Water in the atmosphere

Water in the atmosphere makes all variety of the weather. An important element of the weather is cloudiness. There are many types of clouds. Some of them are beautiful, some gloom, some are terrible.

Of course, a fat lot they care what we think of them, but it is not so for us. The form, shape, and movement of clouds are indicators of the processes occurring in the atmosphere. It means that the clouds can serve as predictors of the weather. Therefore, the real meteorologists should be familiar with all aspects of the cloud “life”.

Precipitation, like cloudiness, are of different kind: rain, snow, drizzle, sleet etc. In turn, the rains can be divided into different forms: widespread, pouring, drizzling. There are some special form of rain. Every of them has its inherent name.

1

The names are: Mushroom, blind, blood, glazed rains. And still there is one particular one the people call “TSAREVNA’S TEARS”. That is the rain which can not be named by any other name but this.

The drops of this rain look larger than usual raindrops, They seem to fall slower from a small cloud. The Sun shinning from a side and reflecting from the drops makes them as if they are made with gold. Being transparent, they bear blue color from that part of the sky which is not covered with clouds.

Gold and blue combination makes them so beautiful that the name “ tsarevna’s tears” seems to be the most appropriate name for this rain.

2

Distinctive properties of the water

The water in the atmosphere is found in all three phases: vapor, liquid, and ice.

Special character of the water density variation.Other kindred

w T 00 C 1g / cm3

Density

substances

Water

0.91g / cm3

ice

T 0

0

C

T°C

0°

4°

Water heat capacity significantly changes when congealing to the

solid state.

C

w

4187 J

kg K

C

2114

J

kg K

That is

ice

not so for other kindred substances.

Water freezing and boiling temperature are much higher than

that of other kindred chemical combinations.

3

Water melting and evaporation latent heat is rather high

L	324 kJ	kg	L 2500 kJ	kg
m

Water is a good solvent, it has chemical activity (iron rusts as contacting water)

Liquid water density varies with temperature a little. It can be

regarded as constant (1 g/cm³), as well as ice (0.91 g/cm³).

Water vapor heat capacity can be also regarded as non- depended on temperature variation.

C	wv	1386 J	kg K	C	pw	1846 J	kg K

C	v	718 J	kg K	C	p	1005 J	kg K

4

Evaporation and condensation

			A number of molecules comes off, Noff
			A number of molecules comes back, Nback
T T0			Noff	Nback					Evaporation	T T
			Noff	Nback					Saturation state at
										0
		At T1 T0 Noff		Nback					Condensation
If the temperature in the closed space increases to become T2 T1,
evaporation will begin again until				Noff Nback
e E		Evaporation goes on		Noff Nback
e E		Saturation has been reached			Noff				Nback
e E		Condensation takes place			Noff Nback

5

Thermodynamics of the water phase transfer

The following processes for the water phase transfer from state 1 to state 2 are possible

Water vapor

Ice

Liquid water

The first law of thermodynamics can be applied to describe the water

phase transfer processes

dq du edv

Let’s introduce the notion of thermodynamic potential Ф u ev T

denotes entropy (it is a term known from general physics) d dq
				T
	dq Td du edv		du edv Td 0

6

Transfer from one phase to another goes at the constant temperature

2

dq T 2 1 u2 u1 E v2 v1

1

T 2 T 1 u2 u1 Ev2 Ev1

u1 Ev1 T 1

u2 Ev2 T 2

Ф1 Ф2

Ф1

Ф2

Thermodynamic potential remains unchanged at the water phase

transfer from one state to another.

At temperature T+dT, Ф+dФ, and E+dE., and

Ф1 dФ1

Ф2 dФ2

Ф u ev T

,

dФ du Edv Td vdE dT

Recal ling that

dE

dФ vdE dT,

0

2

1

v1dE 1dT v2dE 2dT

dT

v

v

2 1 dT v2

v1 dE

2

1

7

dq Td ;

dq

d T ;

2

dq

1

2

L1,2

1 dq

Here L1,2 is specific latent heat

2

1

1 T

T

T

that is released as water

transfers from state 1 to state 2

dE

L1,2

Clausius – Clapeyron

For practical

equation

dT

T v2

v1

purposes the

quantity 2,72 Тis

neglected because it

For the process

1. Liquid water

2. Water vapor

is very small (T°C).

L L 2,72 T 2500 2,72T kJ

L

kg

Therefore, the latent

1,2

0

2500 kJ

const

heat is adopted as

v2 v1

L L

kg

constant.

L

0

T 500 C 2,72 T 136

dE

Ev RwT

dE

LE

L 2364 kJ kg

dT

T v2

RwT

dT

RwT

v E

2

T 500 C 2,72 T 136

L 2636 kJ

kg 8

The formula above can be transformed in the following way:

dE

LE

dE

LdT

dT

R T 2

E

R T 2

w

w

T0 273.15K

Adopting

E0 6.1078hPa

R

460 J

kg K

w

Doing the same reasoning, we’ll obtain the similar formula for sublimation process.

1. Ice Water vapor

Much better results were obtained with empirically determined coefficients “a” and “b”

For water

a=7.63

b=241.9

E

dE

L T dT

E

T T 2

E

R

0

w

0

ln

E

L

1

1

R

E

0

T

T

w

0

8.62T E E0 10273.15 T

9.76T Ei E0 10273.15 T

aT

E E0 10b T

For ice

a=9.5

b=265.5

Magnus formula

9

Magnus curve

70

60

50

hPa

40

Water

Ice

30

B

20

led

C

Water

o

o

r

c

e

p

u

e

vapor

S

dic

n

A

10

ater

a

w

0

T°C

-20

-10

0

10

20

30

40

A-Under saturated air B-Super saturated air

C-Saturated air

10