Upload
baldwin-craig
View
215
Download
0
Embed Size (px)
Citation preview
Climate and Global Change Notes
3-1
Observing Climate - Surface
Density
Gas Laws
Behavior of Gases
Science Concepts
DefinitionMass
Boyle’s LawCharles’ LawIdeal Gas Law
Adiabatic AscentEnergy - Potential Energy
The Earth System (Kump, Kastin & Crane)
• Chap. 4 (p. 57)
Climate and Global Change Notes
3-2
Density
Definition
• MASS per unit volume not weight per unit volume
- Mass ==> inertia- Weight ==> force as a result of gravity
• Don't usually measure atmospheric density
Units
• g / cm3
• slug / in3
Conversion
• 1 lb-mass / in3 = 27.705 gm / cm3
Standard Atmosphere Surface Value
• At 1013.25 mb and 15°C, the atmospheric density is 1.23 kg / m3
Climate and Global Change Notes
3-3
Behavior of Gases
Boyle’s Law
• ( Pressure * Volume ) is proportional to aconstant if the temperature is kept constant during the process
p1 * V1 = constant = p2 * V2
• If density ( is the mass / volume then = m / V or solving for V, V = m / . Replacing V in Boyle’s Law by its equivalent m / yields
p1 * m1 / 1 = constant = p2 * m2 / 2
if the mass within the volume remains unchanged while the pressure andvolume change, then m1 = m2 and can be canceled. Thus, we are left with
p1 / 1 = constant = p2 / 2
Robert Boyle 1627-1691www.th.physik.uni-frankfurt.de/ ~jr/
physlist.html
QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
Climate and Global Change Notes
3-4
Behavior of Gases
Boyle’s Law (Con’t)
• Example
- Take a balloon initially at pressure p1 = 1000 mb and volume V1= 1 m3. Reduce the pressure, while keeping the temperature constant, until the pressure is p2 = 500 mb.
What is the new volume, V2?
p1 * V1 = p2 * V2
( 1000 mb ) * (1 m3) = ( 500 mb ) * V2
V2 = [ 1000 (1) / 500 ] m3*mb / mb
V2 = 2.00 m3
The balloon is now twice as large and the air half as dense.
Climate and Global Change Notes
3-5
Behavior of Gases
Laws of Physics
• Example
- Boyle’s Law
> p1 * V1 = constant = p2 * V2
‡ How are these different from societal laws?‡ What do “laws of physics” tell us?‡ Can we prove a law of physics is true?
When you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the state of science.
Lord Kelvin (1824-1907)
Climate and Global Change Notes
3-6
Charles’ Law
• ( Volume / Temperature ) is proportional to a constant if the pressure is kept constant during the process. Note thetemperature must be in Kelvin.
V1 / T1 = constant = V2 / T2
or as with Boyle’s Law in terms of density
1 * T1 = constant = 2 * T2
Behavior of Gases
Jacques Charles1746-1823
Climate and Global Change Notes
3-7
Behavior of Gases
Charles’ Law (Con’t)
• Example
- Take a balloon initially at temperature T1 = 17°C and volume V1 = 1 m3. Add heat, while keeping the pressure constant,until the temperature is T2 = 37°C. What is the new volume, V2?
V1 / T1 = V2 / T2
( 1 m3 ) / [ ( 17 + 273 ) K ] = V2 / [ ( 37 + 273 ) K ]V2 = [ 1 ( 310 ) / 290 ] m3 * K / KV2 = 1.07 m3
The balloon is now 7% larger and the air 7% less dense.
Climate and Global Change Notes
3-8
Behavior of Gases
Ideal Gas Law or Equation of State
• Combining Boyle’s and Charles’ Law
( p1 * V1 ) / T1 = constant = ( p2 * V2 ) / T2
or as with Boyle’s Law
p1 / ( 1 * T1 ) = constant = p2 / ( 2 * T2 )
Note the constant, R depends on the gas. For dry air R = 287.06 Joules / kg - K.
Climate and Global Change Notes
3-9
Behavior of Gases
Ideal Gas Law or Equation of State (Con’t)
• Consequences of the Gas Law
• Parcel of air
- Imaginary bubble or glob of air
- Envision parcel having invisible,limp skin
- Skin expands or contracts without effort. Thus, pressure inside parcel equals that outside the parcel
• Skin is heat tight (adiabatic) and water tight
Climate and Global Change Notes
3-10
Behavior of Gases
Ideal Gas Law or Equation of State (Con’t)
• Consequences of the Gas Law (Con’t)
- As an air parcel rises in the atmosphere
> Because atmospheric pressure decreases as one ascends, the parcel’s pressure decreases
> Its volume increases
> Its density decreases
> Its temperature decreases
Climate and Global Change Notes
3-11
Ideal Gas Law or Equation of State (Con’t)
• Consequences of the Gas Law (Con’t)
- As an air parcel subsides or sinks in the atmosphere
> Because atmospheric pressure increases as one descends, the parcel’s pressure increases
> Its volume decreases
> Its density increases
> Its temperature increases
- Warm air is less dense than cold air, if the pressure is the same
Behavior of Gases
Climate and Global Change Notes
3-12
Behavior of Gases
Ideal Gas Law or Equation of State (Con’t)
• Consequences of the Gas Law (Con’t)
- If the surface pressure is equal for both locations, then the pressure aloft over the warm airis higher than the pressure Aloftaloft over the cold air.
Surface Cold Warm
- Unequal pressure at the same height causes the air to move. Thus, air in high pressure regions is forced toward lower pressureregions.