# ME 414514 HVAC Systems - Topic 3 Moist Air Properties and by rtu18834

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ME 414/514 HVAC Systems – Topic 3

Moist Air Properties and Conditioning Processes: Psychrometrics

Thermodynamic data for calculations in this class can be obtained from several sources:
• Psychrometric charts supplied in the Appendix of the text (note that these
charts were prepared by the Center for Advanced Thermodynamic Studies
(CATS) at the University of Idaho or from ASHRAE
• PSYPROPS from CATS, download from the course Internet site (Topic 3)
• ALLPROPS from CATS, download from the course Internet site (Topic 3)
• EES (Engineering Equation Solver)

Fundamental Humidity Parameters
Psychrometric Chart
Nomenclature
T - absolute temperature (K or R)
t - °C or °F

Subscripts:    v - water vapor
a - dry air

1. Dry bulb temperature: temperature of the
mixture as measured by a static thermometer (Tdb
or T)

2. Humidity ratio:

mv
W =
ma

If ideal gas approximations are used:

p vVv        R
RT     R p    M p   M p     18.015 p v         p
W = v v = a v = a v = v v =               = 0.6219 v
p aV a Rv p a R p a M a p a 28.965 p a         pa
Ra Ta         Mv

Here we applied Dalton’s Law: Both components in the mixture occupy the same volume
V and exist at the same temperature T. Thus, the pressures of each component are partial
pressures:

P = pa + pv

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Topic03 Psychrometrics.doc

3. Relative humidity

xv                   mole fraction of water vapor
φ=               =
xs   T ,P
mole fraction of water vapor
in a saturated mixture at the same T , P

A saturated mixture: the water vapor is at its vapor pressure for the given T. If the ideal
gas assumption is used:

pv P pv
φ=       =
ps P ps

The state location is sketch below on a T-s diagram for water:

Note that we can use the relative humidity to derive another expression for the specific
humidity:

pv          p
W = 0.6219        = 0.6219φ s
pa          pa

4.Dew Point Temperature: The temperature where water vapor condenses when the
mixture is cooled at constant pressure.

Tdp = Tsaturation at pv

T-s diagram on next page

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Topic03 Psychrometrics.doc

Thermodynamic Properties

In air conditioning calculations, energy transfer rates are determined from mixture
properties and knowledge of the volume flow rate of the mixture. Using the Dalton
model of the mixture, the air and the water vapor exist at the same volume. Therefore,
from a volume flow rate perspective,

V = Vv = V a                   & &       &
V = Vv = V a
The air conditioning industry has chosen to base the specific thermodynamic properties
on a per unit mass of dry air basis.

Specific enthalpy, h

H = Ha + Hv = maha + mvhv
H            m
≡ h = ha + v hv
ma            ma
h = ha + Whv
The units of h are BTU/Lbma or kJ/kga.

Specific volume, v

Assuming that the ideal gas law is valid:
m RT m RT
V = a a = v v
pa    pv
V          RT    RT
≡ v = a =W v
ma          pa    pv

The units of v are ft3/Lbma or m3/kga.

How many properties are required to identify the thermodynamic state of the air-water
vapor mixture?

Apply the Gibbs phase rule:

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Topic03 Psychrometrics.doc

F=C–P+2

F = number of independent properties required
C = number of components in the mixture
P = number of phases present

Single phase mixture: F = 2 – 1 + 2 = 3 properties
Saturation states:    F = 2 – 2 + 2 = 2 properties

Single phase states – Pressure, P, and temperature, tdb, are easily measured. W, φ, h,
and v are not easily measured. However, knowing any one of these additional properties
fixes the single phase thermodynamic state of the mixture.

Adiabatic saturation – a process that can be used to identify a third property (W) in
addition to P and tdb. This fixes the single phase state of the air-water vapor mixture.

Recall, that adiabatic refers to the transfer of energy within the system only, no heat
transfer outside of the system.

Apply the First Law of Thermodynamics to the control volume:

∑m h − ∑m h
&
e
&
e e
i
i i   =0

(ma 2 ha 2 + mv 2 hv 2 ) − (ma1ha1 + mv1hv1 + mw hw ) = 0
&           &              &        &        &

&
mw
ha 2 + W2 hv 2 − ha1 − W1 hv1 −      h =0
& w
ma

Apply mass continuity to the control volume:

ma 2 + mv 2 = ma1 + mv1 + m w
&      &      &     &     &

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Topic03 Psychrometrics.doc

&
mw
1 + W2 = 1 + W1 +
&
ma

&
mw
= W2 − W1
&
ma

Substitute into the 1st Law:

ha 2 + W2 hv 2 − ha1 − W1 hv1 − (W2 − W1 )hw = 0

(ha 2 − ha1 ) + W2 (hv 2 − hw ) − W1 (hv1 − hw ) = 0

fg      (
C pa (t 2 − t1 ) + W2 h ∗ − W1 hv1 − hw = 0
∗
)
C pa (t 2 − t1 ) + W2 h ∗
W1 =
fg

(hv1
∗
− hw    )
The * refers to properties at the adiabatic saturation temperature.

∗                  ∗
pv 2 = p s     at t 2

mv 2         p                p ∗v2
W2 =        = 0.6912 v 2 = 0.6912
ma 2         pa 2          P2 − p ∗ v 2

Therefore, the measurement of P1, P2, t1 and t2 allow the calculation of W1 which is the
3rd property needed to fix the single phase state of the mixture state 1.

A New Problem

What is t2* and how can it be measured conveniently?

The temperature in this special process is called the adiabatic saturation temperature.
This temperature can be very closely approximated by the thermodynamic wet bulb
temperature, twb.

The wet bulb temperature can be measured with a thermometer that has the bulb
exposed to a saturated wick. A sling psychrometer has both wet and dry bulb
thermometers. Reading these values, along with the barometric pressure, fixes the
thermodynamic state of the air. The air properties can be computed using ideal gas
relations, or they can be determined using a psychrometric chart. PSYPROPS is the
‘engine’ that was used to calculate the psychrometric chart properties.

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Topic03 Psychrometrics.doc

Note that thermodynamic data for energy is calculated according to a reference state –
and unfortunately this reference state is different in the metric and British charts! For
example, take the enthalpy of moist air at one set of drybulb and wetbulb temperatures
from a British psychrometric chart. Convert it to SI units. You will calculate a different
value than if you read the enthalpy from the SI chart with the temperatures converted to
centigrade! The message here is that all properties are best taken from their respective
tables/charts in the system of units appropriate for the problem.

Classical Air Conditioning Processes

1.   Heating/cooling without a change in water vapor mass
2.   Heating with humidification
3.   Cooling with dehumidification
5.   Adiabatic mixing of two or more moist air streams

The 1st Law of Thermodynamics

In HVAC analysis, we would like to express energy transfer rates as positive values.
Therefor, it is best to express the steady state version of the 1st Law as

⎡energy transfer ⎤ ⎡energy transfer           ⎤
⎢rate into the C.V .⎥ = ⎢rate out of the C.V .⎥
⎣                   ⎦ ⎣                       ⎦

for all HVAC processes. This means that we need to know which direction the energy
transfers are going.

In nearly all HVAC analyses, we either know, or are interested in, the volume flow rate
of the moist air at some point in the system. Since we have adopted the Dalton model for
the mixture of dry air and water vapor, recall

& &      &
V = Vv = V a

We have also expressed the specific thermodynamic properties of the mixture on a per
unit mass of dry air basis. Therefore, energy transfer rates can be computed by
multiplying the specific energy changes by the mass flow rate of dry air, where the mass
flow rate of the dry air is

&
V Va &
ma =
&         =
v    v

Bring copies of the psychrometric charts from the handout link to class. We will solve
several example problems in class.

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