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
• Psychrometric properties
• Measuring humidity
• Psychrometric chart
• HVAC
2
Dry air
name formula Molar mass M number fraction y
kg/kmol
nitrogen N2 28 0.78
oxygen O2 32 0.21
3
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 PaV = ma RaT, Ra = 0.2870kJ/kgK
Partial pressure of water vapor, Pv PvV = mv RvT, Rv = 0.4615kJ/kgK
Total (barometric) pressure P = Pa + Pv
4
Humidity ratio
absolute humidity, specific humidity
( mass of water vapor )
( humidity ratio)= mass of dry air
( )
mv
w=
ma
mv PvV / RvT Pv / Rv Pv Pv
w= = = = 0.622 = 0.622
ma PaV / RaT Pa / Ra Pa P - Pv
5
Relative humidity
(mass of water vapor)
(relative humidity )= mass of water vapor in saturation
( )
mv
f=
( )
mg T
mv PvV / RvT Pv
f= = =
mg T ( )
PgV / RvT Pg T ( )
PH O
RH = 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%
6
• Human comfort. Relative humidity = 40-60%
Enthalpy
Specific enthalpy of dry air: ha = c pT, c p = 1.005kJ/kgK
Specific enthalpy of water vapor: ( )
hv » hg T = 2500.9+1.82T, (kJ / kT ) T in C
Enthalpy of moist air: ( )
H = maha T + mvhv T ( )
Specific enthalpy in terms of (P,T,w): ( )
h = H / ma = ha T + whv T ( )
7
Plan
• Psychrometric properties
• Measuring humidity
• Psychrometric chart
• HVAC
8
Dew-point
( )
Tdp = Tsat Pv , Pv = Pg Tdp ( )
( )
Pg T
liquid Tsat ( Pv )
Pg
Pv
gas
Tdp
T
9
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 ( )(
Pv = f Pg = 0.5 2.3392kPa )
( )
Pg T Pg
Pv
Tdp
T
10
Frost point
11
Adiabatic saturation temperature
P2
An experiment to measure humidity
ma1 , mv1 ma2 , mv2
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 ( )
w2 = 0.622
( )
Pg T2
saturated air at outlet:
P2 - Pg (T2 )
Algebra: w1 =
( )
c p T2 -T1 + w2h fg T2 ( )
( )
hg T1 - h f T2 ( ) 12
Wet-bulb temperature. Dry-bulb temperature
Sling psychrometer
For air–water vapor mixtures at atmospheric
pressure, Twb is approximately equal to the
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adiabatic saturation temperature.
Hygrometer
humidity sensors
First inventor: Johann Heinrich Lambert (1755)
Humidity affects everything. Everything is a hygrometer.
Today’s opportunity: The Internet of things.
• Bimaterial strip
• Hair-tension hygrometer
• Wet-bulb and dry-bulb
• Dew-point hygrometer
• Capacitor
• Resistor
• Thermal conductivity
• Weight
https://en.wikipedia.org/wiki/Hygrometer 14
Plan
• Psychrometric properties
• Measuring humidity
• Psychrometric chart
• HVAC
15
Psychrometric properties
Name all states of moist air by 3 variables: P,T,w
1. P, (barometric, or total) pressure
2. Pa, dry-air pressure
3. Pv, vapor pressure (partial pressure of water)
4. T, (dry-bulb) temperature
5. Tdp, dew-point temperature
6. Twb, wet-bulb temperature
7. ma, mass of dry air
8. mv, mass of water vapor
9. w, specific humidity (absolute humidity, humidity ratio)
10. f, relative humidity (RH)
11. v, specific volume
12. h, specific enthalpy
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Name all states of moist air by 3 variables: P,T,w
Volume: (
V = ma Ra + mv Rv T / P )
Specific volume in terms of (P,T,w): (
v = V / ma = Ra + w Rv T / P )
Pv
Specific humidity: w = 0.622
P - Pv
wP
Partial pressure of water in terms of (P,T,w): Pv =
0.622 + w
Pv
f=
( )
Relative humidity:
Pg T
wP
f=
(0.622 + w ) Pg (T )
Relative humidity in terms of (P,T,w):
17
Since Chinese invented paper, humans have spent
disproportional amount of time on one particular number:
2
18
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 ( )
wP
f=
(0.622 + w ) Pg (T )
w2 = 0.622
(
Pg Twb )
P - Pg Twb ( )
w=
( )
c p Twb - T + w2h fg Twb ( )
( )
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
wP
Pv =
0.622 + w
w
( )
Pv = Pg Tdp
Tdb
20
https://www.ohio.edu/mechanical/thermo/Applied/Chapt.7_11/Chapter10b.html 21
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
22
Plan
• Psychrometric properties
• Measuring humidity
• Psychrometric chart
• HVAC
23
Engineering a state of happiness
24
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 air-
conditioner. 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 25
Singapore
26
Boston
27
Denver
28
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: ma1 = ma2
Conservation of water: w1 = w2
Conservation of energy: ( ) ( )
Q + ma1h T1 = ma2h T2
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Heating and
humidifying
Conservation of dry air: ma1 = ma2 = ma3
Conservation of water: w1 = w2 , ma2w2 + mw = ma3w3
Conservation of energy: ( ) ( )
Q + ma1h T1 = ma2h T2
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Cooling and
dehumidifying
dry air: m = m = m
a1 a2 a3
water: ma1w1 = mout +ma2w2 , w2 = w3
energy:
( ) ( )
ma1h T1 = qcool + ma2h T2
ma2h (T2 ) + qheat = ma3h (T3 )
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Evaporative Cooling
h = constant
dry air: ma1 = ma2
water: ma1w1 + min = ma2w2
energy:
( ) ( )
h T1 = h T2 33
Senator Rubio, There is no clash of civilization.
Drink more water and study psychrometry!
Evaporative cooling
cloth Desert: T = 50 C, RH = 10%
What is temperature of the cloth?
desert
34
Adiabatic mixing
Rule of mixture
Conservation of dry air: ma1 + ma2 = ma3
Conservation of water: ma1w1 + ma2w2 = ma3w3
Conservation of energy: ma1h1 + ma2h2 = ma3h3
35
Coal power station
coverts coal to electricity
36
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: ma1 + ma2
Conservation of water: ma1w1 + mw3 = ma2w2 + mw4
Conservation of energy: 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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