1 14 gases, pressure, boyle’s law & bernoulli’s principle rq: 4, 13, 15, 17, 20. exercises:...
TRANSCRIPT
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14
• gases, pressure, Boyle’s Law & Bernoulli’s Principle
• RQ: 4, 13, 15, 17, 20.
• Exercises: 7, 56.
• Problems: 1, 2.
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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
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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.
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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.
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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
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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
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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
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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