LESSON 3 THERMODINAMICS OF THE ATMOSPHERE

1. Environmental Physics LESSON 3 THERMODINAMICS OF THE ATMOSPHERE • Equation of state for an ideal gas. Gasses mixture • Work and heat. The first law. • Changes of phase • Air parcel. Adiabatic processes. • Water steam: Moist air. Saturation • Moist air processes. Diagrams • Vertical stability Equipo docente: Alfonso Calera Belmonte Antonio J. Barbero Hurricane Wilma (10/19/2005) Photo from http://www.nasa.gov/mission_pages/station/multimedia/hurricane_wilma.html Departamento de Física Aplicada UCLM

2. Environmental FIRST LAW Physics STATE EQUATION FOR AN IDEAL GAS The first law states the conservation of energy System http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/firlaw.html

3. SYSTEM PROPERTIES Specific enthalpy Specific internal energy Environmental Trabajo Specific heat Physics Mayer relationship Any extensive property has an associated intensive property given by itself divided by the mass of the system Relationship for specific heats for an ideal gas

4. Environmental Physics THE FIRST LAW APPLIED TO AN IDEAL GAS Remark:

5. Environmental Molar fraction Physics IDEAL GASSES MIXTURE. DALTON’S MODEL • An ideal gas consists on a set of non interacting particles whose volume is very little if compared with the total volume occupied by the gas. Non interacting particles minds negligible forces from one particle to another. • Every component in the mixture behaves as if it were the only component occupying the whole volume available at the same temperature the mixture has. • As a consequence: every component exerts a partial pressure, being the sum of all partial pressures the total pressure of the mixture. The partial pressure of a component in a mixture is proportional to its molar fraction.

6. Environmental S L 80 kcal/kg L S 540 kcal/kg Physics PHASE: Aggregation state physically homogeneous having the same properties PHASE CHANGES: Transitions between solid, liquid, and gaseous phases typically involve large amounts of energy compared to the specific heat The latentheat is the energy released or absorbed during a change of state CHANGES OF STATE AT CONSTANT PRESSURE: Entalphy Water:

7. T (ºC) Environmental 100 0 heat Physics CHANGES OF STATE IN WATER Let us consider ice at 1 atm If heat were added at a constant rate to a mass of ice to take it through its phase changes to liquid water and then to steam, the energies required to accomplish the phase changes would be as follows: water + steam ice + water 540 kcal/kg 80 kcal/kg 1 kcal/kg·ºC  0.5 kcal/kg·ºC water ice steam The change líquid steam involves a great amount of energy!

8. Environmental Steam Saturated air Moist air Dry air Physics Líquid MOIST AIR Moist air: dry air + water steam (dry air composition: see following slide) Moist air in contact with liquid water is described according the following model: 1) Dry air and water steam behave as independent ideal gasses (then the presence of each of them do not affect the behaviour of the other) 2) The equilibrium of the liquid water and steam phases is not affected by the presence of the air

9. Dry air (majority components) Environmental Saturated vapour pressure: function of T Physics SATURATED AIR What is the vapour pressure? Pressure of a vapour given off by (evaporated from) a liquid or solid, caused by atoms or molecules continuously escaping from its surface. In an enclosed space, a maximum value is reached when the number of particles leaving the surface is in equilibrium with those returning to it; this is known as the saturated vapour pressure or equilibrium vapour pressure Vapour pressure is increasing up to... QUESTION: WHY IS MOIST AIR LESS DENSE THAN DRY AIR AT SAME TEMPERATURE? http://www.theweatherprediction.com/habyhints/260/

10. Environmental Vapour pressure 0.024 The phase diagram of water http://www.lsbu.ac.uk/water/ phase.html Physics Triple point coordinates: 0.01 ºC, 0.00611 bar Liquid-steam equilibrium (water) SATURATION: Liquid water and steam phases coexists. The saturation vapour pressure is given by the liquid-vapour curve as a function of temperature. Properties of Water and Steam in SI-Units (Ernst Schmidt) Springer-Verlag (1982)

11. Environmental 1 i 2 Physics Linear interpolation

12. Specific humidity Mass of water vapor kg vapor/kg dry air or = Mass of dry air Mixture rate Environmental Physics MOISTURE CONTENT OF THE AIR Specific humidity(or moisture content of air) is the ratio of the mass of water to the mass of dry air in a given volume of moist air Relationship between partial pressure of vapor, total pressure and specific humidity: The partial pressure from a component of a gasses mixture is proportional to its molar fraction (Dalton) Remark: v indicates vapor s indicates dry air

13. . . . . . . . . . Environmental . . . . . . . . . . . . Physics EXEMPLES Determine the vapor pressure in air with specific humidity 6 g kg-1, when the total pressure is 1018 mb. Determine the specific humidity of an air mass at a total pressure of 1023 mb if the partial pressure of vapor is 15 mb. kg vapor/kg dry air Calculator for atmospheric moisture http://www.natmus.dk/cons/tp/atmcalc/atmocalc.htm

14. Environmental Physics RELATIVE HUMIDITY Relative humidity: quotient between the molar fraction of water vapor in a given sample of damp air and the molar fraction of water vapor in saturated air at the same temperature and pressure. As the molar fraction and vapor partial pressure are proportional, the relative humidity can be also expressed as Another form In the troposphere p >> pv,sat

15. Environmental P kgkg-1 pv,sat wsat kgkg-1 pv w T Physics EXEMPLE Consider an air mass at 1010 mb and 20 ºC in which the partial vapor pressure is 10 mb. Calculate its relative humidity, actual specific humidity and saturation specific humidity.

16. Environmental The air keeps its specific humidity but increases its relative humidity 0.012 Physics Dew point  17.5 ºC the temperature at which air must be cooled at constant pressure in order for it to become saturated with respect to a plane surface of water. Dew point: Atmospheric Science: An Introductory Survey by Wallace & Hobbs Pressure vapor of water as a function of temperature Exemple. Damp air mass cooling down from 40 ºC up to 10 ºC (pv = 20 mb, total pressure 1010 mb) What is the initial relative humidity? And the final one? http://weathersavvy.com/Q-dew_point1.html

17.  Constant vapor pressure Environmental 100 35 MAXIMUM OF TEMPERATURE MAXIMUM OF MOISTURE 80 30 Relative humidity % Temperature ºC 60 25 MINIMUM OF MOISTURE MINIMUM OF TEMPERATURE Physics 40 20 0 3 6 9 12 15 18 21 24 Hora TEMPERATURE AND HUMIDITY DAILY CYCLE If the vapor of water in the air remains constant... 24 mb TEMPERATURE DAILY CYCLE MOISTURE DAILY CYCLE

18. Specific enthalpy Specific internal energy Environmental Physics ENTHALPY The heat content, usually called the enthalpy, of air rises with increasing water content. This hidden heat, called latent heat by meteorologists and air conditioning engineers, has to be supplied or removed in order to change the relative humidity of air, even at a constant temperature. This is relevant to conservators. The transfer of heat from an air stream to a wet surface, which releases water vapour to the air stream at the same time as it cools it, is the basis for psychrometry and many other microclimatic phenomena. Control of heat transfer can be used to control the drying and wetting of materials during conservation treatment. The enthalpy of dry air is not known. Air at zero degrees celsius is defined to have zero enthalpy. The enthalpy, in kJ/kg, at any temperature, t, between 0 and 60C is approximately: below zero: h = 1.005t h = 1.007t - 0.026 http://www.natmus.dk/cons/tp/atmcalc/ATMOCLC1.HTM#enthalpy

19. Environmental Specific (kJ/kg dry air) Physics Enthalpy of air-water vapor mixture Remark: v indicates vapor s indicates dry air Sensible heat: Sensible heat is defined as the heat energy stored in a substance as a result of an increase in its temperature Really the sensible heat is the same as enthalpy; the heat absorbed or transmitted by a substance during a change of temperature which is not accompanied by a change of state Units: kJ/kg dry air o en kcal/kg dry air (specific magnitude). Specific heat of dry air is 0.24 kcal/kg Latent heat: The heat released or absorbed per unit mass by a system in a reversible isobaric-isothermal change of phase. In meteorology, both the latent heats of evaporation (or condensation), fusion (melting), and sublimation of water are important http://www.shinyei.com/allabout-e.htm#a19

20. T2 2 Environmental Physics Adiabatic saturation temperature T2 = Tsa ADIABATIC SATURATION PROCESS Adiabatic isolation T1 1 Air flows across a pipe or duct adiabatically insulated where there is an open water reservoir. As air moves around, its specific humidity increases. It is assumed that air and water are in contact time enough until saturation is reached. The enthalpy of the wet air remains constant because the adiabatic isolation. As a consequence, the air temperature decreases when the saturated air leaves the pipe. About adiabatic saturation and humidity http://www.taftan.com/xl/adiabat.htm http://www.shinyei.com/allabout-e.htm

21. Environmental Physics wet dry Psichrometric chart PSYCHROMETER Determination of w specific humidity of the air from three properties: pressure p, temperature T and adiabatic saturation temperature Tsa It consists of two thermometers, one of which (the dry bulb) is an ordinary glass thermometer, while the other (wet bulb) has its bulb covered with a jacket of clean muslin which is saturated with distilled water prior to an observation. When the bulbs are suitably ventilated, they indicate the thermodynamic wet- and dry-bulb temperatures of the atmosphere. Wet bulb temperature  Adiabatic saturation temperature M J Moran, H N Shapiro. Fundamentos de Termodinámica Técnica. Reverté (1994)

22. (kg/m3) Density of the moist air Environmental Specific volume (m3/kg) h  v w, pv Physics T (wet bulb) T (dry) Psychrometric chart VALID FOR A GIVEN PRESSURE http://www.taftan.com/thermodynamics/SPHUMID.HTM

23. Environmental Physics

24. Environmental  = 0.0095-0.0080 = = 0.0015 kg·kg-1 18 ºC 30% 13.5 ºC 0.0095 0.0080 30 ºC Physics 19 ºC EXEMPLE An air mass at 30 ºC having a 30% relative humidity undergoes an adiabatic saturation process. Then it is cooled down to 13.5 ºC, and after it is warmed up to 19 ºC. What is its final relative humidity? How much has been changed its specific humidity ? 70%

25. Environmental Physics AIR PARCEL An air parcel is a glob of atmospheric air containing the usual mixture of non-condensing gases plus a certain amount of water vapor. Its composition remains roughly constant whereas this glob moves across the atmosphere from one site to another. Water in the gaseous form exists in any parcel of air with relative humidity greater than 0%. If the amount of water vapor (and other environmental conditions) is such that the relative humidity of the air parcel reaches 100%, it is said that the parcel is saturated. Under conditions of saturation, water in the vapor form can change its phase from vapor to liquid. Then that water vapor condenses into liquid water droplets When phase changes occur, there is a readjustment of the forms of energy associated with the water molecules. In the vapor phase, water has a relatively large amount of internal energy represented by its looser internal molecular structure. When vapor condenses to liquid, the internal energy of the water molecule in the liquid phase is smaller, owing to its tighter molecular structure. If liquid freezes into solid water (ice), the internal energy is reduced further owing to the much tighter packing of water molecules in the solid phase.

26. Environmental 1 Any air parcel is adiabatically isolated and its temperature changes adiabatially when it rises or descends. 2 The movement of air parcels is slow enough to make possible to assume that their kinetic energy is a very little fraction of their total energy. 3 It is assumed that any air parcel is in hidrostatic equilibrium with its environment: it has the same pressure that its environment has. Physics AIR PARCEL: MODEL We’ll consider that air parcels obey the following model: Are we able to calculate temperatures from that or some related formula? What does hidrostatic equilibrium mean?

27. Environmental Air mass contained in dz: Weight of air contained in dz: p+dp -Sdp Pressure forces: Ascending: Descending: p gSdz Physics HIDROSTATIC EQUATION Air column, density  S dz z Net pressure force: The net pressure force goes upwards, because dp is a negative quantity

28. Environmental S p+dp Weight equilibrates the pressure forces -Sdp dz p gSdz z Physics HIDROSTATIC EQUATION (Continued) We assume that every air layer is near equilibrium As a function of specific volume:

29. V ms mv Moist air = = dru air + + water vapor Environmental s: density that the same dry air mass ms would have if the dry air were the only component in the volume V v: density that the same water vapor mass mv would have if the water vapor were the only component Physics VIRTUAL TEMPERATURE Virtual temperatureis an adjustment applied to the real air temperature to account for a reduction in air density due to the presence of water vapor Density of moist air: “Partial” densities Ideal gas Dalton’s law

30. Environmental Moist air pressure Density of moist air Constant of dry air Physics The ideal gas equation can be written as: Virtual temperature definition Tvirtual Virtual temperature is the temperature that dry air should have so that its density be the same than that of the moist air at the same pressure. Moist air is less dense than dry air  virtual temperature is larger than absolute temperature Virtual temperature calculator: http://www.csgnetwork.com/virtualtempcalc.html

31. Potential temperature  is the temperature that a parcel of dry air would have if it were brought dry adiabatically from its original position to a standard pressure p0 (generally the value 1000 mb is taken as the reference p0). Environmental Physics Dry air POTENTIAL TEMPERATURE ADIABATIC PROCESS

32. 0 All points in this line have the same potential temperature Environmental 10 100 230 K P (mb) Adiabatic dropping 200 =200K =500K =300K =400K =100K 300  constant 400 600 Physics 800 259 K 1000 400 200 300 100 T (K) PSEUDOADIABATIC CHART Exemple. An air parcel at 230 K lies in the 400 mb level and goes down adiabatically up to the 600 mb level. Calculate its final temperature.

33. Environmental Physics

34. Environmental Physics Continuous lines in K: Dry adiabatics Along these lines the potential temperature is constant ( cte) Dashed lines in K: Pseudoadiabatics (for moist air,  wet bulb cte) Continuous lines in g/kg: Saturation mixing ratio lines (specific humidity for saturation ws)

35. Environmental Physics USE OF PSEUDOADIABATIC CHART Exemple An air mass at 1000 mb and 18 ºC has a mixed ratio of 6 gkg-1. Find out its relative humidity and its dew point temperature. * Plot the T, p coordinates on the thermodynamics diagram (red point) * Read the saturation mixing rate. See that ws = 13 gkg-1 * Relative humidity * Dew point temperature: draw a horizontal line across the 1000 mb ordinate up to reaching the saturation mixing ratio line corresponding to the actual mixing ratio (6 gkg-1). Its temperature is 6 ºC, that is to say, when reaching this temperature a water vapor content of 6 gkg-1 become saturating, then liquid water condenses.

36. Environmental ws = 13 gkg-1 Physics 1000 mb 18 ºC Dew point 6 ºC Exemple An air parcel at 1000 mb and 18 ºC has a mixing ratio of 6 gkg-1. Find out its humidity and dew point

37. Environmental Physics LIFTING CONDENSATION LEVEL The level where a wet air parcel ascending adiabatically becomes saturated During the lifting process the mixing ratio w and the potential temperature  remain constant, however the saturation mixing ratio ws drops because the temperature is decreasing. Saturation is reached when the the saturation mixing ratio equals the actual mixing ratio w.

38. Environmental Physics NORMAND’S RULE • The ascending condensation level of an air parcel can be found in the pseudoadiabatic chart in the intersection point of the following lines: • the potential temperature line (dry adiabatic line) in the point determined by the temperature and pressure of the air parcel; • the equivalent potential temperature line (pseudoadiabatic line) passing through the point indicating the wet bulb temperature and the pressure of the air parcel; • the saturation mixing ratio line (constant humidity line) passing through the point indicating the dew point and the pressure of the air parcel;

39. Environmental Condensation level p  constant wsat constant Sat. mixing ratio line Tbh p T TR sat constant 1000 mb Physics bh T Air parcel at pressure p, temperature T, dew point TR and wet bilb temperature Tbh. dry adiabatic line pseudoadiabatic line

40. Environmental Physics EXEMPLE 1. Lifting condensation level A) An air parcel at 15 ºC has a dew point temperature of 2 ºC. It lifts adiabatically from the 1000 mb level. Find out its lifting condensation level and the temperature in this level. B) If this air parcel goes on ascending over the condensation level and reaches a level 200 mb above, find out its final temperature and the amount of water condensed during the ascending process.

41. 2.0 g/kg Environmental 630 mb Condensado: 4.5-2.0=2.5 g/kg 4.5 g/kg 830 mb Physics 1000 mb TR=2 ºC -1 ºC -15 ºC 15 ºC B) If this air parcel goes on ascending over the condensation level and reaches a level 200 mb above, find out its final temperature and the amount of water condensed during the ascending process. A) An air parcel at 15 ºC has a dew point temperature of 2 ºC. It lifts adiabatically from the 1000 mb level. Find out its lifting condensation level and the temperature in this level.

42. 770 mb Environmental 12 g·kg-1 Physics 8.5 ºC 13 ºC 23.5 ºC (50%) EXEMPLE 2 An air parcel at 900 mb and 15 ºC has a dew point temperature of 4.5 ºC. Find out the lifting condensation level, the mixing ratio, relative humidity, its wet bulb temperature, the potential temperature and the wet bulb potential temperature. 6 g·kg-1 TR=4.5 ºC T=15 ºC

43. Environmental Physics THE FIRST LAW APPLIED TO AN IDEAL GAS Remark:

44. Environmental A positive value indicates decrease of T with height Physics LAPSE RATE K/km ºC/km Rate at which temperature decreases with height Troposphere: general decrease in T with height Environmental lapse rate (ELR): it is the actual temperature of air we can measure (observed air temperature at any height) Dry adiabatic lapse rate (DALR): rate which a non-saturated air parcel cools at it rises Saturated (wet) adiabatic lapse rate (SALR): rate which a saturated air parcel cools at it rises

45. Environmental g = 9.81 ms-2 s = 0.0098 Km-1 = 9.8 Kkm-1 cp = 1004 Jkg -1K-1 Physics DRY ADIABATIC LAPSE RATE (DALR) Rate which a non-saturated air parcel cools at it rises Pressure and density decrease with height, then as an air parcel rises it expands and cools Consider a raising air parcel First law Adiabatic process A physical change of the state of the air parcel that does not involve exchange of energy with the air surrounding the air parcel. Hydrostatic equation

46. Environmental Physics 4 K km-1 9 K km-1 MORE MOISTURE LESS MOISTURE SATURATED ADIABATIC LAPSE RATE (SALR) When the air is saturated, condensation occurs Latent heat of vaporization is released That keeps the air parcel warmer than it would otherwise Decrease in temperature with height is not as great as it would be for dry air SALR is dependent on the amount of moisture on the atmophere More moisture in the atmosphere… … warmer the air will remain … the greater will be the release of condensation heat Range for sat

47. What will happen if we consider an ascending movement of the non-saturated air parcel ? Environmental lapse rate  (ELR) Height  STABLE ATMOSPHERE Environmental When raising, the air parcel pressure evens up to that of its environment A B Initial conditions s  A restoring force inhibiting the vertical movement appears TA TB Temperature Physics Positive static stability The air parcel tends to return to its original level instead of remaining on A STATIC STABILITY FOR NON-SATURATED AIR s - >0 Case  <s Density of raising air (A is colder) is bigger than density of environmental air B When the ELR  is SMALLER than dry adiabatic lapse rate s Could you figure out the same problem for descending non-saturated air?

48. What will happen if we consider an ascending movement of the non-saturated air parcel ? Environmental lapse rate  (ELR) Height  STABLE ATMOSPHERE Environmental When raising, the air parcel pressure evens up to that of its environment A B Initial conditions s  A restoring force inhibiting the vertical movement appears TA TB Temperature Physics Negative static stability The air parcel tends to return to its original level instead of remaining on A STATIC STABILITY FOR NON-SATURATED AIR (2) ...and  < 0 Case  <s s - >0 Density of raising air (A is colder) is bigger than density of environmental air B The ELR is negative (of course, it is SMALLER than that of the dry air) Could you figure out the same problem for descending non-saturated air?

49. Environmental Physics THERMAL INVERSION Very cold air Warm air layer Cold air Thermal inversions play a significant role on the contaminants gathering http://www.sma.df.gob.mx/sma/gaa/ meteorologia/inver_termica.htm About thermal inversions http://www.aviacionulm.com/meteotemperatura.html http://www.sagan-gea.org/hojared/hoja20.htm http://www.rolac.unep.mx/redes_ambientales_cd/capacitacion/Capitulo1/1_1_2.htm http://en.wikipedia.org/wiki/Thermal_inversion

50. Environmental lapse rate  (ELR) Height  UNSTABLE ATMOSPHERE Environmental When raising, the air parcel pressure evens up to that of its environment B A Initial conditions  s A force in favor of further vertical movement appears TA TB Temperature Physics Static unstability The air parcel tends to move away from its original level STATIC UNSTABILITY FOR NON-SATURATED AIR s - < 0 Case  >s Density of raising air (A is warmer) is smaller than density of environmental air B ELR is BIGGER than the dry air lapse rate