MA2007 THERMODYNAMICS
Air-Vapour Mixtures and Air-Conditioning
Prof. S.H. Chan
College of Engineering
School of Mechanical and Aerospace Engineering
Content Copyright Nanyang Technological University
1
TIMELINE AND TOPICS TO BE COVERED IN THERMODYNAMICS PART II
1. Gas Power Cycles [6 Mar] ✓
Power cycles
2. Vapor Power Cycles [13 Mar] ✓
3. Ideal Gas Mixtures + Quiz 2 [20 Mar] ✓
4. Air-Vapor Mixtures and Air-Conditioning [27 Mar] ✓
5. Combustion Processes [3 Apr] ✓
Properties
Non-reacting ideal gas mixture
Reacting ideal gas mixture
6. Tutorial #12 [10 Apr]
7. Final Exam [24 Apr ]
Content Copyright Nanyang Technological University
2
ONLINE LECTURE SUMMARY
• Psychrometrics or psychrometry is a specific field of engineering dealing
with the physical and thermodynamic properties of gas-vapour mixtures.
• Air in psychrometry is often referred to dry air
• Hence, moist air = dry air + water vapour
• Temperature: -10oC - 50oC, dry air is assumed to be an ideal gas with a
constant specific heat Cp = 1.005 kJ/kgK and the dry air enthalpy (ha) is
approximated to CpT, where T is in oC without any physical meaning.
• In reality, one can only write ∆ℎ𝑎 = 𝐶𝑝 ∆𝑇 ,where
𝐶𝑝 =
𝑑ℎ𝑎
𝑑𝑇
or the gradient of the ha – T diagram
obtained experimentally.
Saturated with seawater
at different salinity
• At 25oC, cpT (1.005x25) = ~25.125 kJ/kg.
Dry air
Content Copyright Nanyang Technological University
3
ONLINE LECTURE SUMMARY
• Enthalpy of water vapour (hv) can be approximated to hg@T when the partial
pressure of water vapour in moist air is low, i.e.,
ℎ𝑣 (𝑇, low 𝑃) ≈ ℎ𝑔 (𝑇)
• Enthalpy of dry air (ha) can be approximated to CpT, i.e.,
ℎ𝑎 ≈ 𝐶𝑝 𝑇
• Enthalpy of moist air = Enthalpy of dry air + Enthalpy of water vapour
H = maha + mv hv = ma (ha + ω hv)
• Enthalpy of moist air per kg of dry air = H/ma = h = Cp T + ω hg(T)
Content Copyright Nanyang Technological University
4
ONLINE LECTURE SUMMARY
IS WATER VAPOUR AN IDEAL GAS IN THE CONTEXT OF PSYCHROMETRY?
e.g., at Ø = 90%, T = 30oC,
pv = 0.0382, pc = 220.6 bar
and PR = 0.000173
How about TR?
At extremely low PR , Z=~1
Content Copyright Nanyang Technological University
5
ONLINE LECTURE SUMMARY
Three possible types of condensation
constant pressure
constant volume
constant temperature
1→ 2
1→ 3
1→4
Content Copyright Nanyang Technological University
6
WHAT IS RELATIVE HUMIDITY?
Content Copyright Nanyang Technological University
7
ONLINE LECTURE SUMMARY
• Total pressure:
P = Pv + Pa
• Specific humidity:
m v
Pv
=
= 0.622
m a
P − Pv
• Relative humidity:
Pv
 = |T,P
Pg
𝑀𝑣 18.015
=
𝑀𝑎
28.97
→  1
• Heating process: ω will remain unchanged
• Cooling before condensation:
Pv
=
Pg @T
• When condensation occurs:
 = 100%
Content Copyright Nanyang Technological University
8
DETERMINATION OF RELATIVE HUMIDITY Ø
• Dry bulb temperature (T1) is a term used in HVAC (Heating, Ventilation and Air
Conditioning) systems and is the air temperature measured by a thermometer
that is not affected by the moisture content of the air.
• Wet bulb temperature (~T2) is an important parameter used HVAC systems, and
it is defined as the lowest temperature that can be reached by evaporating water
into the air at a constant pressure.
Content Copyright Nanyang Technological University
9
ADIABATIC
MIXING
COOLING
ONLINE LECTURE SUMMARY
Content Copyright Nanyang Technological University
10
ONLINE LECTURE SUMMARY
• Mass Balance and Energy balance for a control volume under steady-state
condition apply.
• Energy balance for air-conditioning:
𝑉2
𝑄ሶ 𝑐𝑣 − 𝑊ሶ 𝑐𝑣 + ෍ 𝑚ሶ ℎ +
+ 𝑔𝑧
2
𝑉2
− ෍ 𝑚ሶ ℎ +
+ 𝑔𝑧
2
𝑖𝑛
=0
𝑜𝑢𝑡
• Energy balance for adiabatic mixing:
𝑉2
𝑄ሶ 𝑐𝑣 − 𝑊ሶ 𝑐𝑣 + ෍ 𝑚ሶ ℎ +
+ 𝑔𝑧
2
• Enthalpy of moist air, H:
•
𝑉2
− ෍ 𝑚ሶ ℎ +
+ 𝑔𝑧
2
𝑖𝑛
=0
𝑜𝑢𝑡
m v
m a ha + m v hv = m a (ha +
hv ) = m a (ha + hv )
m a
ha + hv
Enthalpy of moist air per kg of dry air, h:
Content Copyright Nanyang Technological University
11
AIR-CONDITIONING
Mass balance
Dry air:
 a1 = m
 a2 = m
 a3 = m
a
m
v /m
a
=m
Water vapour:
1-2
2-3
 v1 = m
f + m
 v2
m
 v2 = m
 v3
m
f = m
 a(1 − 2 )
m
2 = 3
Energy balance:
1-2
H1 = H2 + Hf + Q out
 aha1 + m
 v1hv1 ) = (m
 aha2 + m
 v 2hv 2 ) + m
 f hf + Q out
(m
Q out = m a [C pa (T1 − T2 ) + (1hg1 − 2 hg 2 ) + (2 − 1 )h f ]
2-3
H2 + Q in = H3
 aha3 + m
 v 3hv 3 )
 aha2 + m
 v 2hv 2 ) = (m
Q in + (m
 a[C pa(T3 − T2 ) + 3(hg3 − hg2 )]
Q in = m
Content Copyright Nanyang Technological University
12
ADIABATIC MIXING
Mass balance:
Since
Air
 a1 + m
 a2 = m
 a3
m
Vapour
 v1 + m
 v2 = m
 v3
m
Energy balance:
v
m
=
a
m
 a1 + 2m
 a2 = 3m
 a3
1m
H1 + H2 = H3
 a1ha1 + m
 v1hv1) + (m
 a2ha2 + m
 v 2hv 2 ) = m
 a3ha3 + m
 v 3hv 3
(m
Substituting from mass balance equation:
 a1(ha1 + 1hv1) + m
 a2(ha2 + 2hv 2 ) = (m
 a1 + m
 a2 )(ha3 + 3hv 3 )
m
Using expression for air enthalpy ha & water vapour enthalpy hv
ha = C p T
hv  hg
 a1C pa(T1 − T3 ) + m
 a2C pa(T2 − T3 )
m
 a1 + m
 a2 )3hg3 − m
 a11hg1 − m
 a22hg2
= (m
Content Copyright Nanyang Technological University
13
ASHRAE PSYCHROMETRIC CHART
Barometric pressure = 1 atm
Scale for the
mixture
enthalpy per
unit mass of
dry air
Wet-bulb and
dew point
temperature
scales
temperature

Volume
per unit
mass of
dry air
𝑇𝑤𝑏
Dry-bulb temperature
Content Copyright Nanyang Technological University
14
𝑆𝐸𝑁𝑆𝐼𝐵𝐿𝐸 𝐻𝐸𝐴𝑇
𝑇𝑂𝑇𝐴𝐿 𝐻𝐸𝐴𝑇
=
HUMIDITY RATIO (W) GRAMS MOISTURE PER KILOGRAM DRY AIR
ASHRAE PSYCHROMETRIC CHART
∆ℎ
∆𝑊
𝐸𝑁𝑇𝐻𝐴𝐿𝑃𝑌
∆ℎ
=
𝐻𝑈𝑀𝐼𝐷𝐼𝑇𝑌 𝑅𝐴𝑇𝐼𝑂
∆𝑊
DRY BULB TEMPERATURE ℃
Source: McGraw Hill (6)
Content Copyright Nanyang Technological University
15
THE END
Content Copyright Nanyang Technological University
16