METR125: Physical Meteorology:
Lecture: Atmospheric
Thermodynamics (1)
Prof. Menglin S. Jin
San Jose State University, Meteorology
Acknowledgements: modified from Prof Peter Lynch’s online notes
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 G&Y
Outline
1 The Gas Laws
WH 3.1
2 The Hydrostatic Equation
WH3.2, not review in this class?
3 The First Law of Thermodynamics
WH3.3
4 Adiabatic Processes
WH3.4
5 Water Vapor in Air
6 Static Stability
7 The Second Law of Thermodynamics
WH3.5
WH3.6
WH3.7
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.
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.
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.
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 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)
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.
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 ρ= m/V , we may write
p = ρRT .
Defining the specific volume, the volume of a unit
mass of gas, as α = 1/ρ, we can write
pα = RT .
END
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
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=ρRT
50000b = 0.69kg/m3 x 287 JK-1Kg-1 x T
T = 50000bar/(0.69kg/m3 x 287 JK-1Kg-1 )
= 252.48 K
Class Participation
• We know that averaged global surafce
temperature is 15°C. If the average air
density at sea level is 1.226 kg/m3, what
would be the average sea level pressure?
P= ρRT = 1.226 kg/m3 x 287J-1K-1Kg-1 x (15+273.15) K = 1013 mb