LECTURE 2

MOIST AIR PROPERTIES

AND CONDITIONING

PROCESSES

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Chapter 3

Moist air and the standard atmosphere

Ideal gas equation for air:

= Universal gas constant

= 1545.32 (ft-lbf)/(lb mole-R) = 8314 J/ (kg mole-K)

Ma = molecular mass of dry air = 28.965

Similarly, the molecular mass of water is 18.015, so gas constant for

water vapor is

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U.S. standard atmosphere

ASHRAE Handbook, Fundamentals Volume gives the following

definition of the U.S. Standard atmosphere:

1. Temperature at sea level is 59.0 F, 15 C, or 288.1 K

2. Pressure at sea level is 29.921 in. Hg (101.039 kPa)

3. Acceleration due to gravity is constant at g = 32.174 ft/s2 = 9.807

m/s2

4. The atmosphere consists of dry air, which behaves as a perfect

gas

Standard atmospheric pressure is also commonly taken to be 14.696 lbf/in2 or 101.325 kPa, which corresponds to 30.0 in. Hg, and standard atmospheric temperature is sometimes assumed to be 70 F (21 C).

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Higher altitudes Atmospheric pressure may be estimated as a function of

elevation by the following relation up to 60,000 ft (18,291 m):

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Daltons law of partial pressures

Moist air up to about 3 atm pressure obeys the perfect gas law with sufficient

engineering accuracy

The Dalton law for a mixture of perfect gases states that the mixture pressure

is equal to the sum of the partial pressures of the constituents:

Various constituents of the dry air may be considered to be one gas called

dry air, so

Consider a saturated mixture of air and water vapor at 80 F. Saturation

pressure pv of water is 0.507 psi. The mass density is calculated as below:

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Humidity definitions

Humidity ratio W is the ratio of the mass mv of the water vapor to the

mass ma of the dry air in the mixture

Relative humidity f is the ratio of the mole fraction of the water vapor xv in a mixture to the mole fraction xs of the water vapor in a saturated

mixture at the same temperature and pressure

Saturated air is air that has all the water vapor that it can hold

Relative humidity of 100% indicates the dew point is equal to the

current temperature and the air is maximally saturated with water

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For a mixture of perfect gases, the mole fraction is equal to the partial pressure ratio of each constituent. Therefore, the mole fraction of the water vapor is

Since the temperature of dry air and water vapor are assumed to be same in the mixture,

Using perfect gas laws for water vapor and dry air separately

Then

And

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Definitions contd.

Degree of saturation m is the ratio of the humidity ratio W to the humidity ratio Ws of a saturated mixture at the same

temperature and pressure:

Dew point td is the temperature of saturated moist air at

the same pressure and humidity ratio as the given mixture

As a mixture is cooled at constant pressure, the

temperature at which condensation first begins is the dew

point

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Definitions contd.

Enthalpy i of a mixture of perfect gases is equal to the sum of the enthalpies of each constituent,

and for the air-water vapor mixture is usually referenced to the

mass of dry air.

This is because the amount of water vapor may vary during some processes but the amount of dry air typically remains constant.

Each term in the above equation has the units of energy per unit mass of dry air. With the assumption of perfect gas behavior, the enthalpy is a function of temperature only.

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If 0 F or 0 C is selected as the reference state where the

enthalpy of dry air is 0, and if the specific heats cpa and cpvare assumed to be constant, simple relations result:

ig = enthalpy of saturated water vapor at 0 F = 1061.2 Btu/Ibm

cpa = specific heat of dry air = 0.240 Btu/ (Ibm-F)

cpv = specific heat of water vapor = 0.444 Btu/ (Ibm-F)

Plugging in these values, we get in IP units,

Or in SI units,

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Dry bulb temperature

Wet bulb temperature

Dry-bulb temperature is the temperature of air measured by a thermometer freely exposed to the air but shielded from radiation and moisture.

Dry bulb temperature is the temperature that is usually thought of as air temperature, and it is the true thermodynamic temperature.

It is the temperature measured by a regular thermometer exposed to airstream.

Wet-bulb temperature is a type of temperature measurement that reflects the physical properties of a system with a mixture of air and water vapor.

Wet bulb temperature is the lowest temperature that can be reached by the evaporation of water only.

It is the temperature one feels when skin is wet and is exposed to moving air.

Unlike dry bulb temperature, wet bulb temperature is an indication of the amount of moisture in the air.

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Adiabatic saturation The apparatus is assumed to operate so that dry air enters

at point 1 and completely saturated air leaves at point 2:

At temperature t2, the relative humidity f2 =100%

t2* is defined as adiabatic saturation temperature or

thermodynamic wet bulb temperature

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Steady-flow-steady-state

Plugging in and solving equations,

where

Humidity ratio of an air-water vapor mixture can be

determined from the entering and leaving temperatures

and pressures of the adiabatic saturator

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Wet bulb temperature and Psychrometric chart

A practical device used in place of the adiabatic saturator is the psychrometer.

This apparatus consists of two thermometers, one of which has a wetted cotton wick covering the bulb.

The temperatures indicated by the psychrometer are called the wet bulb and the dry bulb temperatures.

The dry bulb temperature corresponds to t1 and the wet bulb temperature is an approximation to t2

*

P1 and P2 are both atmospheric.

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Psychrometric chart

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Physical quantity Position in psychometric chart

Dry-bulb temperature Straight, vertical lines

Wet-bulb temperature Slanted lines within confines of chart

Humidity ratio Horizontal lines within confines of chart

Relative humidity Curved lines within confines of chart

Specific volume of air Slanted lines within the confines of chart

EnthalpyArea to the left of chart; major lines of constant enthalpy also extend through the chart

Saturation temperature Left boundary of chart; used for dew-point temperature

Nomograph Upper-left corner; can be used to find enthalpy

ProtractorUpper left corner; used for determining the sensible heat ratio, SHR, and the ratio of (Di/DW)

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Read the properties of moist air at 75 F db, 60 F wb, and standard sea-level

pressure from ASHRAE psychrometric chart.

The intersection of the 75 F db and 60 F wb lines defines the given state. This point on the chart is the reference from which all the other properties are determined.

Humidity Ratio W. Move horizontally to the right and read W = 0.0077 lbmv/lbma on the vertical scale.

Relative Humidity f. Interpolate between 40% and 50% relative humidity lines and read f = 41%

Enthalpy i. Follow a line of constant enthalpy upward to the left and read i= 26.4 Btu/lbma on the oblique scale.

Specific Volume v. Interpolate between the 13.5 and 14.0 specific volume lines and read v = 13.65 ft3/lbma.

Dew Point td. Move horizontally to the left from the reference point and read td = 50 F on the saturation curve.

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a

h b

g c

f e d

a humidification

b heating and humidifying

c sensible heating

d chemical dehumidifying

e dehumidifying

f cooling and dehumidification

g sensible cooling

h evaporative cooling

Basic air conditioning processes

Selected air conditioning processes

1. Heating or cooling of moist air

2. Cooling and dehumidifying of moist air

3. Heating and humidifying moist air

4. Adiabatic humidification of moist air

5. Adiabatic mixing of two streams of moist air

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Heating or cooling of moist air

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Ex. 3-4

Find the heat transfer rate required to warm 1500 cfm

(ft3/min) of air at 60 F and 90% relative humidity to 110 F

without the addition of moisture.

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Cooling and dehumidifying of moist air

The last term is very small and usually neglected

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Cooling and dehumidifying process involves both sensible and latent heat transfer

Sensible heat transfer rate is associated with the decrease in dry bulb temperature

Latent heat transfer rate is associated with the decrease in humidity ratio

Total heat transfer rate is

Sensible Heat Factor (SHF) is defined as

SHF is negative if absolute value of is greater than

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Numerical problem

Air is cooled from 80 F db and 67 F wb until it is saturated

at 55 F. Using Chart 1a, find

(a) the moisture removed per pound of dry air,

(b) the heat removed to condense the moisture,

(c) the sensible heat removed, and

(d) the total amount of heat removed.

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Heating and humidifying moist air Energy balance equation

Mass balance equation

Solving, or

which describes a straight line that connects the initial and

final states on the psychrometric chart.

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Adiabatic humidification of moist air

When moisture is added to moist air without the addition of heat, = 0.

So

Theoretically, the adiabatic humidification process can take many different paths depending on condition of water used.

In practice, water will vary from a liquid at about 50 F (10 C) to a saturated vapor at about 250 F (120 C).

Practical range of is shown on the chart and protractor of next figure.

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Ex. 3-6

Moist air at 60 F db and 20% relative humidity enters a heater

and humidifier at the rate of 1600 cfm. Heating of the air is

followed by adiabatic humidification so that it leaves at 115 F db

and a relative humidity of 30%. Saturated water vapor at 212 F is

injected. Determine the required heat transfer.

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Combined heating and humidifying process

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Adiabatic mixing of two streams of moist air

Energy balance:

Mass balance on dry air

Mass balance on water vapor:

Combining all equations and eliminating 3

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Ex. 3-72000 cfm of air at 100 F db and 75 F wb are mixed with 1000 cfm of air at 60 F db and 50 F wb. The process is adiabatic, at a steady flow rate and at standard sea-level pressure. Find the condition of the mixed stream using the lever rule.

Lever Rule: The lengths of the various line segments are proportional to the masses of dry air mixed.

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Space air conditioning The complete air-conditioning system may involve two or more

of the processes just considered.

In air conditioning of space during the summer, the air supplied must have a sufficiently low temperature and moisture content to absorb the total cooling load of the space.

As the air flows through the space, it is heated and humidified.

Some outdoor air is usually mixed with the return air and sent to the conditioning equipment, where it is cooled and dehumidified and supplied to the space again.

During the winter months, the same general processes occur, but in reverse.

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The cooling and dehumidifying coil cannot cool all of the air passing through it to the coil surface temperature.

This fact makes the coil perform in a manner similar to what would happen if a portion of the air were brought to

saturation at the coil temperature and the remainder

bypassed the coil unchanged.

where td is the apparatus dew point of the cooling coil

The resulting mixture is unsaturated air at this point.

Sensible Heat Factor and Bypass Factor

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Or , where b is the fraction of air bypassed

The coil sensible heat transfer rate is

The bypass factor is not used extensively for analysis

The ability to model coils with a computer makes the

procedure unnecessary.

However, some manufacturers still use the concept in

catalog data, where the bypass factor is determined from

simulation and experiment.

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