquid or solid state! So, what are we seeing? The vapor in the air above the geyser is turning into droplets of liquid water and that why we see the column of water vapor. Here are a few important ideas about water vapor in the atmosphere There is water present in the atmosphere, even though we can t see it or feel it. We only notice water when it is in the liquid or solid state. What determines the amount of water vapor in the air? You've probably observed that some days feel wetter than others. As you ll see later, this perception actually has more to do with the relative humidity than with the total amount of water in the air, but the two are related. The amount of water in the air varies from day to day and is affected primarily by the temperature. When it gets hotter, there is more water vapor in the air. Why is that? We will talk about this idea as a whole class. A good way to see the relationship between vapor pressure and temperature is to look at the relationship graphically. The table to the right shows the vapor pressure of water at a series of temperatures. These vapor pressures represent the maximum amount of water vapor that can be present in the air at a given temperature. Use a sheet of graph paper to prepare a graph of vapor pressure as a function of temperature. Label the region on the graph where water as a liquid would be found and where on the graph water as a vapor would be found. Use your graph to answer the questions which follow. Temperature (ºC) Maximum possible mbars of water vapor Page 7 of 12

8 Imagine a sample of air at 40 o C in which the vapor pressure of water is 40 mbar. Mark this point on the graph with the letter A. Is the water in the air at this temperature most likely to be a vapor or a liquid? Now imagine that the same sample of air cools to 20 o C. Draw a line on your graph to represent this cooling, marking the final point with the letter B. Is the air above or below its capacity for water vapor at this point? What, if anything, will happen to the sample of air as it cools? Vapor Pressure and Relative Humidity An important concept from the above discussion is that warmer air contains more moisture than colder air. Does this mean that warm air is always more humid than cold air? What exactly is meant by the term humidity? When we hear the term humidity in a weather forecast, it is the relative humidity (abbreviated r.h. ). Relative humidity (r.h.) = the actual amount of water present in the air compared to the maximum amount that could be present at that temperature. We use the following formula to calculate the relative humidity. Relative Humidity = measured vapor pressure maximum possibile vapor pressure x100 For example: imagine a sample of air at 40 o C. If you refer to your graph or data table, you will see that the maximum vapor pressure at this temperature is about 74 mbar. Suppose, however, that the measured vapor pressure was only 30 mbar. Even though the air can contain up to 74 mbar of water vapor, only 30 mbar is actually present. In the example above, the relative humidity is: 30 r. h. = x100 = 40.5% 74 Page 8 of 12

9 Now consider another sample of air. This sample of air has a measured vapor pressure of 25 mbar and is at 25 o C. This second sample of air contains less total moisture than the first sample (25 mbar compared to 30 mbar). Does that mean that it is less humid? Explain your thinking. Calculate the relative humidity for this second sample of air. Show your work below. You will need to use the data table or graph. In the second case, the relative humidity is higher, even though the amount of moisture in the air is actually less. That's because in the second case, the air was closer to its maximum "capacity". Our perception of dampness is related more to the relative humidity than to the actual amount of water vapor in the air. Thus, even though warm air might contain more water vapor than cold air, cool days can often be more humid than warm days. Here are a few more problems for practice. If the measured vapor pressure in Auburn is 15 mbar and it is 20 C, what is the maximum possible vapor pressure at 20 C, and what is the relative humidity? If you have a forced air furnace in your dwelling, the furnace probably pulls cold air in from outside. Imagine that your furnace pulls air that is 60% in humidity at 5 C and heats that same air to 25 C. What is the relative humidity of the air in your house? (Assume that the amount of water vapor (grams of water vapor per cubic meter of air) in the air stays the same through the heating process). Page 9 of 12

10 Dew Point The dew point is another measure of the humidity of the air. The dew point is the temperature at which moisture will begin to condense from the atmosphere. You may notice that during late summer and early fall, there is dew on the ground when you wake up in the morning. This happens because cool air has a lower capacity for moisture than warm air. As the air cools down overnight, some of the moisture in the air condenses. Imagine a sample of air at 30 o C and 57% relative humidity. Find this point on your graph and mark it with an X. Imagine that the sample of air cools. At what temperature will the moisture in the air begin to condense? Use your graph to find the answer. Explain your thinking. We can do a quick experiment to measure the dew point of the air in the room today. Gather the following equipment before beginning. Equipment: A can 1/2 to 2/3 full with room temperature water A thermometer A cup full of ice Procedure Make sure that the outside of the can is dry before beginning. Put the thermometer in the can and note the temperature. Begin adding ice to the can a few cubes at a time. Use the thermometer to stir, and monitor the temperature of the water. Watch the outside of the can carefully. The air immediately surrounding the can will cool down as the can cools down. At some point, the air will cool to its dew point, and drops of water will begin to form on the can. Record this temperature. Summarize your results in the space below. From the results of your experiment, you should be able to make a rough estimate of the relative humidity in the room today. Ask an instructor if you need help with this part. Page 10 of 12

11 Let s use another example to test our understanding of the dew point concept. Where is there more moisture in the air? a) at Snoqualmie Pass in the winter (temperature 1 C ; dew point 2 C ) or b) at Hanford in the summer (eastern Washington) (temperature 35 C, dew point 8 C ). Explain your logic. When you reach this point, find a computer and go to the following web site: This simulation will help you understand why the western slopes of the Cascade Mountains are wetter than the eastern slopes. Do as many of the questions on the page as possible given the time we have. Answer those questions on your paper. Let us know when you have questions. End of Module Questions: 1. The atmospheric pressure on your body right now is about 14.7 pounds per square inch. The atmosphere around you is about 79% nitrogen, 20% oxygen, and 1% water vapor (this last number is a guess the other two don t change much). a) How much of the pressure that is exerted on your body right now is due to nitrogen? b) How much of the pressure that is exerted on your body right now is due to oxygen? c) How much of the pressure that is exerted on your body right now is due to water vapor? 2. On a July day in Seattle, the temperature is 32 o C and the relative humidity is 40 %. The forecast calls for the nighttime temperature to drop to 14 o C. Will dew form overnight? Show your work/explain your reasoning. 3. During the winter months, houses that are heated by drawing in and heating outside air often ends up feeling especially dry. What is it about both (a) the weather conditions outside and (b) the heating of the air that causes these dry conditions indoors? Explain clearly. Page 11 of 12

12 4. In a simple experiment, a can full of room temperature water (21 o C) is cooled by adding ice to the water. When the water temperature reaches 6 o C, condensation is observed on the outside of the can. (a) Based on the results of this experiment, what is the dew point? Explain. (b) Based on the results of this experiment, what is the relative humidity of the air around the can? Explain/show work. (c) Why is it necessary that this experiment be carried out in a metal can? Explain 5. The weather forecast for Acapulco Mexico on February 15, 2001 called for a daytime high of 33 o C (92 o F) and a relative humidity of 47%. What is the dew point? 6. On a summer day in Florida, the temperature is 35 o C (95 o F) and the relative humidity is 100 %. What is the vapor pressure of water in the air that day? Explain. Page 12 of 12