Physical and chemical properties of water Gas Laws Chemical Potential of Water Rainfall/Drought

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1 Lecture 14, Water, Humidity, Pressure and Trace Gases, Part 1 Physical and chemical properties of water Gas Laws Chemical Potential of Water Rainfall/Drought Atmospheric Gas Composition constitue nt percent by volume percent by mass molecular weight (g mole -1 ) N O Ar CO H2O? 18 1

2 Water Gas Liquid Solid Soil-Plant-Atmosphere-Water Continuum -50 MPa atmosphere R boundary Layer R stomata leaf -0.7 MPa Xylem Water Moves UPWARD because it flows DOWNHILL Energetically R xylem -0.2 MPa Root R root/soil Soil MPa ESPM 129 Biometeorology 2

3 Triple Point for Water Phase Changes of Water How can we Exploit the Triple Point Curve to prevent water from condensing on our air sampling tube? 3

4 Properties of Water Property Value molecular weight 18 g mole 1 melting point boiling point latent heat of vaporization latent heat of sublimation dialectric constant 80 thermal conductivity heat capacity of water molecular diffusivity, water in air Density K K MJ kg 1 or kj mol 1 at 20 C MJ kg 1 or kj mol 1at 0 C W m 1 at 20 C 4182 J kg 1 at 20 C m 2 s 1 at 20 C kg m 3 at 4 C Properties of Water, f(t) temperature density latent heat of evaporation o C Mg m -3 kj mol -1 mm 2 s kinematic viscosity 4

5 Measures of Atmospheric Moisture Water Potential, Pa Relative Humidity Dew Point Temperature Wet Bulb Temperature Vapor Pressure, Pa Vapor Pressure Deficit, Pa Density, mole m -3 Mixing Ratio Charles Law and Boyle's Law pressure, volume and temperature are inter-related. PV nrt R is the universal gas constant, J mol -1 K -1, T is absolute temperature (K), P is pressure (Pa, N m -2 ), V is volume n is the number of moles 5

6 the molar volume of air (volume occupied by one mole of air, n=1) for standard pressure ( MPa, kpa, 1013 mb) and temperature ( K), V nrt P liters mole -1 or m 3 mol -1. Gas Law used by Meteorologists P RT m P RT m m is the molecular weight of a gas (g mol-1) is the mass density (g m-3) is 1/. 6

7 Partial Pressure Law P p p p p p N O Ar CO H O p R m T a v c... ma mv m c p RT Air Density ( P em ) a emv RT RT T dry Saturated o C Kg m 3 kg m Does a baseball fly Less far on a humid day? 7

8 Water Potential of atmospheric humidity is function of its mole fraction -400 p RT V w e P a ln( ) MPa R: Universal gas constant T: absolute temperature e a : vapor pressure P: pressure V w : molal volume of water, m 3 mole e a (hpa) mass gas density (grams of a gas molecule per unit volume) nm V pm RT c c c c c n c is the number of moles V is volume R is universal gas constant m c is the molecular mass (g mole -1 ) of the compound. 8

9 molar gas density (moles of a gas molecule per unit volume) nc pc c c V RT m c n c is the number of moles V is volume m c is the molecular mass (g mole -1 ) of the compound. Mass fraction (mass per unit mass of air) M c c a cm m a c m a is the molecular weight of dry air (g mol -1 ) m c is molecular weight of trace gas a is the mass density of dry air (g m -3 ) c is the mass density of trace gas air (g m -3 ) 9

10 Mole fraction, the number of moles of a trace gas divided by the total number of moles present in the mixture C c Moist air nc ma c n m c pc p Dry air C c nc pc n p d d p a pc p 2 H O Mixing Ratio of Water Vapor, Saturated Atmosphere T dry Saturation vapor pressure Mixing Ratio o C Kg m -3 g m -3 mmol m 3 ppt

11 Saturation Vapor Pressure When a pool of water is at constant temperature in a closed container, some water molecules are leaving the liquid and others are condensing and returning to the liquid. Molecules in the head space exert a partial pressure on the system. The equilibrium vapor pressure that occurs is called the saturation vapor pressure. It is a function of temperature and is independent of pressure. Saturation Vapor Pressure-Temperature Function btc es( Tc) aexp( ) c T c kpa Over Water a=0.611 b= c= Over Ice a=0.611 b= c= e s (T) (kpa) T ( o C) 11

12 Boiling Point: Pressure equals Saturation Vapor Pressure Saturation Vapor Pressure-Temperature Saturation Vapor Pressure, kpa Sea Level Mountains Temperature, C Relative Humidity, h r, the ratio between the actual (e a ) and saturation vapor pressures (e s (T). It ranges between zero and 1.0, with one indicating saturation. 1.0 h r ea e ( T ) s Relative Humidity e a =p H2O Time (hours) 12

13 Absolute humidity or vapor density (g m -3 ): em ea ( kpa) RT v ( gm ) T v a v (R= J mol -1 K -1 m v =18 g mol -1 ) k k Boardman, OR D158, v (g m -3 ) Time (hours) 3 vapor pressure (kpa) 2 1 e s e a Time (hours) 13

14 Humidity vs Temperature e =1.0 kpa e s (T) RH=0.5 v (g m -3 ) Temperature (K) Virtual Temperature. is the temperature dry air would have if it had the same density as moist air at the same pressure it is related to the speed of sound and v sound C C p v P C C p v RTv m air buoyancy of the air. ( parcel ) a g parcel ' ' T Tv v Acceleration, a 14

15 Air Temperature and Virtual Temperature temperature dry air g/g g/g air density (g m-3) Virtual Temperature is the Temperature Dry air would have if its Pressure and specific volume were equal to those of a sample of moist air Derivation: Virtual Temperature RT RT P ( Pe) dry e moist RT( ) m m m m a v a v a v a T Tv e mv 1 (1 ) P m a 15

16 Chemical Potential of Water Chemical potential quantifies the driving force for movement of water between two locations The chemical potential of water is related to the amount of change in the Gibbs free energy of the system, subjected by pressure, temperature and minor constituents, e,g., salts,. It relates to the free energy needed for a transition from State A to B It is a function of its chemical concentration, pressure, electrical potential and gravity The chemical potential has units of energy (J mol -1 ). 16

17 Water Potential The potential energy of water is related to the difference between its chemical potential ( w ) and a reference state ( wo ): o w w V w By convention, Water potential is normalized by V w, the partial molal volume of water ( m 3 mol -1 ), giving it units of Pressure. Chemical Potential is a function of: Chemical activity: RT ln(a); a = vc Pressure: (VP) Electrical Potential: (zpe) Gravity: (mgh) 0 RT ln( a) VP zfe mgh 17

18 The total water potential of a system consists of the sum of water potentials associated with Turgor (pressure), osmotic, matrix and gravitational forces p m g Units, Pressure: Pa Turgor (pressure) potential is related to the hydrostatic pressure, as when someone is blow on or sucking on straw that is inserted in a reservoir of water. Its sign can be positive or negative. osmotic potential The presence of solutes reduces the activity of water. matric potential interactions between water and solid surfaces act to reduce the activity of water. gravity Potential gravitational force is a function of the density of water, the acceleration due to gravity and the height of the water reservoir above or below a reference height: g gh w 18

19 Water Potential of atmospheric humidity is function of its mole fraction -400 p RT V w e P a ln( ) MPa R: Universal gas constant T: absolute temperature e a : vapor pressure P: pressure V w : molal volume of water, m 3 mole e a (hpa) Probability of Time between Storms f ( ) exp( ) is the rate of rain (units of rain events per day). It is computed by summing the number of rain days per year and dividing by 365 Probability of amount of rain per storm 1 h f( h) exp( ) 1/ is the depth of the rain. is computed by summing the amount of rain per year and dividing by the number of rainy days. Stochastic Rain Fall 5 4 rain (cm) day 19

20 Drought Meteorological Periods when precipitation is significantly below the long-term average Hydrological When water level in lakes and rivers fall significantly below normal conditions Agricultural Occurrence of low levels of plant available water Sociological When drought disrupts societies and/or societies disrupt supplies of water, eg via civil war, famine, political decisions Drought Metrics Palmer Drought Index Budyko Aridity Index Thornthwaite Index Ratio of between potential and actual evaporation Ratio between precipitation and available energy 20

21 Summary The concept of chemical potential energy quantifies the driving force for movement of water between two locations, such as in the soil, in a plant and between the soil, plant and atmosphere. Matrix, pressure, osmotic, gravitational potential sum to determine the chemical potential of water. Saturation vapor pressure is an exponential function of temperature The probability of rainfall events and its amount can be computed with a Poisson probability distribution 21

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