1. 1 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 Departamento de Física Aplicada UCLM PhysicsPhysics EnvironmentalEnvironmental Hurricane Wilma (10/19/2005) Photo from http://www.nasa.gov/mission_pages/station/multimedia/hurricane_wilma.html

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

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

4. 4 THE FIRST LAW APPLIED TO AN IDEAL GAS PhysicsPhysics EnvironmentalEnvironmental Remark:

5. 5 Molar fraction The partial pressure of a component in a mixture is proportional to its molar fraction. 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. PhysicsPhysics EnvironmentalEnvironmental

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

7. 7 T (ºC) heat 0 ice ice + water CHANGES OF STATE IN WATER Let us consider ice at 1 atm 100 water steam water + steam 80 kcal/kg 540 kcal/kg 1 kcal/kg·ºC The change líquid  steam involves a great amount of energy!  0.5 kcal/kg·ºC 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: PhysicsPhysics EnvironmentalEnvironmental

8. 8 Moist air: dry air + water steam Dry air Moist air Saturated air Líquid 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 (dry air composition: see following slide) MOIST AIR Steam PhysicsPhysics EnvironmentalEnvironmental

9. 9 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... Saturated vapour pressure: function of T WHY IS MOIST AIR LESS DENSE THAN DRY AIR AT SAME TEMPERATURE? http://www.theweatherprediction.com/habyhints/260/ SATURATED AIR What is the vapour pressure? Dry air (majority components) PhysicsPhysics EnvironmentalEnvironmental QUESTION:

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

11. 11 PhysicsPhysics EnvironmentalEnvironmental Linear interpolation 1 2 i

12. 12 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) kg vapor/kg dry air Mass of water vapor Mass of dry air = Specific humidity Mixture rate or 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 Remark: v indicates vapor s indicates dry air PhysicsPhysics EnvironmentalEnvironmental

13. 13 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................ EXEMPLES kg vapor/kg dry air http://www.natmus.dk/cons/tp/atmcalc/atmocalc.htm Calculator for atmospheric moisture PhysicsPhysics EnvironmentalEnvironmental

14. 14 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 >> p v,sat RELATIVE HUMIDITY PhysicsPhysics EnvironmentalEnvironmental

15. 15 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. P T pv pv p v,sat w w sat kg  kg -1 PhysicsPhysics EnvironmentalEnvironmental

16. 16 PhysicsPhysics EnvironmentalEnvironmental Dew point: 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  17.5 ºC 0.012 Exemple. Damp air mass cooling down from 40 ºC up to 10 ºC (p v = 20 mb, total pressure 1010 mb) The air keeps its specific humidity but increases its relative humidity Atmospheric Science: An Introductory Survey by Wallace & Hobbs Pressure vapor of water as a function of temperature What is the initial relative humidity? And the final one? http://weathersavvy.com/Q-dew_point1.html

17. 17 TEMPERATURE AND HUMIDITY DAILY CYCLE 40 60 80 100 20 25 30 35 03691215182124 Hora Temperature ºC Relative humidity % If the vapor of water in the air remains constant... Constant vapor pressure  24 mb MINIMUM OF TEMPERATURE MAXIMUM OF MOISTURE MINIMUM OF MOISTURE MAXIMUM OF TEMPERATURE TEMPERATURE DAILY CYCLE MOISTURE DAILY CYCLE PhysicsPhysics EnvironmentalEnvironmental

18. 18 ENTHALPY The heat content, usually called the enthalpy, of air rises with increasing water content. Specific enthalpy Specific internal energy 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: h = 1.007t - 0.026 below zero: h = 1.005t http://www.natmus.dk/cons/tp/atmcalc/ATMOCLC1.HTM#enthalpy PhysicsPhysics EnvironmentalEnvironmental

19. 19 Specific (kJ/kg dry air) Enthalpy of air-water vapor mixture Sensible heat: Sensible heat is defined as the heat energy stored in a substance as a result of an increase in its temperature 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 Remark: v indicates vapor s indicates dry air 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 PhysicsPhysics EnvironmentalEnvironmental

20. 20 ADIABATIC SATURATION PROCESS 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. T11T11 T22T22 About adiabatic saturation and humidity http://www.taftan.com/xl/adiabat.htm http://www.shinyei.com/allabout-e.htm Adiabatic saturation temperature T 2 = T sa Adiabatic isolation 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. PhysicsPhysics EnvironmentalEnvironmental

21. 21 PSYCHROMETER Determination of w specific humidity of the air from three properties: pressure p, temperature T and adiabatic saturation temperature T sa dry Wet bulb temperature  Adiabatic saturation temperature Psichrometric chart wet M J Moran, H N Shapiro. Fundamentos de Termodinámica Técnica. Reverté (1994) PhysicsPhysics EnvironmentalEnvironmental 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.

22. 22 Density of the moist air (kg/m 3 ) Specific volume (m 3 /kg) w, p v T (dry) h T (wet bulb)  v Psychrometric chart VALID FOR A GIVEN PRESSURE http://www.taftan.com/thermodynamics/SPHUMID.HTM PhysicsPhysics EnvironmentalEnvironmental

23. 23 PhysicsPhysics EnvironmentalEnvironmental

24. 24 PhysicsPhysics EnvironmentalEnvironmental 30 ºC 30% 18 ºC 13.5 ºC 19 ºC 0.0080 0.0095  = 0.0095-0.0080 = = 0.0015 kg·kg -1 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. 25 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. An air parcel is a glob of atmospheric air containing the usual mixture of non-condensing gases plus a certain amount of water vapor. 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. AIR PARCEL Its composition remains roughly constant whereas this glob moves across the atmosphere from one site to another. PhysicsPhysics EnvironmentalEnvironmental

26. 26 PhysicsPhysics EnvironmentalEnvironmental AIR PARCEL: MODEL We’ll consider that air parcels obey the following model: Any air parcel is adiabatically isolated and its temperature changes adiabatially when it rises or descends. 1 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. 2 It is assumed that any air parcel is in hidrostatic equilibrium with its environment: it has the same pressure that its environment has. 3 What does hidrostatic equilibrium mean? Are we able to calculate temperatures from that or some related formula?

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

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

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

30. 30 Virtual temperature definition T virtual The ideal gas equation can be written as: 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 Density of moist air Constant of dry air Moist air pressure Virtual temperature calculator: http://www.csgnetwork.com/virtualtempcalc.html PhysicsPhysics EnvironmentalEnvironmental

31. 31 PhysicsPhysics EnvironmentalEnvironmental 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 p 0 (generally the value 1000 mb is taken as the reference p 0 ). POTENTIAL TEMPERATURE Dry air ADIABATIC PROCESS

32. 32 1000 600 100 200 300 400 800 0 10 100 200 300 400 P (mb) T (K)  =100K  =200K  =300K  =400K  =500K 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. 230 K Adiabatic dropping  constant All points in this line have the same potential temperature 259 K PhysicsPhysics EnvironmentalEnvironmental

33. 33 PhysicsPhysics EnvironmentalEnvironmental

34. 34 PhysicsPhysics EnvironmentalEnvironmental 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 w s )

35. 35 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. USE OF PSEUDOADIABATIC CHART * Plot the T, p coordinates on the thermodynamics diagram (red point) * Read the saturation mixing rate. See that w s = 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. PhysicsPhysics EnvironmentalEnvironmental

36. 36 w s = 13 g  kg -1 6 ºC 18 ºC 1000 mb Dew point 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 PhysicsPhysics EnvironmentalEnvironmental

37. 37 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 w s drops because the temperature is decreasing. Saturation is reached when the the saturation mixing ratio equals the actual mixing ratio w. PhysicsPhysics EnvironmentalEnvironmental

38. 38 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; NORMAND’S RULE PhysicsPhysics EnvironmentalEnvironmental

39. 39 Air parcel at pressure p, temperature T, dew point T R and wet bilb temperature T bh.  constant  sat constant w sat constant 1000 mb p T T T R Condensation level T bh  bh p dry adiabatic line pseudoadiabatic line Sat. mixing ratio line PhysicsPhysics EnvironmentalEnvironmental

40. 40 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. PhysicsPhysics EnvironmentalEnvironmental

41. 41 15 ºC 1000 mb 830 mb 630 mb -15 ºC T R =2 ºC 4.5 g/kg 2.0 g/kg Condensado: 4.5-2.0=2.5 g/kg -1 ºC 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. PhysicsPhysics EnvironmentalEnvironmental

42. 42 PhysicsPhysics EnvironmentalEnvironmental 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 -1 770 mb 12 g·kg -1 (50%) 8.5 ºC 13 ºC 23.5 ºC T=15 ºC T R =4.5 ºC

43. 43 THE FIRST LAW APPLIED TO AN IDEAL GAS PhysicsPhysics EnvironmentalEnvironmental Remark:

44. 44 LAPSE RATE Rate at which temperature decreases with height K/km ºC/km A positive value indicates decrease of T 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 PhysicsPhysics EnvironmentalEnvironmental

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

46. 46 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… … the greater will be the release of condensation heat … warmer the air will remain Range for  sat 4 K km -1 9 K km -1 MORE MOISTURE LESS MOISTURE PhysicsPhysics EnvironmentalEnvironmental

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

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

49. 49 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 http://www.sma.df.gob.mx/sma/gaa/ meteorologia/inver_termica.htm THERMAL INVERSION Cold air Warm air layer Very cold air Thermal inversions play a significant role on the contaminants gathering PhysicsPhysics EnvironmentalEnvironmental

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

51. 51 Stable  <  s Positive static stability  <0  <  s Negative static stability (inversion) Unstable  >  s Convective mixing Neutral stability:  =  s STATIC STABILITY NON-SATURATED AIR (SUMMARY)  ss   ss PhysicsPhysics EnvironmentalEnvironmental

52. 52 Ground EXEMPLE ON STABIBLITY AND UNSTABILITY Environmental lapse rate  (ELR) Dry Adiabatic Lapse Rate (DALR) As the air parcel is unsaturated, it lifts along the dry adiabatics temperature The air parcel temperature here is lower than sourrounding air temperature Any air parcel which overtakes this level sinks to equilibrium level Inversion level ELR  > DALR  s What will happen to an unsaturated air parcel initially lying on the ground?

53. 53 http://www.adi.uam.es/docencia/elementos/spv21/sinmarcos/graficos/entalpiadevaporizacion/evapor.html Enthalpy of change of state data http://www.adi.uam.es/docencia/elementos/spv21/sinmarcos/graficos/entalpiadefusion/efusion.html http://www.usatoday.com/weather/wwater0.htm Other related sites http://www.usatoday.com/weather/whumdef.htm BIBLIOGRAPHY http://www.usatoday.com/weather/wstabil1.htm (usa unidades inglesas) Stability and unstability discussions http://www.qc.ec.gc.ca/meteo/Documentation/Stabilite_e.html http://www.cesga.es/telecursos/MedAmb/medamb/mca2/frame_MCA02_3.html http://www.geocities.com/silvia_larocca/Temas/emagrama2.htm http://www.usatoday.com/weather/whumdef.htm On humidity and its measure M J Moran, H N Shapiro. Fundamentos de Termodinámica Técnica. Reverté (1994) Basic books: John M Wallace, Peter W Hobbs, Atmospheric Science. An introductory survey. Academic Press (1997) On specific heat http://www.engineeringtoolbox.com/36_339qframed.html http://seaborg.nmu.edu/Clouds/types.html Clouds http://www.gordonengland.co.uk/conversion/specific_energy.htm PhysicsPhysics EnvironmentalEnvironmental http://www.indiana.edu/~geog109/topics/08_stability/LapseStability_CB_L.pdf

54. 54 -10 -5 0 5 1015 2025 30 3540 1050 1000 950 900 850 800 750 700 temperature ºC pressure mb Continuous red lines labelled in K: dry adiabatics Continuous black lines labelled in g·kg -1 : saturation mixing ratio Discontinuous grey unlabelled lines: pseudoadiabatics 2.03.04.06.08.010.012.015.020.025.030.0 280 290 300 310 320 PSEUDOADIABATIC CHART PhysicsPhysics EnvironmentalEnvironmental

55. 55 -10 -5 0 5 1015 2025 30 3540 1050 1000 950 900 850 800 750 700 temperature ºC pressure mb Continuous red lines labelled in K: dry adiabatics Continuous black lines labelled in g·kg -1 : saturation mixing ratio Discontinuous grey unlabelled lines: pseudoadiabatics 2.03.04.06.08.010.012.015.020.025.030.0 280 290 300 310 320 PSEUDOADIABATIC CHART PhysicsPhysics EnvironmentalEnvironmental