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Cold Air is Dense

Introduction:

We wish to set up a learning situation in which students will discover, through the examination and manipulation of real data from a natural environment, that:

• air has mass and density, and
• cold air is denser than warm air.

These insights are absolutely fundamental to understanding virtually everything about weather and climate. Until a student has his or her mind firmly around these two concepts, he or she is not ready to understand how storms work, not ready to understand why the prevailing winds blow the way they do, not ready to understand why deserts occur where they do.

Although these two concepts are fundamental underpinnings of virtually every physical process in the atmosphere, they are not intuitively obvious--in fact, they are counter-intuitive. The student looks around at the air skeptically-- if there are so many molecules in that air, why can't we see them? If air has weight, why doesn't it register on a scale? On hot summer nights, the air feels oppressive, heavy--don't tell me that hot August air is low density "Air has mass", "air has density", and "cold air is dense" are the kinds of statements that students tend to memorize and parrot back, without actually altering their world-view, because these statements don't fit with their day-to-day experience of real-life air.

Because an understanding of the relationship between density and temperature of air is fundamental to so many natural processes, yet is counter-intuitive, it is a good investment of student and instructor time to construct this understanding upwards from a solid basis in the observation of real data.

Insights/Curriculum Highlights:

• Air is made of molecules, and therefore has mass.
• Barometric pressure is a measure of how much mass of air, i.e. how many air molecules, exist above the point of measurement, all the way up to the top of the atmosphere.
• Therefore, barometric pressure decreases with elevation.
• Any given volume of air has density. The density of air can vary from place to place and from time to time.
• The difference in barometric pressure between observation sites at different elevations is a measure of the density of air in a column of air between those two elevations.
• Cold air is denser than warm air.

Thinking Skills / Pedagogical Highlights:

• Making a connection between laboratory scale observations and atmosphere-scale data sets.
• Drawing on hands-on observations to explain an aspect of a natural system.
• Thinking about a phenomenon (density of air) that is invisible.
• Imagining boundaries or limits, and thinking about phenomena within those boundaries (a column of air, a parcel of air)
• Linking properties that are detectable to the human senses (e.g. air temperature) with molecular scale phenomena (molecules per volume of air).
• Linking properties that are measurable at the macroscopic scale (e.g. barometric pressure) to molecular scale phenomena (number of molecules).
• Building a chain of reasoning from cause to effect.
• Building a chain of reasoning from observation to interpretation.
• Using time series graphs; comparing how different parameters vary through time.
• Recognizing that a measurable property varies through time (barometric pressure rises and falls as weather systems pass) and also through space (barometric pressure decreases with increasing elevation).
• Recognizing covariance: two properties varying in the same direction under the influence of the same circumstances (barometric pressure at the Open Lowland site covaries with that at the Ridgetop site).
• Using a scatterplot; thinking about two or three data parameters simultaneously.

Procedure:

1. Introductory Hands-on Investigation: Make a Barometer

• Students create home made barometers and discuss how they work. Instructions for this activity are contained in many middle school science books. See, for example: R. L. Bonnet and G. D. Keen, Earth Science: 49 Science Fair Projects, TAB Books, 1990, pp. 127-131.

2. Video : Torricelli's discovery of air pressure

• Students view and discuss the section of the "Connections" video in which Torricelli's discovery of air pressure is illustrated. In this video, a mercury barometer is carried up a mountainside, and the mercury is seen to fall as the climber ascends. (Alternatively, students can read a description of the same discovery in the book Connections by James Burke, 1978, Little, Brown & Co, Boston, pp. 74-17.)
• The interpretation is that the weight of the mercury balances the weight of the overlying air. The weight of the overlying air decreases as the climber rises higher in the atmosphere; thus less weight of mercury is needed to balance the diminished weight of the overlying air.

3: Reproduce Torricelli's experiment in a tall building

• Using a handheld barometer, students will measure the barometric pressure at street level. Then, emulating the experimenter in the "Connections" video, they will climb the stairs or ascend the elevator of a tall building, measuring barometric pressure at each landing or at several stops along the way.
• They observe that the air pressure at the street level is higher than at rooftop level (figure 1). For a twelve story building the difference in air pressure is about 4 mb. The building needs to be at least 8 stories high to register an unambiguous barometric pressure difference.

4. Data-based investigation: barometric pressure from BRF

• Students examine barometric pressure data sets that were recorded at Open Lowland and Ridgetop sensor sites at Black Rock Forest. (figure 2). Display should be zoomed so that a month of two at a time is visible. Each pair of students can be responsible for several months of data. Data can be printed out and scotch taped together to form a long time series of a year or more duration. (If printouts from different students are combined, be sure that all students set the plot vertical scale the same.)

• Points to observe:
  • Over time, the barometric pressure at each site goes up and down, up and down. The periodicity is about a week, but the pattern is not very regular.
  • Barometric pressure at the Ridgetop site is always less than at the Open Lowland site.
  • Barometric pressure at Ridgetop and at Open Lowland covary: in other words, when one goes up, the other goes up; when one goes down, the other goes down.
  • The difference between the barometric pressure at Ridgetop and Open Lowland is larger than the difference between the high and low pressures at either Ridgetop or Open Lowland. In other words, the variability in space is greater than the variability in time in this data set.

• Points to figure out and/or discuss:
  • The up and down wiggles of each barometric pressure record reflect weather systems passing across the field area. (This could be the subject of a separate investigation, in which students discover the relationship between barometer trends and sunny or rainy weather.)
  • Barometric pressures at the two sites covary because they are subject to the same weather systems.
  • Which site do you think is at higher elevation? Think about the hands-on experiment with the hand-held barometer, and about the experimenter in the connections video. The Ridgetop Site must be at higher elevation than the Open Lowland Site because it always has a lower barometric pressure. Ridgetop has a lower barometric pressure than Open Lowland because fewer molecules of air lie between the Ridgetop site and the top of the atmosphere than lie between the Open Lowland site and the top of the atmosphere.
  • We normally think about barometric pressure variation in the context of changes through time ("the barometer is falling" or "the barometer is rising"), related to the passage of weather systems. Quantitatively, however, the spatial variation of barometric pressure with elevation is larger than the temporal variation at any given site.

• (Optional) Using your results from the hands-on investigation with the barometer and the tall building, plus your observations of barometric pressure at Black Rock Forest, estimate the difference in elevation between the Ridgetop Site and the Open Lowland Site.

5. Data-based investigation: qualitative relationship between density & temperature of air

• Returning to the long time series of barometric pressure versus time over the course of the year, students will observe that the pressure difference between the ridgetop and lowland is not always exactly the same. The difference in pressure between the two sites is a measure of the mass or density of the column of air in between the lower and higher elevations. What is changing the density of the column of air between the ridgetop and lowland elevations?

• Students examine digital photographs recorded at the same time and place each week. Each student or student pair is responsible for one day of data, with data sets spaced one or two weeks apart (the entire class should span half a year of data). For their day, each student-pair assembles a sheet of paper with the digital photograph, plus a number representing the difference between the barometric pressure recorded at the ridgetop and the lowland stations on their day (figure 3). The sheets of paper will then be arranged along a wall in order from lowest to highest number; i.e. in order from least dense to most dense column of air between ridgetop and lowland elevations.

• The students will then examine the photographs, looking for patterns or trends. We anticipate that the students will observe that the snowy cold-looking photographs are clustered at the high air-density end of the continuum, and the summery hot- looking photographs are clustered at the low air-density end of the continuum (figure 3).

• Students try to explain the relationship between the time of year and the density of the column of air. Teacher guides discussion with examples of materials that become less dense as they get warmer, for example mercury in a barometer. Class eventually hypothesizes that a cold column of air is more dense than a warm column of air (figure 4).

6. Data-based investigation: quantitative relationship between density & temperature of air

• (for strong high school students or undergraduates) Students test the hypothesis (figure 4) that cold air is denser than warm air, and that this is why the difference in barometric pressure between the Ridgetop and Open Lowland site is larger is cold weather. They make a graph showing the air temperature as the independent variable, and the difference between barometric pressure at Open Lowland and Ridgetop as the independent variable. (figure 5). The difference in barometric pressure between the Open Lowland site and the Ridgetop site is a measure of the mass or density of the column of air between the two elevations.

• Students observe a strong correlation between temperature and barometric pressure difference (figure 5). This supports the hypothesis that air temperature is influencing the weight (density) of the column of air between the ridgetop and lowland elevations.

• Teacher can discuss this observation in terms of the behavior of gas molecules in response to heating or cooling.

Created by Kim Kastens, Lamont-Doherty Earth Observatory (kastens@ldeo.columbia.edu).
May be freely used for educational purposes provided appropriate credit is given.