Chapter 14: Gasses

Gasses differ from fluid and solids in that the atoms or molecules in the gas are usually not in physical contact with each other. The forces that would hold them together are weak (relative to the thermal energy of the individual atoms or molecules) and cannot hold them together. If you look at the spacing between the air molecules in the air around us, they are about 10 times as far apart as the water molecules in liquid water.

Pressure in a Gas

• The air around us exerts a pressure on us and on everything else it contacts. This pressure is necessary to support the weight of the rest of the atmosphere above it, just like the pressure in a liquid must support the liquid above it. As a result this pressure varies with altitude, decreasing as you move to higher elevations.
  
• The pressure that the atmosphere exerts on us at sea level is about 100,000N/m² or 100,000Pa. (1Pa = 1N/m².) This amounts to 14.7 pounds per square inch, or more than 2,000 pounds per square foot. At an elevation of about 5500m, the pressure is about 50,000Pa.
  
• The air outside a door of surface area 2m² exerts a force of

F = PxA = 200,000N

on the door pushing it in. This is over 20 tons! It does not push the door in because the air inside the room is pushing it back out with very nearly the same force, because the pressure inside is very close to the pressure outside. If the pressure were different, even by 1%, the air would exert a net force of 2,000N or about 440 pounds on the door, pushing it in if the pressure outside is greater. It is usually pressure differences that are important. If we could remove all the contents of a soda can, so the pressure inside is zero, the pressure from the air outside would crush it.

• This is how straws and barometers work. If I suck on a straw, I lower the air pressure in the straw and the greater air pressure outside pushes the liquid up the straw.

Boyle’s Law

• This states that for an ideal gas, the product of the pressure and the volume is constant if the temperature does not change and the same number of atoms or molecules are present. It is sometimes written

PV = Constant

Therefore if the pressure increases the volume occupied by the gas decreases.

• For instance, if I blow up a balloon here in Turlock, the pressure of the gas inside is very close to atmospheric pressure here in Turlock. (The pressure inside the balloon equalizes with the pressure outside the balloon since the walls of the balloon are flexible.) If I go to Pinecrest (1500m higher) the outside pressure decreases, and as a result the pressure of the air inside the balloon correspondingly decreases. But the balloon will expand, increase its volume, to keep PV constant.
  
• If the pressure triples the volume must decrease to one third its original value.

Bernoulli’s Principle

• This is the observation that the pressure in rapidly moving fluids and gasses is lower than the pressure in nearby fluids or gasses that are not moving so fast. If you blow air between two pieces of paper, the pieces of paper move closer together, because the pressure in the air moving between the pieces pushing them apart is less than the pressure in the still air "outside" pushing them together. If let a piece of paper hang down over the edge of a table and blow over the top of it, it will rise, because the pressure in the air moving over the top pushing it down is less than the pressure in the still air below pushing it up.