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

2 The Hydrostatic Equation

3 The First Law of Thermodynamics

4 Adiabatic Processes

5 Water Vapor in Air

6 Static Stability

7 The Second Law of Thermodynamics

WH 3.1

WH3.2, not review in this class?

WH3.3

WH3.4

WH3.5

WH3.6

WH3.7

The Kinetic Theory of GasesThe 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 firstunderstand the way in which a gas behaves, especially whenheat is added or removed. Thus, we begin by studyingthermodynamics and its application in simple atmosphericcontexts.

The Kinetic Theory of Gases

Fundamentally, a gas is an agglomeration of molecules. Wemight consider the dynamics of each molecule, and the interactionsbetween the molecules, and deduce the properties ofthe gas from direct dynamical analysis. However, consideringthe enormous number of molecules in, say, a kilogram ofgas, 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 considerthe average behavior of the gas. This is the approach calledthe 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 thethermodynamic 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 LawsThe pressure, volume, and temperature of any material arerelated by an equation of state, the ideal gas equation. For

most purposes we may assume that atmospheric gases obeythe ideal gas equation exactly.

The ideal gas equation may be writtenpV = 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 writep = 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