1

14

• gases, pressure, Boyle’s Law & Bernoulli’s Principle

• RQ: 4, 13, 15, 17, 20.

• Exercises: 7, 56.

• Problems: 1, 2.

2

Gases

• (almost) independent molecular motion (an “ideal” gas supposes no interaction)

• expand to fill space

• “fluid” (but not liquid)

• exert “isotropic” pressure (same amount in all directions)

3

Archimedes’ Principle for Air

• Air provides a small buoyancy, noticeable when object has very low density

• Examples: helium or hot-air balloon.

Temperature Density (kg/m3)

0°C (32°F) 1.29

10°C (50°F) 1.25

20°C (68°F) 1.21

30°C (86°F) 1.16

4

Boyle’s Law

• for a confined gas, (pressure)x(volume) = constant, i.e., PV = constant.

• Ex. A balloon squeezed to half its original size has double its internal pressure.

• Reasoning: in a smaller container, the molecules will hit the walls more often, exerting more force on them.

5

Bernoulli’s Principle

• When the speed of a fluid* increases, internal pressure in the fluid* decreases.

*or gas

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Why does speed decrease pressure?

• before the air blows, air molecules exert isotropic pressure, moving in all directions.

• air motion removes the isotropy, i.e. gives a preferred direction for air molecules at top of tube. The air molecules below are able to move up and out with the stream, leaving a vacuum behind.

7

Examples: Roof, Ball

8

Bernoulli’s Principle: Curve Ball

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Bernoulli’s Principle: Currents

10

summary

• gases exert isotropic pressure, but loose this effect when flowing (Bernoulli).

• gases exert a small buoyant force on all objects

• confined gases have constant product of pressure and volume

11

Plasma

• plasma: gas containing ions and free electrons

12

Atmospheric Pressure• 101 kpascal = 101,000 pascal

• pascal = newton per square meter

• significance of differential pressure

Example: 100kg is hung as shown. How large is the piston?

22

2

1001.0

/000,101

)/10)(100(

cmmA

mN

kgNkg

P

mgA

mgPA

13

Gas Densities(at 0°C and 1 atm pressure)

Gas Density (kg/m3)

hydrogen 0.090

helium 0.178

nitrogen 1.25

oxygen 1.43

air 1.29

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Gas Densities(at 0°C and 1 atm pressure)

Gas Density (kg/m3)

hydrogen 0.090

helium 0.178

nitrogen 1.25

oxygen 1.43

air 1.29

15

Air Density

Temperature Density (kg/m3)

0°C (32°F) 1.29

10°C (50°F) 1.25

20°C (68°F) 1.21

30°C (86°F) 1.16