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.