#### Air and Water Vapor, Physics tutorial

Air around Us:

Air we breathe is readily available near surface of earth. It is composed of nitrogen (78%), oxygen (21%), argon (0.9%) and other gases (0.1%). At room temperature, mean molecular weight of air, M = 28.97; specific heat capacity at constant pressure, cp = 1.005kJkg-1K-1; specific heat capacity at constant volume; cv = 0.718kJkg-1K-1 the gas constant, R = 287.1Jkg-1K-1 and ratio of principal specific heat capacities, g = cp/cv = 1.4.

For water vapor at room temperature, molecular weight, M = 18.02; specific heat capacity at constant pressure cp = 1867Jkg-1K-1 the specific heat capacity at constant volume, cv = 1407Jkg-1K-1 the gas constant, R = 460.6jkg-1K-1; and ratio of principal specific heat capacities, g = cp/cv = 1.33.

Water and its Vapor:

Ordinary water may exist in seven phases, that is:

(i) Pure solid phase known as ice

(ii) Pure liquid phase commonly known as water

(iii) Pure vapor phase called steam

(iv) Equilibrium mixture of liquid and vapor phases

(v) Equilibrium mixture of liquid and solid phases

(vi) Equilibrium mixture of solid and vapor phases

(vii) Equilibrium mixture of solid, liquid and vapor phases.

Fusion occurs when solid changes to a liquid; vaporization occurs when liquid changes to a vapor; sublimation occurs when solid changes directly to a vapor. (At atmospheric pressure, sublimation temperature for CO2 is about -780C).

Macroscopic Properties of Pure Water:

Consider the piece of ice at state point S. If piece of ice is heated at constant pressure temperature rises until fusion line is reached. As soon as fusion line is encountered, melting starts. Melting procedure continues at constant temperature until all solid ice is changed to liquid. Further heating produces the increase in temperature. Temperature of liquid water continues to rise until vaporization line is encountered. As soon as vaporization line is reached, liquid water starts to change to vapor.

Pressure p0 is atmospheric. Horizontal line, passing through solid phase (S), liquid phase (L) and vapor phase (V), is a constant-pressure line. It illustrates that water at atmospheric pressure may be made to exist in solid, liquid and vapor phases. The vaporization process continues at constant temperature until all liquid water is changed to water vapor. Additional heating produces rise in temperature of the vapor. At atmospheric pressure, fusion temperature for water is 0oC and the vaporization temperature is 100oC.

The fusion line is almost vertical and large increase in pressure is required to lower melting temperature substantially. Solid-liquid mixture is signified by fusion line; liquid-vapor mixture is represented by vapor line; and solid-vapor mixture is represented by sublimation line. Triple point is state point where it is possible to maintain the equilibrium mixture of solid phase, liquid phase and the vapor phase. At triple point, all three stages of water co-exist in equilibrium.

Saturation Regions:

Liquid-Vapor Saturation Region:

Fusion line, the vaporization line and sublimation line represent saturation regions. Fusion line signifies saturation region between solid stage and liquid stage; vaporization line designates saturation region between liquid phase and vapor phase; sublimation line signifies saturation region between solid phase and the vapor phase. The vapor present in such a mixture is known as a saturated vapor. In saturation regions, temperature and the pressure stay constant. Though, there is a significant change in specific volume (that is volume per unit mass) in saturation regions.

To measure properties of liquid-vapor saturation region, we state quality x of saturation region as fraction of mass present in the vapor phase. We also state moisture y as fraction of mass present in liquid phase. Obviously, the sum of two fractions should be equal to unity. Thus, we may write.

x+ y = 1 or y = 1- x  or

Moisture = 1- x,

Here x = mass in vapor phase/total mass m

Wet Mixture:

The wet mixture is liquid-vapor mixture which has a quality x that is less than 100%. Subscripts s, l and v utilized to represent solid phase, liquid phase and vapor phase, respectively. Lower-case v used to designate specific volume (i.e. v = V m). This signifies that specific volume of saturated liquid becomes vl while specific volume of saturated vapor becomes vv. Of course, total volume V is given by

V = mlvl + mvvv

And total mass m is provided by

m = ml + mv

So that specific volume v of equilibrium liquid-vapor mixture would be provided by

v = V/m

Here ml is mass of liquid phase and mv is mass of the vapor phase. Therefore,

v = (mlvl + mvvv)m

v = (ml/m)vl + (mv/m)vv

v = (1-x)vl + xvv

Here x = mv/m and y = ml/m

Therefore v = vl+(vv - vl)x

Thus,

v = vl + xvlv

Where

vlv = vv - vl

Equation relates specific volume (v) to specific volume in liquid phase (vl), specific volume in vapor phase (vv) and quality (x) of saturation region.

Super-Cooled Liquid and Super-Heated Vapor:

Compressed liquid is one that exists at temperature which is lower than saturation temperature corresponding to its pressure. Compressed liquid is also known as a sub-cooled liquid. Superheated vapor is one which exists at temperature greater than saturation temperature corresponding to its pressure.

Energy Properties of Pure Substance:

Only two independent properties are essential to define state of simple, pure substance. Two independent properties are temperature and specific volume. In saturation regions, temperature and pressure are not independent properties. In fact, line of constant temperature is also line of constant pressure in all saturation regions. Temperature, pressure and specific volume are not the only properties of interest when considering pure substances. Other significant properties comprise specific internal energy u and specific enthalpy h. These energy properties may be defined as functions of temperature T and specific volume v in following way:

u = u(T,v) and h = h(T,v)

Equation relates specific volume v to vl, vv and x as

v = vl + xvlv in wet mixture region. By similar argument, you may write

u = vl + xvlv and h = hl + xhlv in wet mixture region. Here, ulv = uv - ul and hlv = hv - hl,

Here ulv is internal energy of vaporization and hlv is enthalpy of vaporization. At last, entropy s is another property which is very helpful in solving practical problems. Like specific internal energy u and specific enthalpy h, entropy s may be written in characteristic form

S = Sl + xSlv

Here

Slv = Sv - Sl and Slv is entropy of vaporization.

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