In order to study the atmospheric flows, a parcel of air is defined using the state variables. These variables define the state of an element of the atmosphere. The three important state variables are density, pressure and temperature. For an explanation of atmospheric pressure and experiments you can perform to examine the force exerted by the weight of air, go to "http://kids.mtpe.hq.nasa.gov/air_pressure/index.html"

The units and dimensions for the state variables are given in the following table.

Humidity is the fourth important variable in the study of atmospheric flows which tells us about the amount of water vapor present in a sample of moist air.

Meteorologists also use the term specific volume instead of density. The specific volume is defined as:

Specific Volume, = 1 / Density

Problem 1

Determine the pressure, both absolute and gauge, exerted at the bottom of the column of liquid 1 meter high, with density of 1200 kg / m3

Solution

Pgauge = (density of liquid) X ( acceleration due to gravity) X (height of liquid column)

Pgauge = ( 1200 kg/m³ ) X ( 9.7 m/s² ) X ( 1 N/kg/m/s²)

Pgauge = 11.760 kN/m2

Pgauge = 11.760 kPa
 

Pabsolute = Pgauge + Patmospheric

Pabsolute = 11.760 kPa + 101.3 kPa

Pabsolute = 113.06 kPa

EQUATION OF STATE

The relationship between the three state variables may be written as:

For a perfect gas,

where,

The specific gas constant for dry air, R d = 0.287 Joules / gm /^oK, and for water vapor, R v = 0.461 Joules / gm /^oK. The specific gas constant for wet air will not be constant quantity but will depend on mixing ratio.
 

Problem 2

Calculate the density of a gas with a molecular weight of 29 @ 1 atm(absolute) and 80 ^oF. Gas constant, R = 0.7302 ft³atm/lb-mole^oR

Solution

Absolute Temperature = 80 ^oF + 460 = 540 ^oR

Density = P ( molecular weight) / RT

Density = ( 1atm. ) . (29 lb/lb mole) / ( 0.7302 ft³atm/lb-mole^oR). (540 ^oR)

Density = 0.073546 lb/ ft³

Solve this problem online using applet DENS 1.0.

First Law of Thermodynamics

The first law of thermodynamics is based on the law of conservation of total energy of a thermodynamic system which undergoes a change of state. Mathematically one can write it as:

Heat added per unit mass = (Change in internal energy per unit mass) + (work done by a unit mass)
 

Second Law of thermodynamics

There are several different statements for the second law of thermodynamics in the physics books. In summary, the law can be stated as "no cyclic process exists having the transference of heat from a colder to hotter body as its sole effect".

Specific Heats

The specific heat is defined as the amount of heat needed to change the temperature of unit mass by 1^oK. The specific heat can be computed at the constant volume or at constant pressure. The definitions are:

Specific Heat at Constant Volume

Specific Heat at Constant Pressure

The Carnot's Law provides a relationship between Cp and Cv. For a perfect gas,

C p - C v = R
 

For a perfect diatomic gas ( approximation to dry air), Cp and Cv can be obtained from,

C p = (7/2) . R, and

C v = (5/2) . R
 

For dry air, the value of

C pd = 1.003 Joules / gm / ^oK, and

C vd = 0.717 Joules / gm / ^oK

The ratio of Cp, and Cv is given by = Cp / Cv = 1.4 (for dry air). The value of  for dry air is 1.4. The value of  will be different for different gases.