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

2. 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 / cm 3 slug / in 3 Conversion 1 lb-mass / in 3 = 27.705 gm / cm 3 Standard Atmosphere Surface Value At 1013.25 mb and 15°C, the atmospheric density is 1.23 kg / m 3

3. Climate and Global Change Notes 3-3 Behavior of Gases 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 (  is the mass / volume then  = m / V or solving for V, V = m / . Replacing V in Boyle’s Law by its equivalent m /  yields p 1 * m 1 /  1 = constant = p 2 * m 2 /  2 if the mass within the volume remains unchanged while the pressure and volume change, then m 1 = m 2 and can be canceled. Thus, we are left with p 1 /  1 = constant = p 2 /  2 Robert Boyle 1627-1691 www.th.physik.uni-frankfurt.de/ ~jr/ physlist.html

4. Climate and Global Change Notes 3-4 Behavior of Gases 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. Climate and Global Change Notes 3-5 Behavior of Gases 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 (1824-1907)

6. 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 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  1 * T 1 = constant =  2 * T 2 Behavior of Gases Jacques Charles 1746-1823

7. Climate and Global Change Notes 3-7 Behavior of Gases 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 ) / [ ( 17 + 273 ) K ] = V 2 / [ ( 37 + 273 ) 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. Climate and Global Change Notes 3-8 Behavior of Gases 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 / (  1 * T 1 ) = constant = p 2 / (  2 * T 2 ) Note the constant, R depends on the gas. For dry air R = 287.06 Joules / kg - K.

9. 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

10. 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

11. 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

12. 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 air is higher than the pressure Aloft aloft 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 pressure regions.