The behavior of gasses in the atmosphere (atmospheric thermodynamics)

 

Thermodynamics is the study of the relationship between mechanical work and the internal energy of a gas (its heat content)

 

 

The state variables

 

State: The condition of the system (or part of the system) at an instant of time measured by its properties.

 

The thermodynamic properties of a gas are specified by the three state variables:

 

1.     Pressure    

2.     Temperature  T

3.     Density       

(or its inverse, specific volume )

 

Pressure

is force per unit area exerted by the molecular motions of a gas.

 

Units: a) the unit of force in the MKS system (SI) is the Newton (N)  kg m s-2

(F=ma, mass x acceleration)

 

A force of 1 N will cause an acceleration of 1 m s-2 in a mass of 1 kg

 

b) the unit of pressure is Newtons per square meter, which is called the Pascal (Pa).

 

1 Pa  1 N m-2  kg m-1 s-2

 

c) the common meteorological unit of pressure is the millibar (1 bar/1000). The conversion to Pa is as follows:

 

        1 mb  100 Pa

So,  1000 mb  100 k Pa (kilopascals)

 

d) other units in common usage are inches or cm of mercury (the height of a column of mercury in a barometer)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A “standard atmosphere” pressure is the globally averaged MSL atmospheric pressure and is numerically equal to

        A standard atmosphere

        = 1013.25 mb

        = 1013.25 h Pa (hecto Pascal)

        = 101.325 k Pa

        = 76.0 cm of Hg

        = 29.92 inches of Hg

        = 14.7 lb/sq inch

 

 

Temperature T

 

The degree of hotness, which determines the direction of heat transfer (hot to cold). It is related to the internal energy of a body or mass of material.

 

(Units: oC, oF, K)

 

 

Density

 

is mass per unit volume (kg m-3)

 

 is volume per unit mass (m3 kg-1)

 

 

The gas laws and the equation of state

 

We need to know that happens to a gas when it is subjected to a change in pressure (air spirally in towards a low pressure center, or being forced upwards over a mountain range, or being lifted by the action of thermal convection). A relationship is needed between the state variables. This is provided by the equation of state which is derived from two empirically laws:

 

1.  Boyle’s law:  at constant T

 

              p1 V1 = p2 V2 (for a fixed mass of gas)

 

              where V is the volume.

 

2. Charles’ law: at constant pressure

                   (for a fixed mass of gas)

 

               as long as T is expressed in Kelvin

               (K = oC + 273.15)

 

 

Combing the gas laws and taking a fixed mass of gas from one state to another. i.e.

 

     p1, V1, T1 => p2, V2, T2

 

 

We obtain the equation of state

                                                                                

 

From Avogadro’s hypothesis, gases containing the same number of molecules occupy the same volumes at the same temperature and pressure. Therefore,

 

    

 

where * is the universal gas constant (= 8314.3 J/K/kmol) and n the number of kilomoles of a gas.

 

 

m: mass of the gas

M: molecular weight (one kilomore of a gas) in kilograms

       

             

 

R: (specific) gas constant for 1 kg of a gas

 

 

Equation of state

 

 

Isothermal process:

 

T is constant, pressure increased density increases

 

Isobaric process:

 

p is constant, T increased density decreases

 

 

Dry air

 

For example, for dry air with a molecular weight of 29

 

       

        : gas constant for 1 kg of dry air

                  

                 

Water vapor

 

For water vapor with a molecular weight of 18

 

       

        : gas constant for 1 kg of water vapor

 

 


Is the gas constant for moist air larger or smaller than for dry air? (Larger!)