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by: Cordie Miller

MeteorologyLab ESCI 241

Cordie Miller

GPA 3.65

Alex DeCaria

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Alex DeCaria
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This 8 page Class Notes was uploaded by Cordie Miller on Thursday October 15, 2015. The Class Notes belongs to ESCI 241 at Millersville University of Pennsylvania taught by Alex DeCaria in Fall. Since its upload, it has received 36 views. For similar materials see /class/223517/esci-241-millersville-university-of-pennsylvania in Earth Sciences at Millersville University of Pennsylvania.


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Date Created: 10/15/15
ESCI 241 Meteorology Lesson 6 Humidity Reading MT Chapter 5 PARTIAL PRESSURE O In a mixture of gases each gas species contributes to the total pressure 0 The pressure exerted by a single gas species is known as the partial pressure for that species 0 For a mixture of ideal gases the partial pressure of any species can be found from the ideal gas law applied to that species only For example in air the partial pressures of 02 N2 and Ar would be 11an nazRT pa PazR zT pNZV quotNZRT pN PNZRRIZT pmV quotMT pm pAngrT 0 The densities used in the above equations are partial densities O The total pressure is equal to the sum of the partial pressures and the total density is equal to the sum of the partial densities O The partial pressure of a species is proportional to the number of moles of the species 0 The partial pressure of a species can be found by multiplying the total pressure by the volume or mole fraction of the species For example the partial pressure of 02 is found by multiplying atmospheric pressure by 021 21 VAPOR PRESSURE 0 If you have a substance in liquid form some of the molecules will escape into the vapor phase The partial pressure due to these vapor molecules is known as the vapor pressure 0 Since the vapor pressure due to water molecules is proportional to the number of water vapor molecules in the atmosphere vapor pressure is one measure of humidity We usually denote vapor pressure as e From now on we will use the term vapor pressure to mean the vapor pressure due to water 0 Absolute humidity is defined as the mass of water vapor per unit volume It is merely the density of the water vapor 0 Vapor pressure is related to absolute humidity via the ideal gas law e p M where RV is the speci c gas constant for water vapor 462 J kg 1K 1 SATURATION VAPOR PRESSURE The vapor molecules are colliding with each other Some may stick together brie y to form tiny water droplets However these tiny water droplets are also constantly breaking apart If enough vapor molecules are present there may be enough collisions to form a stable population of liquid water droplets This is called saturation and the vapor pressure at this point is called the saturation vapor pressure es 0 Note You often hear this expressed in terms of the air not being able to hold any more water vapor This is really poor terminology because it doesn t matter what other gasses are present There could be only pure nitrogen pure helium or even nothing else present The saturation vapor pressure would not change The saturation vapor pressure is a function of temperature It is given by the ClausiusClapeyron equation e eexiii pRVTO T where e0 is the vapor pressure at some known temperature To and L is the latent heat of vaporization We typically use To 27315K e0 611 Pa and L 25x106 Jkg39l The saturation vapor pressure rapidly increases as temperature increases This means that at warmer temperatures there can be more water vapor present without reaching saturation 0 This is why you hear that warm air can hold more water than cold air but again this is poor terminology because it is not the air that is holding the water vapor SPECIFIC HUMIDITY AND MIXING RATIO O Vapor pressure and absolute humidity are not very convenient expressions for humidity at least for meteorologists We define some other measures of humidity Mixing ratio The mass of water vapor per mass of dry air This would be dimensionless if expressed as kgkg or gg However it is more often expressed as grams of water vapor per kg of dry air so the units of mixing ratio are usually expressed as gkg O Mixing ratio can be related to vapor pressure via L v RVT R e e rz z Pd z gzglj e R dT where e RdRv 0 The saturation mixing ratio rs is found by using es in the formula 0 Specific humidity The mass of water vapor per mass of air 0 Speci c humidity is very close to mixing ratio as shown amp qI0v A Pd zler 0 Pd l39Pv 1 7 pd since r ltlt 1 expressed as gg or kgkg 0 In meteorology mixing ratio is used far more than specific humidity and for most purposes the two can be considered as equivalent DEW POINT TEMPERATURE The saturation vapor pressure is a function of temperature and decreases with decreasing temperature If you cool moist air eventually the saturation vapor pressure will equal the vapor pressure and saturation will be reached The temperature at which this occurs is called the dew point or dew point temperature It is important to note that it is the saturation vapor pressure and not the actual vagor gressure that is changing as you cool the air The dew point temperature can be found from the ClausiusClapeyron equation by using the actual vapor pressure instead of the saturation vapor pressure and solving for T This gives RELATIVE HUMIDITY Specific humidity mixing ratio vapor pressure and dew point remain unchanged if the air parcel is heated or cooled at constant pressure 0 In other words if I want to compare two air samples to find which has more water vapor I can directly compare their mixing ratios vapor pressures specific humidities or dew points The one with the higher number will have more water vapor O I can compare the samples without worrying about whether they are at the same temperature or not however vapor pressure will have to be compared at the same air pressure 0 This is not true of absolute humidity which will change as the air parcel is heated or cooled Relative humidity as its name implies is a relative measure of humidity It is defined as the ratio of the vapor pressure to the saturation vapor pressure RH Eix100 es O In terms of mixing ratio relative humidity becomes pr RH r rsiL 100 pr 5r rs rs e rs 0 This means we can use mixing ratio rather than vapor pressure to find relative humidity 0 Relative humidity tells us how close an air parcel is to saturation 0 It does not directly tell us how much water vapor is in the parcel O A parcel with higher relative humidity may actually have less water vapor than another parcel with lower relative humidity KEY DIFFERENCE BETWEEN THE MEASURES OF HUMIDITY 0 There are two ways to change the relative humidity or absolute humidity of an air parcel 0 Add or subtract water vapor 0 Change the temperature 0 There is only one way to change mixing ratio specific humidity or dew point 0 Add or subtract water vapor HUMIDITY MEASUREMENT O Meteorologists commonly measure humidity by measuring the wetbulb temperature 0 The wetbulb temperature is the lowest temperature that can be achieved by evaporating water into the air parcel at constant pressure the evaporation requires heat which is supplied by the air parcel 0 Wetbulb temperature is measured using a psychrometer O The difference between the air temperature drybulb temperature and the wet bulb temperature is called the wetbulb depression 0 The wetbulb depression is a relative measure of the moisture content of the air Dry air can be cooled much further by evaporation than moist air so a larger wetbulb depression means less humidity for the same drybulb temperature The dewpoint temperature and relative humidity are found by using psychrometric tables with drybulb temperature and wetbulb depression as the independent variables VIRTUAL TEMPERATURE Moist air can be considered a mixture of two ideal gases dry air and water vapor The ideal gas law for moist air is ppd epde pvRVT We can manipulate this in the following manner p szdTampamp deT amp P P Rd P P Rd Pt Ry P Rd deT1 v JdeT1 qq If we define a new temperature TV such that TV T1qq then we can write the ideal gas law for moist air as P de Tv 39 TV is called the virtual temperature For moist air we can use the ideal gas law for dry air only using the virtual temperature in place of the actual temperature Virtual temperature is always greater than or equal to the actual temperature 0 The addition of water vapor causes the air to behave as though it is warmer This makes sense because moist air is lighter than dry air Since 8 0622 we have Tv T 1 061 q Virtual Temperature Virtual temperature can also be written in terms of mixing ratio as TV T 1 re 1r 6 0 Since mixing ratio and speci c humidity are so close we often write virtual temperature using mixing ratio as Tv ET1061 r O In all of the preceding equations for virtual temperature we must use the absolute Kelvin temperature and the dimensionless form of mixing ratio or specific humidity 0 However there is an approximate formula for virtual temperature in Celsius that uses the dimensional gkg form of mixing ratio or specific humidity This formula is and is often used in operational meteorology if you are interested you can find a derivation of this formula at this link EXERCISES 1 Show that the speci c gas constant for water vapor RV is 462 J kg391K 1 R 83145 J mol 1K 1 and the molecular weight of water is 18001 gmol 2 Use the ClausiusClapeyron equation to nd the saturation vapor pressure at a T 1 C b T 10 C c T 20 C d T 30 C 3 An air sample at standard sea level pressure and with a volume of 1m3 at 20 C contains 7 grams of water vapor a What is the vapor pressure b What is the relative humidity c What is the absolute humidity d What is the mixing ratio e What is the specific humidity f What is the dewpoint temperature 4 The air parcel in question 3 is cooled at constant pressure to 10 C Now find the vapor pressure relative humidity absolute humidity mixing ratio speci c humidity and dewpoint temperature 5 a What is the virtual temperature of the air parcel in problem 3 b What is the density of the parcel in problem 3


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