Properties of Air and Water Vapor

Air can be considered as an ideal gas, which has a definition

Pv = RT, (4.17)

Or

P = pRT. (4.18)

This is the state equation of an ideal gas, where p is pressure, v is specific vol­ume, p is density, R is the gas constant, and T is absolute temperature. In an

Airflow there is a transfer of heat from one layer to another. This change of

TABLE 4.2 Constants for Gases Pa (kg nr3) Co (m s-‘) R O ^ -• K-1) Vo (kg s-‘nr1) T Air 1.275 332 287.04 1.717 x JO“5 1.402 O, 1,409 315 259.78 1.928 x ID-* 1.399 N2 1.234 37 296.75 1.625 x 10-‘ 1.400 H2 0.0887 1260 4124.0 8.350 x 10-J 1.409 CO, 1.949 259 188.88 1.370 xlO"-5 1.301

Pn = 100 kPa, T0 = 273. J 5 K

State is adiabatic and reversible. Such an adiabatic reversible process is called an isentropic state change: one in which the entropy remains constant.

The thermodynamic equations to be considered at this stage are

T ds = dh — v dp, (4.’19)

W7here

S is the entropy, kj kg-i Kr1 h is the enthalpy, kj kg-1

For isentropic process we can w7rite

Dh = v dp. (4.20)

The specific enthalpy change is defined as

Dh = Cp dT. (4.21)

The state equation gives

P dv + v dp = R dT. (4.22)

When dT is eliminated from this equation, the following differential equation results:

/

Dv V

1 R _ VP /

Solving,

Puc/(‘-p R) _ _ (4.24)

When Cp and R can be treated as constants, the equation is usually written as

PvT = constant. (4.25)

For a gas of one-atom molecules к = 5/3 = 1.67. For a gas of two-atom mole­cules к = 7/5 = 1.4. For gas of molecules containing three or more atoms

К = 9/7 = 1.3.

For air (mostly a mixture of N2 and 02) the following is valid:

PvlA = Po^o’4 = constant. (4.26)

Water vapor is considered as an ideal gas and is defined by

Pv = ah + h, (4.27)

Where a and b are constants. Converting,

P dv + v dp = a dh (4.28)

And as

Dh = v dp, (4.29)

Giving

Pv/(i-a) _ constant, (4.30)

Pvk = constant, (4.31)

Where k is an empirically determined constant. For water vapor (H70) k = 1.3.

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