Chapter 14: Gases and Plasmas How do Gases Compare to Liquids and Solids? We know what we mean when we say something is a liquid or solid, and so on. In general terms, we recognize that solids are rigid and/or malleable structures, liquids can flow but the atoms, molecules, or ions that make them up still interact and are sticky (cohesion). In this Chapter, we indicate how gases differ from solids but are similar to liquids in a certain sense, and some effects of gases in everyday life. The atmospheric pressure changes with height (NOAA) are at left. The pressure unit for this plot is millibarsis where 1,000 millibars is 1 bar or 1 atmosphere (1 atm). Note that there is no upper surface to the atmosphere; the atmosphere simply fades away as the gas rises as far as it can (due to the confinement of gravity).

What makes a Gas versus a Liquid or Solid? In a solid, the molecules and ions are forced to settle into a rigid structure where they arrange themselves to try and minimize their interaction. When we heat a solid, the particles gain kinetic energy, and start to move about a little. At sufficiently high temperatures, the ions and molecules can start to move rather freely and flow. In a liquid, although able to move, the molecules and ions are still not completely free as they still feel the pull of their neighbors. The molecules and ions tend to move but they do not change their volume (the total amount of space which they occupy--however, recall water). In gases, ions and molecules are free of this interaction and are able to move freely. If there were no restraining forces, gas particles would in fact fill the Universe. Because gases and liquids are both free to flow, both are referred to as Fluids. In physics, Fluids carries a different meaning than in general usage. At right is what is referred to as a Phase Diagram . This is the Phase Diagram for water. At the surface of the Earth where the Pressure is 1 atm, we see that as we increase the temperature, water makes transitions from ice (solid) to liquid to gas. Interestingly, we note that at low pressure (0.006 atm), ice, oceans, and steam can exist at nearly the same temperature (T~0.01 Centigrade). This is the Triple Point of water. at low pressure, the melting point of ice and the boiling point of water are smaller than at sea level, pressure 1 atm. On Mars, the surface pressure is 0.006-0.007 atm and we likely find either ice (solid) or water vapor.

Atmospheric Pressure Atmospheric pressure arises from the weight of the air sitting above the observer. The mass of air in the column above the head of the observer (see the upper panel on the right) is pulled down by the gravity of the Earth and exerts a force (and pressure) on the observer. At the surface of the Earth the pressure is 14.7 pounds per square inch (1 atmoshphere, 101,000 Pascals, 1 kPa, 1 bar). At higher altitudes, less air sits above an observer and so there is a smaller atmospheric pressure (see the bottom panel on the right). 14.7 pounds per square inch is a lot. A shot put weighs 16 pounds. Why don't we feel this pressure? Air, unlike water is compressible (we can change its volume through pressure). Consequently, we find that as we move away from the surface of the Earth, the density of the atmosphere decreases. Consequently, it takes larger volumes of air to increase the weight of the overlying atmosphere ===> atmospheric pressure changes more slowly with height than the pressure changes with depth in the ocean. Near the surface of the Earth, a cubic centimeter of air has a mass of 0.00125 grams. Recall that a cubic centimeter of water has a mass of 1 gram. At an altitude of 10 kilometers, a cubic centimeter of air has a mass of 0.0004 grams. At an altitude of 10 kilometers, a cubic centimeter of water still has a mass of 1 gram.

Manometers, Barometers, Straws, Pipettes, Medicine Droppers, ... Manometers, barometers, straws, pipetters, medicine droppers, types of water pumps rely on the same principle. All use atmospheric pressure to cause water or some other fluid to rise.

Buoyancy and Flotation The phenomena Buoyancy and flotation, as found in liquids also happen in gases. The fate of the rock depends on its density compared to the density of the fluid. The general result is (again): If the density of the rock is larger than the density of the liquid (in this case water) then the rock sinks. If the density of the rock is smaller than the liquid the rock is buoyant and rises. If the density of the rock is the same as the liquid the rock floats, neither rising nor sinking.

Archimedes' Principle Archimedes' treatise On floating bodies states that: Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object (Archimedes of Syracuse) with clarifications that for a sunken object, the volume of displaced fluid is the volume of the object, and for a floating object on a liquid, the weight of the displaced liquid is the weight of the object. In short, buoyancy = weight of the displaced liquid. If the displaced weight is the same as the object, then buoyancy balances gravity and the object feels neither an upward or downward push If the displaced weight is larger than the object's weight, then buoyancy overcomes gravity and the object rises If the displaced weight is smaller than the object's weight, then buoyancy cannot overcome gravity and the object sinks This translates to the relationship between the density and sinking/rising/floating given above.

Flotation I From Archimedes' treatise On floating bodies, proposition 5, states that: Any floating object displaces its own weight of fluid (Archimedes of Syracuse). Although made of metal, the interior of the buoy is hollow and so its density is low allowing it to float.

Hot Air Balloon: heated air in balloon

Helium filled balloons

Flotation II The planes illustrate another effect that arises in fluids. The airfoil (below) exerts lift:

Bernoulli Principle The Bernoulli's effect arises in moving fluids, both liquids and gases. The general idea is that there is a relationship between the flow of a fluid and the pressure in the fluid.

Whenever the flow speed in a fluid changes, the pressure in the fluid changes in the sense that the faster the flow, the lower the pressure. What can cause the flow in a fluid to change? Imagine a flow of water down a pipe. Suppose 1 gallon of water per second flows. In the wide part of the pipe, the flow moves with a certain speed. As the water flows into the constriction, what happens? The nozzle (area) through which the flow moves gets smaller. Because the water doesn't compress, fewer water molecules can pass through the gap at a single time. This means that the rate at which the water flows through must increase. That is, the rate at which the water flows per unit area must increase. [Comment-a flow per unit area is called a Flux.]

Lift The shape of the wing (airfoil) forces air to compress more above the wing than below and so the speed-up increases more on top of the wing ===> Pressure goes down more above the wing with a resultant net upward lift.

Curve Ball The air rushes past the baseball in the rightward direction (because the ball moves to the left). For the counter-clockwise spin in the picture, the spin of the baseball slows the airspeed on top of the ball while speeding up the airspeed on the bottom of the ball ===> pressure changes push the ball downward (in the direction of its spin).

Passing Ships The water feels more compression between the ships causing a greater water flow speed between the ships which deceases the pressure between the ships compared to that outside the ships ===> pressure pushses ships closer together.