Column with unit cross-sectional area Pressure = p + p p - PowerPoint PPT Presentation

Column with unit cross-sectional area Pressure = p + δ p – δ p Pressure = p δ z g ρδ z z Ground

A B ln p 2 C ln p E ln p 1 From radiosonde D data T v Virtual temperature, T v (K)

W A 12 R Height (km) M W C A O L R D M 0 (b) (a)

Cylinder F Working substance Piston Distance, x A p 1 p Pressure P Q p 2 B V 1 V V 2 ↔ dV Volume

C Adiabat Pressure B A Isotherm Volume

0 10 θ = 500 K θ = 400 K θ θ = 100 K θ = = 3 2 0 0 0 0 K K Pressure p (hPa) 100 200 300 400 600 800 1000 0 100 200 300 400 Temperature T (K)

400 C ° 0 2 Dry Adiabat Pressure (hPa) – = C m T ° 600 r e 0 h θ = 293 K = t o T s I C 800 ° θ = 273 K 0 2 = θ = T 2 5 3 K 1000

· · · · · · · · · · T, e s T, e · · · · · · · · · · · · · · · · · · · · · · · · · Water Water (a) Unsaturated (b) Saturated

60 Saturation vapor pressure e s over pure water (hPa) 50 40 0.28 30 0.24 e s –e si 0.20 e s – e si (hPa) 20 0.16 e s 0.12 10 0.08 0.04 0 0 –50 –40 –30 –10 –20 0 10 20 30 40 Temperature (°C)

400 Pressure (hPa) w s constant 600 800 Lifting condensation C level for air at A θ constant 1000 B A ( p , T d , w s (A)) ( p , T , w )

T T d T w w s w s p 400 600 800 1000 400 600 800 1000 LCL q e ฀ q ) a P h ( ฀ e r u s s e r P q q w

A B B A O O Height Height Γ Γ d Γ d Γ T A T B T B T A Temperature Temperature (a) (b)

ρ g ρ , T ρ′ , T ′ z ρ′ g Surface

LFC B LCL Height A O Γ s Γ Γ d Temperature

A B A B A B A B (a) (b) (c) (d)

T d T Height B A Temperature

Force P Y B T 1 T 2 H S C

Adiabat Adiabat B C Pressure T 1 Isotherm A T 2 Isotherm D Volume

Pressure T 3 T 2 T 1 θ 1 θ 2 θ 3 Volume

Adiabat Adiabat T 1 B C Isotherm Temperature, T T 2 Isotherm A D X Y Entropy, S

Saturated vapor pressure Saturated vapor pressure e s B C e s B, C e s – de s e s – de s A, D A D T – dT T Volume Temperature (a) (b)

D D C C A A B B T-dT T – dT T – dT T T T – dT T – dT T T e s – de s e s e s e s – de s e s e s e s – de s e s – de s SOURCE SINK T T – dT (b) (c) (d) (a)

p atmos p atmos Pressure T < T B T = T B inside Water Water bubble = e s ( T B ) = p atmos (a) (b)

Source θ 1 Q 1 Q 1 R I Q 2 Q 2 – q Sink θ 2