Temperature and Thermodynamics, Part II. Topics to be Covered

Transcription

1 Teperature and Therodynaics, Part II Topics to be Covered Profiles of Teperature in the Boundary Layer Potential teperature Adiabatic Lapse Rate Theral Stratification 1/8/17

2 Why are We Interested in Theral Stratification of the Atosphere? Copare Teperatures easured at Different Heights and Altitudes Creates or Suppresses Turbulence and Diffusion Adiabatic Lifting can Cause Cooling It can cause water to change phases Condensation Prootes the Foration of Clouds and Rain Adiabatic Copression can Cause Heating Downslope Santa Ana winds, Hot and Dry Microcliate Modification Wind achines Break the Nocturnal Inversion Layer and Prevent Frost

3 Changes in Air Pressure and Density with Height, Ideal Conditions Height, dp 1000 = ρa g dz a ( P e) ρa = Height, RT Pressure, kpa Air Density, kg -3 Air Parcel Lifted Expands and Becoes Less Dense because Surrounding Pressure is Less, Consequently Its Teperature Drops as the Parcel Expends

4 Teperature Profiles in the Boundary Layer: Adiabatic Lapse Rate Γ= 9.8Kk 1 Height, T air, K

5 Potential Teperature, θ The Teperature a Parcel of Air would have if it were Expanded or Copressed, Adiabatically, fro its Existing Teperature and Pressure to a Standard, near sea level (P=101.3 kpa): Wallace and Hobbs, 1977 θ = T P R c ( 0 ) /( ) p θ = T( P 0 ) / P P R C p T, Teperature (K) R, Universal Gas Constant, P, Pressure, kpa P 0, reference pressure, eg kpa C p, Heat Capacity of air at constant pressure c p, specific heat capacity of air at constant pressure

6 Teperature Profiles in the Boundary Layer: Adiabatic Lapse Rate and Potential Teperature Height, Pressure, kpa T air, K Potential Teperature, K

7 Profiles of Air and Potential Teperature 700 June 1, 1999, 1800 UT Oak Ridge, TN 750 Virtual Potential Teperature Dry Bulb Teperature Pressure, b Stable neutral 950 unstable

8 Fundaentals of Theral Stratification Height, T = Γ z near neutral stability Height, unstable theral stratifiation Tparcel > Tair T z = Γ Height, T = Γ z stable theral stratification Tparcel < Tair Height, θ =0 z Height, θ =0 z Height, θ =0 z

9 Theral stratification causes the atosphere to be either buoyant or stable The atosphere is neutrally stratified if: z θ v = 0 T z v = Γ The atosphere is unstably stratified if: z θ v < 0 T z v < Γ The atosphere is stably stratified if: z θ v > 0 T z v > Γ

10 Upcoing Features Describe Adiabatic Processes and Potential Teperature in ters of variables we easure, P and T Start with 1 st Law of Therodynaics Noralize 1 st Law by Mass, yielding Specific Equation Substitute Ters with Gas Laws, converting Equation fro a function of heat capacity for volue, Cv, to that for pressure, Cp Rearrange Equation so T is on one side and P is on the other Integrate both sides, yielding equations Ln(T) and Ln(P) Take anti-log and solve for potential teperature

11 Adiabatic Process An air parcel changes its physical state (either its pressure, volue or teperature) without heat being added or withdrawn fro the surrounding environent. dq = 0

12 Understanding Adiabatic Copression and Expansion, And its Ipact on Teperature Profiles With the First Law of Therodynaics dq = CV dt + PdV = 0 C dt V = PdV Change in internal Energy Change in Work No Heat is Exchanged, But Teperature Can Change Change in Internal Energy Equals Change in Work Done on the Parcel

13 Understanding Adiabatic Processes in the Atosphere by considering Parcels of Air per unit Mass (), Specific quantities Q q = w = W U u = Cv cv = Cp cp = Change in Volue per unit Mass is Equivalent to the change of the inverse in density, ρ dv = d( 1 ρ ) = d α

14 The Specific For of the 1 st Law of Therodynaics 1 dq = cvdt + Pd( ) = cvdt + Pdα ρ

15 Algebraic Tricks to Express dq as f(t, P) and solve for Pdα P = ρrt Pα = RT d ( P α) = α dp + Pd α = 1 d( RT) = 1 RdT Pd α = adp + R dt

16 Algebraic Tricks to Express dq as f(t, P), things we can easure Pd α = adp + R dt dq = c dt Pdα v dq R = ( c + ) v dt α dp

17 Change in Specific Heat, dq, is a function of the Specific Heat Capacity, c p, ties a change in Teperature, inus A change in pressure, dp.ters we can MEASURE R dq = ( cv + ) dt αdp c p = c + v R dq = cpdt αdp

18 Define specific heat capacity at constant P Isobaric case, dp equals 0 dq R = ( c dt dp v + ) α dq dt R = c + = c p v p

19 Adiabatic Process, dq=0 dq = 0 = cpdt αdp c dt p = αdp = dp ρ

20 cdt p = αdp= dp ρ ρ = P RT c dt c p p dt T = = RTdP P R dp P P: Pressure V: volue n: nuber of oles R: Universal Gas Constant : ass per ole T: absolute air teperature ρ: air density

21 dt R dp R dp = = T c P C P p p T dt = R T c p θ P P 0 dp P T R P ln ln θ = c P p 0

22 T R P ln ln θ = cp P0 T R P exp(ln ) exp( ln ) θ = c P p 0 0 R T P c = θ P p

23 Potential Teperature θ = R c ( 0 ) /( ) p T P P R C p θ = T( P 0 ) / P

24 Adiabatic lapse rate, How Teperature Changes with Height 0 = ρ c dt dp p ρ c dt = p dp Hydrostatic Equation dp dz = ρg Change in Pressure with height is a function of the density of Air ties the acceleration due to gravity, g

25 Dry Adiabatic Lapse Rate ρc p dt dz dp = = ρg dz dt dz g = =Γ adiabatic cp The dry adiabatic lapse rate, 9.8 K k -1

26 Moist Adiabatic water vapor condenses and latent heat of condensation is released. dt dz g oist = =Γ de oist s cp + λ dt λ is the latent heat of vaporization de s /dt is the slope of the saturation vapor pressure-teperature curve.

27 Key Points Define Theral Stratification Neutral, Stable and Unstable Conditions Define Potential Teperature Define Adiabatic Processes Dry and Moist Adiabatic Lapse Rate Define First Law of Therodynaics

28 Suary Potential teperature is the teperature of a parcel of air that is oved Adiabatically fro a level in the atosphere to a reference Pressure. It is defined for conditions when changes heat energy are zero (dq=0). Theral stratification causes the atosphere to be either buoyant or stable The atosphere is neutrally stratified if: The atosphere is unstably stratified if: The atosphere is stably stratified if: z θ v = 0 z θ v < 0 z θ v > 0