Observing Climate - Surface

Transcription

1 Observing Climate - Surface 3-1 Density Science Concepts Definition Mass Gas Laws Behavior of Gases Boyle s Law Charles Law Ideal Gas Law Adiabatic Ascent Energy - Potential Energy The Earth System (Kump, Kastin & Crane) Chap. 4 (p. 57)

2 Density 3-2 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 / cm 3 slug / in 3 Conversion 1 lb-mass / in 3 = gm / cm 3 Standard Atmosphere Surface Value At mb and 15 C, the atmospheric density is 1.23 kg / m 3

3 3-3 Boyle s Law ( Pressure * Volume ) is proportional to a constant if the temperature is kept constant during the process p 1 * V 1 = constant = p 2 * V 2 If density (ρ) is the mass / volume then ρ = m / V or solving for V, V = m / ρ. Replacing V in Boyle s Law by its equivalent m / ρ yields p 1 * m 1 / ρ 1 = constant = p 2 * m 2 / ρ 2 Robert Boyle ~jr/ if the mass within the volume remains physlist.html unchanged while the pressure and volume change, then m 1 = m 2 and can be canceled. Thus, we are left with p 1 / ρ 1 = constant = p 2 / ρ 2

4 3-4 Boyle s Law (Con t) Example - Take a balloon initially at pressure p 1 = 1000 mb and volume V 1 = 1 m 3. Reduce the pressure, while keeping the temperature constant, until the pressure is p 2 = 500 mb. What is the new volume, V 2? p 1 * V 1 = p 2 * V 2 ( 1000 mb ) * (1 m 3 ) = ( 500 mb ) * V 2 V 2 = [ 1000 (1) / 500 ] m 3 *mb / mb V 2 = 2.00 m 3 The balloon is now twice as large and the air half as dense.

5 3-5 Laws of Physics Example - Boyle s Law > p 1 * V 1 = constant = p 2 * V 2 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 ( )

6 3-6 Charles Law ( Volume / Temperature ) is proportional to a constant if the pressure is kept constant during the process. Note the temperature must be in Kelvin. V 1 / T 1 = constant = V 2 / T 2 or as with Boyle s Law in terms of density ρ 1 * T 1 = constant = ρ 2 * T 2 Jacques Charles

7 3-7 Charles Law (Con t) Example - Take a balloon initially at temperature T 1 = 17 C and volume V 1 = 1 m 3. Add heat, while keeping the pressure constant, until the temperature is T 2 = 37 C. What is the new volume, V 2? V 1 / T 1 = V 2 / T 2 ( 1 m 3 ) / [ ( ) K ] = V 2 / [ ( ) K ] V 2 = [ 1 ( 310 ) / 290 ] m 3 * K / K V 2 = 1.07 m 3 The balloon is now 7% larger and the air 7% less dense.

8 3-8 Ideal Gas Law or Equation of State Combining Boyle s and Charles Law ( p 1 * V 1 ) / T 1 = constant = ( p 2 * V 2 ) / T 2 or as with Boyle s Law p 1 / ( ρ 1 * T 1 ) = constant = p 2 / ( ρ 2 * T 2 ) Note the constant, R depends on the gas. For dry air R = Joules / kg - K.

9 3-9 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

10 3-10 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

11 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

12 3-12 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 air is higher than the pressure aloft over the cold air. Aloft Surface Cold Warm - Unequal pressure at the same height causes the air to move. Thus, air in high pressure regions is forced toward lower pressure regions.