PSYCHROMETRY AND HVAC
Psychrometry (hygrometry): science of moist air
HVAC: Heating, ventilating, and air-conditioning
• I am teaching Engineering Thermodynamics to a class of 75 undergraduate students.
• I plan to go through these slides in one 90-minute lecture.
Zhigang Suo, Harvard University
https://www.youtube.com/playlist?list=PL2E9_TlQKsGQ4PbJ0KJEvIFxjVUCw7s30
Watch this tutorial on psychrometry
Plan
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Psychrometric properties
Measuring humidity
Psychrometric chart
HVAC
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Dry air
name
formula
Molar mass M
kg/kmol
number fraction y
nitrogen
N2
28
0.78
oxygen
O2
32
0.21
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Moist air
a mixture of many gases and water vapor, modeled as an ideal-gas mixture
Dry air is far from the dome
Water vapor is near the dome
Partial pressure of dry air, Pa
Partial pressure of water vapor, Pv
Total (barometric) pressure
PaV = ma RaT, Ra = 0.2870kJ/kgK
PvV = mv RvT, Rv = 0.4615kJ/kgK
P = Pa + Pv
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Humidity ratio
absolute humidity, specific humidity
mass of water vapor )
(
( humidity ratio)= mass of dry air
(
)
w=
w=
mv
ma
=
PvV / RvT
PaV / RaT
=
mv
ma
Pv / Rv
Pa / Ra
= 0.622
Pv
Pa
= 0.622
Pv
P - Pv
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Relative humidity
(mass of water vapor)
(relative humidity )= mass of water vapor in saturation
(
)
f=
mv
( )
mg T
mv
PvV / RvT
Pv
f=
=
=
PgV / RvT Pg T
mg T
( )
RH =
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•
•
•
( )
PH O
2
( )
PH O, sat T
2
Obtain the saturated pressure Pg(T) from the steam table.
Dry air. Relative humidity = 0%
Air saturated with water. Relative humidity = 100%
Human comfort. Relative humidity = 40-60%
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Enthalpy
Specific enthalpy of dry air:
Specific enthalpy of water vapor:
Enthalpy of moist air:
Specific enthalpy in terms of (P,T,w):
ha = c pT, c p = 1.005kJ/kgK
( )
hv » hg T = 2500.9+1.82T, (kJ / kT ) T in C
( )
( )
H = maha T + mvhv T
( )
( )
h = H / ma = ha T + whv T
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Plan
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Psychrometric properties
Measuring humidity
Psychrometric chart
HVAC
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Dew-point
( )
( )
Tdp = Tsat Pv , Pv = Pg Tdp
( )
Tsat ( Pv )
Pg T
liquid
Pg
Pv
Tdp
gas
T
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http://www.climate.be/textbook/glossary_s.xml
Foggy morning
At sunset, the temperature is 20 C and the relative humidity is 50%. In the
morning, how much must the temperature have dropped for fog to form?
Assume that the partial pressure of water remains fixed.
dew point
sunset
Tdp » 8C
( )
Pg T
( )(
Pv = f Pg = 0.5 2.3392kPa
Pg
Pv
Tdp
T
10
)
Frost point
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Adiabatic saturation temperature
P2
An experiment to measure humidity
ma2 , mv2
ma1 , mv1
Conservation of dry air: ma1 = ma2
mf
Conservation of water: ma1w1 + m f = ma2w2
( )
( )
( )
Conservation of energy: ma1h T1 + m f h f T2 = ma2h T2
saturated air at outlet:
w2 = 0.622
(
( )
P2 - Pg (T2 )
Pg T2
)
( )
( )
( )
c p T2 -T1 + w2h fg T2
Algebra: w1 =
hg T1 - h f T2
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Wet-bulb temperature. Dry-bulb temperature
Sling psychrometer
For air–water vapor mixtures at atmospheric
pressure, Twb is approximately equal to the
adiabatic saturation temperature.
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Hygrometer
humidity sensors
First inventor: Johann Heinrich Lambert (1755)
Humidity affects everything. Everything is a hygrometer.
Today’s opportunity: The Internet of things.
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Bimaterial strip
Hair-tension hygrometer
Wet-bulb and dry-bulb
Dew-point hygrometer
Capacitor
Resistor
Thermal conductivity
Weight
https://en.wikipedia.org/wiki/Hygrometer
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Plan
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Psychrometric properties
Measuring humidity
Psychrometric chart
HVAC
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Psychrometric properties
Name all states of moist air by 3 variables: P,T,w
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
P, (barometric, or total) pressure
Pa, dry-air pressure
Pv, vapor pressure (partial pressure of water)
T, (dry-bulb) temperature
Tdp, dew-point temperature
Twb, wet-bulb temperature
ma, mass of dry air
mv, mass of water vapor
w, specific humidity (absolute humidity, humidity ratio)
f, relative humidity (RH)
v, specific volume
h, specific enthalpy
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Name all states of moist air by 3 variables: P,T,w
Volume:
Specific volume in terms of (P,T,w):
Specific humidity:
(
)
V = ma Ra + mv Rv T / P
(
w = 0.622
Pv
P - Pv
wP
Pv =
0.622 + w
Relative humidity:
f=
Pv
Relative humidity in terms of (P,T,w):
f=
Partial pressure of water in terms of (P,T,w):
)
v = V / ma = Ra + w Rv T / P
( )
Pg T
wP
(0.622 + w ) Pg (T )
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Since Chinese invented paper, humans have spent
disproportional amount of time on one particular number:
2
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Psychrometric chart
Henry Ford: “You can have Model T in any color, so long as it’s black.”
You can draw figure in any dimensions, so long as it’s two-dimensional.
(
)
v = Ra + w Rv T / P
Fix P = 1 atm
(
h = 1.005T + w 2500.9+1.82T
f=
)
wP
(0.622 + w ) Pg (T )
w2 = 0.622
(
(
Pg Twb
(
)
P - Pg Twb
)
)
( )
( )
c p Twb - T + w2h fg Twb
w=
hg T - h f Twb
( )
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Psychrometric chart
Name all states of moist air using 3 variables: P,T,w
P = 1 atm
Pv =
w
wP
0.622 + w
( )
Pv = Pg Tdp
Tdb
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https://www.ohio.edu/mechanical/thermo/Applied/Chapt.7_11/Chapter10b.html
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Foggy morning
At sunset, the temperature is 20 C and the relative humidity is 50%. In the
morning, how much must the temperature have dropped for fog to form?
Assume that the partial pressure of water remains fixed.
dew point
sunset
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Plan
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Psychrometric properties
Measuring humidity
Psychrometric chart
HVAC
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Engineering a state of happiness
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Lee Kuan Yew
The founder of Singapore died on 23 March 2015, aged 91
Among a number of 20th-century luminaries asked by the Wall Street Journal in 1999
to pick the most influential invention of the millennium, he alone shunned the printing
press, electricity, the internal combustion engine and the internet and chose the airconditioner. He explained that, before air-con, people living in the tropics were at a
disadvantage because the heat and humidity damaged the quality of their work.
http://www.economist.com/news/asia/leekuanyew
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Singapore
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Boston
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Denver
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HVAC processes
approach the comfort zone by changing temperature and humidity
1. Hardware: duct, fan, heater, cooler, source
and sink of water, flow of air
2. Psychrometric chart
3. Steady-flow, control-volume analysis.
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Heating
w = constant, but f drops
Conservation of dry air:
Conservation of water:
Conservation of energy:
ma1 = ma2
w1 = w2
( )
( )
Q + ma1h T1 = ma2h T2
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Heating and
humidifying
Conservation of dry air:
Conservation of water:
Conservation of energy:
ma1 = ma2 = ma3
w1 = w2 , ma2w2 + mw = ma3w3
( )
( )
Q + ma1h T1 = ma2h T2
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Cooling and
dehumidifying
dry air: m = m = m
a1
a2
a3
water: ma1w1 = mout +ma2w2 ,
energy:
w2 = w3
( )
( )
ma2h (T2 ) + qheat = ma3h (T3 )
ma1h T1 = qcool + ma2h T2
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Evaporative Cooling
h = constant
dry air:
ma1 = ma2
water: ma1w1 + min = ma2w2
energy:
( ) ( )
h T1 = h T2
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Senator Rubio, There is no clash of civilization.
Drink more water and study psychrometry!
cloth
Evaporative cooling
Desert: T = 50 C, RH = 10%
What is temperature of the cloth?
desert
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Adiabatic mixing
Rule of mixture
Conservation of dry air:
Conservation of water:
Conservation of energy:
ma1 + ma2 = ma3
ma1w1 + ma2w2 = ma3w3
ma1h1 + ma2h2 = ma3h3
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Coal power station
coverts coal to electricity
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Cooling tower
The moist air in the tower has a high water-vapor
content, and is lighter than the outside air. The
light air in the tower rises, and the heavier outside
air fills the vacant space, creating an airflow from
the bottom of the tower to the top.
Conservation of dry air:
Conservation of water:
Conservation of energy:
ma1 + ma2
ma1w1 + mw3 = ma2w2 + mw4
ma1h1 + mw3h3 = ma2h2 +mw4h4
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Summary
• Name all states of moist air by 3 psychrometric properties:
(total) pressure P, (dry-bulb) temperature T, and humidity
ratio w.
• Hygrometer
• Psychrometric chart: Fix P, and represent all other
psychrometric properties on a plane by lines of constant
values.
• Comfort zone (T = 22-27 C, RH = 40%-60%).
• Reach comfort zone by HVAC processes.
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