METR125: Physical Meteorology: Lecture: Atmospheric Thermodynamics (1)

1
METR125 Physical MeteorologyLecture
Atmospheric Thermodynamics (1)

• Prof. Menglin S. Jin
• San Jose State University, Meteorology

Acknowledgements modified from Prof Peter
Lynchs online notes
2
Atmospheric Thermodynamics

• Thermodynamics plays an important role in our
  quantitative understanding of atmospheric
  phenomena, ranging from the smallest cloud
  microphysical processes to the general
  circulation of the atmosphere.
• The purpose of this section of the course is to
  introduce some fundamental ideas and
  relationships in thermodynamics and to apply them
  to a number of simple, but important, atmospheric
  situations.
• The course is based closely on the text of
  Wallace Hobbs and GY

3
Outline
WH 3.1
1 The Gas Laws
WH3.2, not review in this class?
2 The Hydrostatic Equation
WH3.3
3 The First Law of Thermodynamics
WH3.4
4 Adiabatic Processes
5 Water Vapor in Air
WH3.5
6 Static Stability
WH3.6
WH3.7
7 The Second Law of Thermodynamics
4
The Kinetic Theory of Gases
The atmosphere is a gaseous envelope surrounding
the Earth. The basic source of its motion is
incoming solar radiation, which drives the
general circulation. To begin to understand
atmospheric dynamics, we must first understand
the way in which a gas behaves, especially
when heat is added or removed. Thus, we begin by
studying thermodynamics and its application in
simple atmospheric contexts.
5
The Kinetic Theory of Gases
Fundamentally, a gas is an agglomeration of
molecules. We might consider the dynamics of each
molecule, and the interactions between the
molecules, and deduce the properties of the gas
from direct dynamical analysis. However,
considering the enormous number of molecules in,
say, a kilogram of gas, and the complexity of the
inter-molecular interactions, such an analysis is
utterly impractical.
6
The Kinetic Theory of Gases
We resort therefore to a statistical approach,
and consider the average behavior of the gas.
This is the approach called the kinetic theory of
gases. The laws governing the bulk behavior are
at the heart of thermodynamics. We will not
consider the kinetic theory explicitly, but will
take the thermodynamic principles as our starting
point.
7
The Gas Laws

• The pressure, volume, and temperature of any
  material are related by an equation of state, the
  ideal gas equation. For most purposes we may
  assume that atmospheric gases obey the ideal gas
  equation exactly.

8
The Gas Laws
The pressure, volume, and temperature of any
material are related by an equation of state, the
ideal gas equation. For most purposes we may
assume that atmospheric gases obey the ideal gas
equation exactly. The ideal gas equation may be
written pV mRT Where the variables have the
following meanings p pressure (Pa) V volume
(m3) m mass (kg) T temperature (K) R gas
constant (JK-1 kg-1)
9
Again, the gas law is pV mRT The value of
R depends on the particular gas. For dry air, its
value is R 287 JK-1 kg-1.
Exercise Check the dimensions of R.
10
Again, the gas law is pV mRT The value of
R depends on the particular gas. For dry air, its
value is R 287 JK-1 kg-1.
Class Exercise Check the dimensions of R.
Since the density is ? m/V , we may write p
?RT . Defining the specific volume, the volume
of a unit mass of gas, as a 1/?, we can
write pa RT .
11
(No Transcript)
12
(No Transcript)
13
(No Transcript)
14
(No Transcript)
15
(No Transcript)
16
(No Transcript)
17
(No Transcript)
18
(No Transcript)
19
(No Transcript)
20
(No Transcript)
21
(No Transcript)
22
(No Transcript)
23
(No Transcript)
24
(No Transcript)
25
(No Transcript)
26
(No Transcript)
27
(No Transcript)
28
(No Transcript)
29
(No Transcript)
30
(No Transcript)
31
(No Transcript)
32
(No Transcript)
33
(No Transcript)
34
(No Transcript)
35
(No Transcript)
36
(No Transcript)
37
(No Transcript)
38
(No Transcript)
39
(No Transcript)
40
(No Transcript)
41
(No Transcript)
42
(No Transcript)
43
(No Transcript)
44
(No Transcript)
45
(No Transcript)
46
(No Transcript)
47
(No Transcript)
48
(No Transcript)
49
(No Transcript)
50
END
51
Class Practice

• At an altitude of 5600 m above sea level, where
  the standard sir pressure is 500 millibars and
  the standard air density is 0.69 kg/m3, calculate
  the standard air temperature

52
Class Practice

• At an altitude of 5600 m above sea level, where
  the standard sir pressure is 500 millibars and
  the standard air density is 0.69 kg/m3, calculate
  the standard air temperature
• P?RT
• 50000b 0.69kg/m3 x 287 JK-1Kg-1 x T
• T 50000bar/(0.69kg/m3 x 287 JK-1Kg-1 )
• 252.48 K

53
Class Participation

• We know that averaged global surafce temperature
  is 15C. If the average air density at sea level
  is 1.226 kg/m3, what would be the average sea
  level pressure?

P ?RT 1.226 kg/m3 x 287J-1K-1Kg-1 x
(15273.15) K 1013 mb
54
(No Transcript)