Chapter 20

Gases

• Gases are similar to liquids in that both flow and are both considered fluids.

• The primary difference between liquids and gases is the distance between molecules. In liquids, molecules are close together, in gases they are spread apart.

• If two molecules of a gas colide, if one gains speed in the collision, the other loses speed, but their total kinetic energy is unchanged

• Gases expand to fill all the space available to it and thus takes the shape of its container

• The earth’s atmosphere can be though of as an ocean of air, with the greatest air pressure near the surface and decreasing air pressure as altitude increases

• Air pressure at sea level:

101 kPa760 mm Hg or Torr14.691 psi1013.25 millibars

• 50% of the earth’s atmosphere is under 18,000 feet altitude

• 75% of the earth’s atmosphere is under 56,000 feet altitude

The SI unit for pressure is the pascal.

1 pascal (Pa) = 1 N/m2

Air pressure at sea level is 101,325 Pa or 101.3 kPa

Pascal(Pa)

Bar(bar)

Technical atmosphere

(at)

Atmosphere(atm)

Torr(Torr)

Pound-force persquare inch(psi)

1 Pa ≡ 1 N/m2 10−5 1.0197×10−5 9.8692×10−6 7.5006×10−3 145.04×10−6

1 bar 100,000 ≡ 106 dyn/cm2 1.0197 0.98692 750.06 14.5037744

1 at 98,066.5 0.980665 ≡ 1 kgf/cm2 0.96784 735.56 14.223

1 atm 101,325 1.01325 1.0332 ≡ 1 atm 760 14.696

1 torr 133.322 1.3332×10−3 1.3595×10−3 1.3158×10−3 ≡ 1 Torr; ≈ 1 mmHg 19.337×10−3

1 psi 6.894×103 68.948×10−3 70.307×10−3 68.046×10−3 51.715 ≡ 1 lbf/in2

• The barometer is used for measuring air pressure.

• A simple mercury barometer can be a glass tube longer than 76 centimeters closed at one end, tipped upside down in a dish of mercury

Boyle’s Law

P1V1 = P2V2

If the temperature of a gas is constant, when the pressure of a gas increases, the volume that it contains decreases

Practice Problems:

1. If you squeeze a balloon to one-third its volume, by how much will the pressure inside increase?

Three times

2. A piston in an airtight pump is withdrawn so that the volume of the air chamber is increased five times. What is the change in pressure?

Decreases to 1/5th

3. A scuba diver 10.3 meters deep breathes compressed air. If she holds her breath while returning to the surface, by how much does the volume of her lungs tend to increase?

Twice the volume

Charle’s Law

V1 V2

T1 T2

At constant pressure, the volume of a given mass of an ideal gas increases or decreases by the same factor as its temperature on the absolute temperature scale

=

Buoyancy

An object surrounded by air is buoyed up by a force equal to the weight of the air displaced

For example, a cubic meter of air at ordinary atmospheric pressure and room temperature has a mass of about 1.2 kg, so its weight is about 12 N. If the mass of the 1 cubic meter object is greater than 1.2 kg, it will fall to the ground. If it is less than 1.2 kg, it will rise in the air.

Gay-Lussac’s Law

P1 P2

T1 T2

The pressure of a gas of fixed mass and fixed volume is directly proportional to the gas's absolute temperature.

=

Combined Gas Law

From our three equations:

P1V1 = P2V2 V1 V2 P1 P2

T1 T2 T1 T2

We get the following relationship:

PV (where k is a constant) T

This relationship can also be expressed in the Ideal Gas Law which states:

PV = nRT

P = Pressure (atmospheres)V = Volume (Liters)n = moles of gas R = gas constant (.082 L * atm K-1 mol-1)T = Temperature (Kelvin degrees)

= =

= k

Bernoulli’s Principle:

When the speed of a fluid increases, the pressure drops.

Air Flow through a pipe

Low speedHigh Pressure

High SpeedLow Pressure

Bernoulli’s Principle Provides the lift for an airplane’s wing: