Atmospheric moisture

Gas lawsAir & vapor pressure

Moisture content in air

Evaporation/condensation

The ideal gas law

The ideal gas law:

P = pressure [mb]ρ = density of gas [g/cm3]T = absolute temperature [°K]R = gas constant (depends on the molecular weight of the

gas and the other units)

Decrease in pressure ⇒ Decrease in temperature and density (and vice versa).Water vapor can be considered an ideal gas

RTP ρ=

Dalton's law

Each gas in a mixture creates pressure as if the other gases were not present. The total pressure is the sum of the pressures created by the gases in the mixture

Total air pressure (P) is the sum of dry air pressure (pd) and water vapor pressure (e).Water vapor pressure is typically 1-2% of total air pressure.

Dalton's Law of Partial Pressures:

Example

Determine the mass of 1 m3 of dry air at 20°C and a pressure of 1013 mb (= 1 atmosphere).

Solution:The dry air gas constant is given at page 21 as

R = 2.87x103 mb cm3/g °KFrom the ideal gas law:

1 m3 of dry air weighs 1.2 kg.

3

d

cm/g0012.0)20273(2870

1013RTP

=

+×==ρ

Definition:Mass of water vapor contained in a unit of moist air [g/g]. It can be calculated as ρw/ ρm.

Calculation:Ideal gas law:

Dry air:

Vapor:

Specific humidity

RTP ρ=

TReP

TRp

dd

dd

−==ρ

]622.0/RR[TR

e622.0TR

edw

dww ===ρ

Specific humidity

Density of moist air:

Specific humiditye378.0P

e622.0qm

w

−=

ρρ

==

[ ]e378.0PTR

1d

wdm −=ρ+ρ=ρ

Saturation vapor pressure & dew point temperature

Saturation vapor pressure (= maximum vapor pressure)

(Eq. 1.6)

Td = dew point temperature [°C]es = saturation vapor pressure [mb]

Saturation vapor pressure depends only on temperature. It increases with temperature.

Dew point:Temperature to which a parcel of moist air would have to be cooled (under constant pressure and water content) before condensation starts.

+

−×=79.242T

6.4278exp107489.2ed

8s

Relative humidity

Relative humidity is a measure of the degree of saturation of the air. Precipitation is associated with a relative humidity of 100%.

see

pressurevaporsaturationpressurevaporactualRH ==

Example

At a weather station, the air pressure is measured to be 101.1 kPa, the air temperature is 22 °C and the dew point temperature is 18 °C . Calculate the corresponding

a) Vapor pressure

b) Relative humidity

c) Specific humidity

d) Air density

Conversion: 101.1 kPa = 1011 mb (Appendix B)

First calculate vapor pressure e and saturation vapor pressure es using:

+

−×=79.242T

6.4278exp107489.2ed

8s

Solution

Relative humidity = RH = 20.60/26.40 = 78%

mb40.2679.24225

6.4278exp107489.2e

mb60.2079.24218

6.4278exp107489.2e

8s

8

=

+−×=

=

+−×=

Specific humidity:

Air density:

airkg/waterkg0128.06.20378.01011

6.20622.0e378.0P

e622.0q

=

×−×

=−

=

[ ]

[ ]

3

33

3

ddwm

m/kg2.1cm/g102.1

60.20378.01011)22273(1087.2

1

e378.0PTR

1

=

×=

×−+×

=

−=ρ+ρ=ρ

−

Phase changes

Phase change requires/produces heat (energy)

Latent heat of evaporation = Latent heat of condensation

Latent heat of melting / freezing:

CinT],g/cal[T57.03.597LL oce −=−=

]g/cal[7.79LL fm =−=

SolidIce

FluidWater

GasVapor

Example

Calculate the energy required to heat 1 liter of water from 0ºC to 100ºC. Then calculate the energy required to evaporate the water (at 100ºC).

Solution

Specific heat: energy required to raise the temperature of 1g of a substance by 1ºC.

Specific energy of water: C)-cal/(g1C Ow =

1 liter of water = 1000g water. Energy required to heat 1 liter of water from 0ºC to 100ºC:

Evaporation energyLatent heat of evaporation at 100ºC:

Required evaporation energy:

cal000,100C100C)cal/(g1g1000TMC oow =××=∆

cal/g3.540)0100(57.03.597Le =−−=

cal300,540cal/g3.540g1000MLe =×=

Measurement of vapor pressure: The psychrometer

Psychrometer:– Two identical glass thermometers– One has a wet fabric applied to the liquid bulb– A fan blows air over the thermometers

Dry-bulb thermometer measures air temperature.Wet-bulb temperature is reduced due to evaporation.

t: dry-bulb temperature, [°C]tw : wet-bulb temperature, [°C]ew: saturation vapor pressure corresponding to the

wet-bulb temperature, [mb]: psychrometer constant

)tt(ee ww −γ−=

C/mb66.0 o=γ

Sling psychrometer

Example

A psychrometer indicates a dry-bulb temperature of 40°C and a wet-bulb temperature of 30°C. What are the vapor pressure and the relative humidity?

Solution:Saturation vapor pressure corresponding to the wet-bulb temperature:

The psychrometer equation yields:

mb4.4279.242)30T(

6.4278exp107489.2e 8w =

+=

−×=

mb8.35)3040(66.04.42)tt(ee ww

=−−=

−γ−=

The saturation vapor pressure at air temperature:

Relative humidity = RH = 35.8/73.9 = 48.5%.

mb9.7379.242)40T(

6.4278exp107489.2e 8s =

+=

−×=