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8/10/2019 Fe Thermodynamics Reference Handbook1
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THERMODYNAMICS
THERMODYNAMICS
PROPERTIES OF SINGLE-COMPONENT SYSTEMS
Nomenclature1. Intensive properties are independent of mass.2. Extensive properties are proportional to mass.
State Functions (properties)Absolute Pressure, P (lbf /in2 or Pa)Absolute Temperature, T (R or K)Volume, V (ft3 or m 3)
v V m= (ft3/lbm or m 3/kg)Internal Energy, U (Btu or kJ)
u U m= (usually in Btu /lbm or kJ /kg)
Enthalpy, H (Btu or KJ) Enthalpy,
h = u + Pv = H/m (usually in Btu /lbm or kJ /kg)
Entropy, S (Btu /R or kJ /K) s = S/m [Btu /(lbm- R) or kJ /
Gibbs Free Energy, g = h Ts (usually in Btu /lbm or kJ /kg)Helmholz Free Energy,
a = u Ts (usually in Btu /lbm or kJ /kg)
Heat Capacity at Constant Pressure, c T h
p P 2
2= b l
Heat Capacity at Constant Volume, c T u
vv2
2= b l
Quality x (applies to liquid-vapor systems at saturation) is
x = m g / (m g + m f ) , wherem g = mass of vapor, andm f = mass of liquid.
can be written:v = xv g + (1 x)v f or v = v f + xv fg , wherev f v g v fg = v g v f
Similar expressions exist for u, h, and s:u = xu g + (1 x) u f or u = u f + xu fg h = xh g + (1 x) h f or h = h f + xh fg
s = xs g + (1 x) s f or s = s f + xs fg
For an ideal gas, Pv = RT or PV = mRT , and P 1v1 /T 1 = P 2v2 /T 2, where
P = pressure,v m = mass of gas,
R = gas constant, andT = absolute temperature.V = volume
R is but can be found from
., R
mol wt R where= ^ h
R = the universal gas constant = 1,545 ft-lbf/(lbmol- R) = 8,314 J / (kmol K).
For ideal gases , c p cv = R
Also, for ideal gases :
P h vu0 0T T 22
22
= =b bl lFor cold air standard, heat capacities are assumed to beconstant at their room temperature values. In that case, thefollowing are true:
u = cvT ; h = c p T s = c p ln (T 2 /T 1) R ln ( P 2 /P 1); and s = cv ln (T 2 /T 1) + R ln (v2 /v1).
For heat capacities that are temperature dependent, the valueto be used in the above equations for h is known as the meanheat capacity c p
` j and is given by
c T T c dT
p
pT
T
2 1
1
2
=-
#
Also, for constant entropy processes:
;
,
P P
vv
T T
P P
T T
vv k c cwhere
k k
k
k
p v
1
2
2
1
1
2
1
2
1
1
2
2
11
= =
= =
-
-
d dd
n nn
For real gases, several equations of state are available; one
such equation is the van der Waals equation with constants based on the critical point:
,
P va v b RT
a P
R T b P
RT 6427
8where
2
c
c
c
c2 2
+ - =
= =
c ^
c fm h
m pwhere P c and T c are the pressure and temperature at the critical
point, respectively, and v
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THERMODYNAMICS
FIRST LAW OF THERMODYNAMICSThe First Law of Thermodynamics is a statement ofconservation of energy in a thermodynamic system. The netenergy crossing the system boundary is equal to the change inenergy inside the system.
Heat Q is energy transferred due to temperature differenceand is considered positive if it is inward or added to thesystem.
Closed Thermodynamic System No mass crosses system boundary
Q W = U + KE + PE where KE = change in kinetic energy, and PE = change in potential energy.Energy can cross the boundary only in the form of heat orwork. Work can be boundary work, w b, or other work forms(electrical work, etc.)
Work W w mW =b l is considered positive if it is outward or
work done by the system. Reversible boundary work is given by w b = P dv .
Special Cases of Closed SystemsConstant Pressure ( ):
w b = P v (ideal gas) T/v = constant
Constant Volume:w b = 0
(ideal gas) T/P = constant
Isentropic (ideal gas): Pv k = constant
w = ( P 2v2 P 1v1)/(1 k ) = R(T 2 T 1)/(1 k )
Constant Temperature ( ): (ideal gas) Pv = constant w b = RT ln (v2 / v1) = RT ln ( P 1/ P 2)
Polytropic (ideal gas): Pv n = constant
w = ( P 2v2 P 1v1)/(1 n)
Open Thermodynamic SystemMass crosses the system boundary
Pv) done by mass entering the system.
wrev = v dP + ke + peFirst Law applies whether or not processes are reversible.FIRST LAW (energy balance)
/ /
/ ,
m h V gZ m h V gZ
Q W d m u dt
2 2
where
i i i i e e e e
in net s s
2 2+ + - + +
+ - =
R Ro o
o o _ i8 8B B
W net o = rate of net or shaft work transfer,m s
u s Qo = rate of heat transfer (neglecting kinetic and potential
energy of the system).
Special Cases of Open SystemsConstant Volume:
wrev = v ( P 2 P 1)
Constant Pressure:wrev = 0
Constant Temperature:(ideal gas) Pv = constant
wrev = RT ln (v2 /v1) = RT ln ( P 1 / P 2)
Isentropic (ideal gas): Pv k = constant
wrev = k ( P 2v2 P 1v1) / (1 k ) = k R (T 2 T 1) / (1 k )
w k k RT P
P 1 1
/
rev
k k
11
21
=-
-
-
d ^
n h> H
Polytropic:
Pv n = constantwrev = n ( P 2v2 P 1v1) / (1 n)
Steady-State SystemsThe system does not change state with time. This assumptionis valid for steady operation of turbines, pumps, compressors,throttling valves, nozzles, and heat exchangers, including
boilers and condensers.
/ /m h V gZ m h V gZ Q W
m m
2 2 0
and
where
i i i e e e e in out
i e
2 2+ + - + + + - =
=
R R
R R
o o o o
o o
` `j j
mo i and e refer to inlet and exitstates of system),
g = acceleration of gravity, Z = elevation,V = velocity, andW o = rate of work.
Special Cases of Steady-Flow Energy Equation Nozzles , Diffusers : elevation change, no heat transfer, and no work. Single massstream.
/ /h V h V 2 2i i e e2 2+ = +
,h h
V V 2
wherei es
e i2 2
-
-
_ ihes = enthalpy at isentropic exit state.
Turbines , Pumps , Compressors: Often considered adiabatic(no heat transfer). Velocity terms usually can be ignored.
hi = h e + w
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THERMODYNAMICS
h hh hi es
i e-
-
h hh h
e i
es i-
-
Throttling Valves and Throttling Processes: No work, noheat transfer, and single-mass stream. Velocity terms are often
hi = h e
Boilers , Condensers , Evaporators , One Side in a Heat Exchanger: mass stream, the following applies:
hi + q = h e
Heat Exchangers: m1o and m2o :
m h h m h hi e e i1 1 1 2 2 2- = -o o_ _i i
See MECHANICAL ENGINEERING section.
Mixers , Separators ,
mh m h
m m
andi i e e
i e
=
=
R R
R R
o o
o o
BASIC CYCLES Heat engines take in heat Q H at a high temperature T H , produce a net amount of work W , and reject heat Q L at a lowtemperature T L of a heat engine is given by:
= W/Q H = (Q H Q L) /Q H Carnot Cycle . Its
c = (T H T L) /T H , whereT H and T L = absolute temperatures (Kelvin or Rankine).
The following heat-engine cycles are plotted on P-v and T-sdiagrams (see later in this chapter):
Carnot, Otto, Rankine
Refrigeration cycles are the reverse of heat-engine cycles.Heat is moved from low to high temperature requiring work,W . Cycles can be used either for refrigeration or as heat
pumps.
COP = Q H /W for heat pumps, and asCOP = Q L/W for refrigerators and air conditioners.
Upper limit of COP is based on reversed Carnot Cycle:COP c = T H /(T H T L) for heat pumps andCOP c = T L /(T H T L) for refrigeration.
1 ton refrigeration = 12,000 Btu / hr = 3,516 W
IDEAL GAS MIXTURESi = 1, 2, , n constituents. Each constituent is an ideal gas.Mole Fraction:
xi = N i / N ; N = N i; xi = 1where N i = number of moles of component i.
Mass Fraction: yi = m i /m; m = mi; yi = 1Molecular Weight: M = m/N = xiM i
Gas Constant: / R R M =
To convert mole fractions x i to mass fractions y i:
y x M
x M i
i i
i i=R _ i
To convert mass fractions to mole fractions :
x y M
y M i
i i
i i=
R _ iPartial Pressures: ; P P P V
mR T i i
i i= =R
Partial Volumes: ;V V V P m R T
i ii i= =! , where
P , V , T = the pressure, volume, and temperature of themixture.
xi = P i /P = V i /V
Other Properties:u = ( yiui); h = ( yihi); s = ( yi si)ui and hi are evaluated at T , and
si is evaluated at T and P i.
PSYCHROMETRICSWe deal here with a mixture of dry air (subscript a) and watervapor (subscript v):
P = P a + P v
(absolute humidity, humidity ratio) : = m v /ma , where
mv = mass of water vapor andma = mass of dry air. = 0.622 P v / P a = 0.622 P v / ( P P v)
Relative Humidity (rh) := P v /P g , where
P g = saturation pressure at T .
Enthalpy h: h = ha + hv Dew-Point Temperature T dp:
T dp = T sat at P g = P v
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THERMODYNAMICS
Wet-bulb temperature T wb is the temperature indicated by athermometer covered by a wick saturated with liquid waterand in contact with moving air.
Humid Volume : Volume of moist air / mass of dry air.
Psychrometric Chart
temperature plotted for a value of atmospheric pressure.(See chart at end of section.)
PHASE RELATIONSClapeyron Equation for Phase Transitions:
,dT dP
Tvh
v s
where sat fg
fg
fg
fg = =b l
h fg = enthalpy change for phase transitions,
v fg = volume change,
s fg = entropy change,
T = absolute temperature, and
(dP/dT ) sat = slope of phase transition (e.g.,vapor-liquid)saturation line.
Clausius-Clapeyron EquationThis equation results if it is assumed that (1) the volumechange ( v fg ) can be replaced with the vapor volume ( v g ),(2) the latter can be replaced with P R T from the ideal gaslaw, and (3) h fg is independent of the temperature ( T ).
ln P P
R
hTT
T T e
fg
1
2
1 2
2 1:= -d n
Gibbs Phase Rule (non-reacting systems ) P + F = C + 2, whereP = number of phases making up a systemF = degrees of freedom, andC = number of components in a system
COMBUSTION PROCESSESFirst, the combustion equation should be written and balanced.For example, for the stoichiometric combustion of methane inoxygen:
CH 4 + 2 O 2 CO 2 + 2 H 2O
Combustion in AirFor each mole of oxygen, there will be 3.76 moles of nitrogen.
For stoichiometric combustion of methane in air:CH 4 + 2 O 2 + 2(3.76) N 2 CO 2 + 2 H 2O + 7.52 N 2
Combustion in Excess AirThe excess oxygen appears as oxygen on the right side of thecombustion equation.
Incomplete CombustionSome carbon is burned to create carbon monoxide (CO).
Air-Fuel Ratio ( A/F ): A/F =mass of fuelmass of air
Stoichiometric (theoretical) air-fuel ratio is the air-fuel ratiocalculated from the stoichiometric combustion equation.
Percent Theoretical Air = A F
A F 100
stoichiometric
actual #_
_i
i
Percent Excess Air = A F
A F A F 100
stoichiometric
actual stoichiometric #-
__ _
ii i
SECOND LAW OF THERMODYNAMICSThermal Energy Reservoirs
S reservoir = Q/T reservoir , whereQ is measured with respect to the reservoir.
Kelvin-Planck Statement of Second Law No heat engine can operate in a cycle while transferring heat
with a single heat reservoir.COROLLARY to Kelvin-Planck: No heat engine can have a
same reservoirs.
Clausius Statement of Second Law No refrigeration or heat pump cycle can operate without a network input.
COROLLARY : No refrigerator or heat pump can have ahigher COP than a Carnot Cycle refrigerator or heat pump.
VAPOR-LIQUID MIXTURES
Henrys Law at Constant TemperatureAt equilibrium, the partial pressure of a gas is proportionalto its concentration in a liquid. Henrys Law is valid for lowconcentrations; i.e., x 0.
P i = Py i = hx i , whereh = Henrys Law constant,
P i = partial pressure of a gas in contact with a liquid, xi = mol fraction of the gas in the liquid, yi = mol fraction of the gas in the vapor, and P = total pressure.
Raoults Law for Vapor-Liquid EquilibriumValid for concentrations near 1; i.e., xi 1.
P i = x i P i*, where P i = partial pressure of component i, xi = mol fraction of component i in the liquid, and P i* = vapor pressure of pure component i at the temperature
of the mixture.
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THERMODYNAMICS
ENTROPYds T Q
s s T Q
1
12 1 12
rev
rev
=
- =
d
d
__
ii #
Inequality of Clausius
T Q
T Q s s
1 0
1 2 112
rev #
# -
d
d
__
ii #
#
Isothermal, Reversible Process s = s 2 s 1 = Q/T
Isentropic Process s = 0; ds = 0
A reversible adiabatic process is isentropic.
Adiabatic ProcessQ = 0; s 0
Increase of Entropy Principle
/
s s s s m s m s Q T
0
0
total system surroundings
total out out in in external external
$
$
= +
= - -
D D D
D R R Ro o o o_ iTemperature-Entropy ( T-s ) Diagram
= 21 sd T Q rev
s
1
2
AREA = HEAT
T
Entropy Change for Solids and Liquidsds = c (dT/T)
s2 s 1 = c (dT/T) = c mean ln (T 2 /T 1) ,where c equals the heat capacity of the solid or liquid.
Irreversibility I = w rev w actual
EXERGYExergy is the portion of total energy available to do work.
Closed-System Exergy (Availability)(no chemical reactions)
= (u u o) T o ( s s o) + p o (v vo)where the subscript o designates environmental conditions
wreversible = 1 2
Open-System Exergy (Availability) = (h h o) T o ( s s o) + V 2/2 + gz wreversible = 1 2
Gibbs Free Energy, G Energy released or absorbed in a reaction occurring reversiblyat constant pressure and temperature.
Helmholtz Free Energy, AEnergy released or absorbed in a reaction occurring reversiblyat constant volume and temperature.
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THERMODYNAMICS
COMMON THERMODYNAMIC CYCLES
Carnot Cycle Reversed Carnot
Otto Cycle(Gasoline Engine)
= 1 r1 k
r = v 1 /v 2
Rankine Cycle Refrigeration(Reversed Rankine Cycle)
( ) ( )3 4 2 13 2
h h h h
h h
=
p 2 = p 3
12
32HP
12
41ref hh
hhCOPhhhhCOP
=
=
p 2 = p 3
q = 0
q
q
w
w
q
q
T
c
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THERMODYNAMICS
STEAM TABLESSaturated Water - Temperature Table
Specific Volumem 3/kg
Internal EnergykJ/kg
EnthalpykJ/kg
EntropykJ/(kgK)Temp.
oCT
Sat.Press.kPa
p sat
Sat.liquid
v f
Sat.vapor
v g
Sat.liquid
u f
Evap.
u fg
Sat.vapor
u g
Sat.liquid
h f
Evap.
h fg
Sat.vapor
h g
Sat.liquid
s f
Evap.
s fg
Sat.vapor
s g 0.015
101520253035404550556065707580859095
0.61130.87211.22761.70512.3393.1694.2465.6287.3849.593
12.34915.75819.94025.0331.1938.5847.3957.8370.1484.55
0.001 0000.001 0000.001 0000.001 0010.001 0020.001 0030.001 0040.001 0060.001 0080.001 0100.001 0120.001 0150.001 0170.001 0200.001 0230.001 0260.001 0290.001 0330.001 0360.001 040
206.14147.12106.38
77.9357.7943.3632.8925.2219.5215.2612.03
9.5687.6716.1975.0424.1313.4072.8282.3611.982
0.0020.9742.0062.9983.95
104.88125.78146.67167.56188.44209.32230.21251.11272.02292.95313.90334.86355.84376.85397.88
2375.32361.32347.22333.12319.02304.92290.82276.72262.62248.42234.22219.92205.52191.12176.62162.02147.42132.62117.72102.7
2375.32382.32389.22396.12402.92409.82416.62423.42430.12436.82443.52450.12456.62463.12569.62475.92482.22488.42494.52500.6
0.0120.9842.0162.9983.96
104.89125.79146.68167.57188.45209.33230.23251.13272.06292.98313.93334.91355.90376.92397.96
2501.32489.62477.72465.92454.12442.32430.52418.62406.72394.82382.72370.72358.52346.22333.82321.42308.82296.02283.22270.2
2501.42510.62519.82528.92538.12547.22556.32565.32574.32583.22592.12600.92609.62618.32626.82635.32643.72651.92660.12668.1
0.00000.07610.15100.22450.29660.36740.43690.50530.57250.63870.70380.76790.83120.89350.95491.01551.07531.13431.19251.2500
9.15628.94968.74988.55698.37068.19058.01647.84787.68457.52617.37257.22347.07846.93756.80046.66696.53696.41026.28666.1659
9.15629.02578.90088.78148.66728.55808.45338.35318.25708.16488.07637.99137.90967.83107.75537.68247.61227.54457.47917.4159
MPa100105110115120125130135140145150155160165170175180
185190195200205210215220225230235240245250255260265270
275280285290295300305310315320330340350360370374.14
0.101 350.120 820.143 270.169 060.198 530.23210.27010.31300.36130.41540.47580.54310.61780.70050.79170.89201.0021
1.12271.25441.39781.55381.72301.90622.1042.3182.5482.7953.0603.3443.6483.9734.3194.6885.0815.499
5.9426.4126.9097.4367.9938.5819.2029.856
10.54711.27412.84514.58616.51318.65121.0322.09
0.001 0440.001 0480.001 0520.001 0560.001 0600.001 0650.001 0700.001 0750.001 0800.001 0850.001 0910.001 0960.001 1020.001 1080.001 1140.001 1210.001 127
0.001 1340.001 1410.001 1490.001 1570.001 1640.001 1730.001 1810.001 1900.001 1990.001 2090.001 2190.001 2290.001 2400.001 2510.001 2630.001 2760.001 2890.001 302
0.001 3170.001 3320.001 3480.001 3660.001 3840.001 4040.001 4250.001 4470.001 4720.001 4990.001 5610.001 6380.001 7400.001 8930.002 2130.003 155
1.67291.41941.21021.03660.89190.77060.66850.58220.50890.44630.39280.34680.30710.27270.24280.21680.194 05
0.174 090.156 540.141 050.127 360.115 210.104 410.094 790.086 190.078 490.071 580.065 370.059 760.054 710.050 130.045 980.042 210.038 770.035 64
0.032 790.030 170.027 770.025 570.023 540.021 670.019 9480.018 3500.016 8670.015 4880.012 9960.010 7970.008 8130.006 9450.004 9250.003 155
418.94440.02461.14482.30503.50524.74546.02567.35588.74610.18631.68653.24674.87696.56718.33740.17762.09
784.10806.19828.37850.65873.04895.53918.14940.87963.73986.74
1009.891033.211056.711080.391104.281128.391152.741177.36
1202.251227.461253.001278.921305.21332.01359.31387.11415.51444.61505.31570.31641.91725.21844.02029.6
2087.62072.32057.02041.42025.82009.91993.91977.71961.31944.71927.91910.81893.51876.01858.11840.01821.6
1802.91783.81764.41744.71724.51703.91682.91661.51639.61617.21594.21570.81546.71522.01596.71470.61443.91416.3
1387.91358.71328.41297.11264.71231.01195.91159.41121.11080.9
993.7894.3776.6626.3384.5
0
2506.52512.42518.12523.72529.32534.62539.92545.02550.02554.92559.52564.12568.42572.52576.52580.22583.7
2587.02590.02592.82595.32597.52599.52601.12602.42603.32603.92604.12604.02603.42602.42600.92599.02596.62593.7
2590.22586.12581.42576.02569.92563.02555.22546.42536.62525.52498.92464.62418.42351.52228.52029.6
419.04440.15461.30482.48503.71524.99546.31567.69589.13610.63632.20653.84675.55697.34719.21741.17763.22
785.37807.62829.98852.45875.04897.76920.62943.62966.78990.12
1013.621037.321061.231085.361109.731134.371159.281184.51
1210.071235.991262.311289.071316.31344.01372.41401.31431.01461.51525.31594.21670.61760.51890.52099.3
2257.02243.72230.22216.52202.62188.52174.22159.62144.72129.62114.32098.62082.62066.22049.52032.42015.0
1997.11978.81960.01940.71921.01900.71879.91858.51836.51813.81790.51766.51741.71716.21689.81662.51634.41605.2
1574.91543.61511.01477.11441.81404.91366.41326.01283.51238.61140.61027.9
893.4720.3441.6
0
2676.12683.82691.52699.02706.32713.52720.52727.32733.92740.32746.52752.42758.12763.52768.72773.62778.2
2782.42786.42790.02793.22796.02798.52800.52802.12803.32804.02804.22803.82803.02801.52799.52796.92793.62789.7
2785.02779.62773.32766.22758.12749.02738.72727.32714.52700.12665.92622.02563.92481.02332.12099.3
1.30691.36301.41851.47341.52761.58131.63441.68701.73911.79071.84181.89251.94271.99252.04192.09092.1396
2.18792.23592.28352.33092.37802.42482.47142.51782.56392.60992.65582.70152.74722.79272.83832.88382.92942.9751
3.02083.06683.11303.15943.20623.25343.30103.34933.39823.44803.55073.65943.77773.91474.11064.4298
6.04805.93285.82025.71005.60205.49625.39255.29075.19085.09264.99604.90104.80754.71534.62444.53474.4461
4.35864.27204.18634.10144.01723.93373.85073.76833.68633.60473.52333.44223.36123.28023.19923.11813.03682.9551
2.87302.79032.70702.62272.53752.45112.36332.27372.18212.08821.89091.67631.43351.13790.68650
7.35497.29587.23877.18337.12967.07757.02696.97776.92996.88336.83796.79356.75026.70786.66636.62566.5857
6.54656.50796.46986.43236.39526.35856.32216.28616.25036.21466.17916.14376.10836.07306.03756.00195.96625.9301
5.89385.85715.81995.78215.74375.70455.66435.62305.58045.53625.44175.33575.21125.05264.79714.4298
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THERMODYNAMICS
Superheated Water Tablesv
m 3/kgu
kJ/kgh
kJ/kg s
kJ/(kg K)v
m 3/kgu
kJ/kgh
kJ/kg s
kJ/(kg K)T
Temp.oC p = 0.01 MPa (45.81 oC) p = 0.05 MPa (81.33 oC)
Sat.50
100150200250300400500600700800900
1000110012001300
14.67414.86917.19619.51221.82524.13626.44531.06335.67940.29544.91149.52654.14158.75763.37267.98772.602
2437.92443.92515.52587.92661.32736.02812.12968.93132.33302.53479.63663.83855.04053.04257.54467.94683.7
2584.72592.62687.52783.02879.52977.33076.53279.63489.13705.43928.74159.04396.44640.64891.25147.85409.7
8.15028.17498.44798.68828.90389.10029.28139.60779.8978
10.160810.402810.628110.839611.039311.228711.409111.5811
3.240
3.4183.8894.3564.8205.2846.2097.1348.0578.9819.904
10.82811.75112.67413.59714.521
2483.9
2511.62585.62659.92735.02811.32968.53132.03302.23479.43663.63854.94052.94257.44467.84683.6
2645.9
2682.52780.12877.72976.03075.53278.93488.73705.13928.54158.94396.34640.54891.15147.75409.6
7.5939
7.69477.94018.15808.35568.53738.86429.15469.41789.65999.8852
10.096710.296410.485910.666210.8382
p = 0.10 MPa (99.63 oC) p = 0.20 MPa (120.23 oC)Sat.
100150
200250300400500600700800900
1000110012001300
1.69401.69581.9364
2.1722.4062.6393.1033.5654.0284.4904.9525.4145.8756.3376.7997.260
2506.12506.72582.8
2658.12733.72810.42967.93131.63301.93479.23663.53854.84052.84257.34467.74683.5
2675.52676.22776.4
2875.32974.33074.33278.23488.13704.43928.24158.64396.14640.34891.05147.65409.5
7.35947.36147.6134
7.83438.03338.21588.54358.83429.09769.33989.56529.77679.9764
10.165910.346310.5183
0.8857
0.9596
1.08031.19881.31621.54931.78142.0132.2442.4752.7052.9373.1683.3993.630
2529.5
2576.9
2654.42731.22808.62966.73130.83301.43478.83663.13854.54052.54257.04467.54683.2
2706.7
2768.8
2870.52971.03071.83276.63487.13704.03927.64158.24395.84640.04890.75147.55409.3
7.1272
7.2795
7.50667.70867.89268.22188.51338.77709.01949.24499.45669.65639.8458
10.026210.1982
p = 0.40 MPa (143.63 oC) p = 0.60 MPa (158.85 oC)Sat.
150200
250300350400500600700800900
1000110012001300
0.46250.47080.5342
0.59510.6548
0.77260.88931.00551.12151.23721.35291.46851.58401.69961.8151
2553.62564.52646.8
2726.12804.8
2964.43129.23300.23477.93662.43853.94052.04256.54467.04682.8
2738.62752.82860.5
2964.23066.8
3273.43484.93702.43926.54157.34395.14639.44890.25146.85408.8
6.89596.92997.1706
7.37897.5662
7.89858.19138.45588.69878.92449.13629.33609.52569.70609.8780
0.3157
0.3520
0.39380.43440.47420.51370.59200.66970.74720.82450.90170.97881.05591.13301.2101
2567.4
2638.9
2720.92801.02881.22962.13127.63299.13477.03661.83853.44051.54256.14466.54682.3
2756.8
2850.1
2957.23061.63165.73270.33482.83700.93925.34156.54394.44638.84889.65146.35408.3
6.7600
6.9665
7.18167.37247.54647.70798.00218.26748.51078.73678.94869.14859.33819.51859.6906
p = 0.80 MPa (170.43 oC) p = 1.00 MPa (179.91 oC)Sat.
200250300350400500600700800900
1000110012001300
0.24040.26080.29310.32410.35440.38430.44330.50180.56010.61810.67610.73400.79190.84970.9076
2576.82630.62715.52797.22878.22959.73126.03297.93476.23661.13852.84051.04255.64466.14681.8
2769.12839.32950.03056.53161.73267.13480.63699.43924.24155.64393.74638.24889.15145.95407.9
6.66286.81587.03847.23287.40897.57167.86738.13338.37708.60338.81539.01539.20509.38559.5575
0.194 440.20600.23270.25790.28250.30660.35410.40110.44780.49430.54070.58710.63350.67980.7261
2583.62621.92709.92793.22875.22957.33124.43296.83475.33660.43852.24050.54255.14465.64681.3
2778.12827.92942.63051.23157.73263.93478.53697.93923.14154.74392.94637.64888.65145.45407.4
6.58656.69406.92477.12297.30117.46517.76228.02908.27318.49968.71188.91199.10179.28229.4543
0.7137 2884.6 3170.1 7.7324
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THERMODYNAMICS
P- h DIAGRAM FOR REFRIGERANT HFC-134a
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THERMODYNAMICS
ASHRAE PSYCHROMETRIC CHART NO. 1
1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 0
1 0 0
1 1 0
1 1 0
1 2 0
1 2 0 E
N T H A L P Y -
K J P E R K I L O G R A M
O F D R Y A I R
1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 0
1 0 0
E N T H
A L P Y
- K J P
E R K I L O
G R A M
O F D
R Y A I
R
S A T U
R A T I O
N T E
M P E R
A T U R
E - C
5
1 0
1 5
2 0
2 5
3 0
3 5
4 0
4 5
5 0
D R Y B U L B T E M P E R A T U R E - C
. 0 0 2
. 0 0 4
. 0 0 6
. 0 0 8
. 0 1 0
. 0 1 2
. 0 1 4
. 0 1 6
. 0 1 8
. 0 2 0
. 0 2 2
. 0 2 4
. 0 2 6
. 0 2 8
. 0 3 0
1 0 %
R E L A T I V E H U M I D I T Y
2 0 %
3 0 %
4 0 %
5 0 %
6 0 %
7 0 %
8 0 %
9 0 %
5
5
1 0
1 0
1 5
1 5
2 0
2 0
2 5
2 5
3 0 W E T
B U L B
T E M P
E R A T U R
E - C
3 0
0. 7 8
0. 8 0
0. 8 2
0. 8 4
0. 8 6 V O
L U M E - C
U B I C M
E T E R P
E R K G
D R Y A I R
0. 8 8
0. 9 0
0. 9 2
0. 9 4
H U M I D I T Y R A T I O - K I L O G R A M S M O I S T U R E P E R K I L O G R A M D R Y A I R
R
R
A S H R A E P S Y C H R O M E T R I C C H A R T N O
. 1
N O R M A L T E M P E R A T U R E
B A R O M E T R I C P R E S S U R E : 1
0 1 . 3
2 5 k P a
C o p y r i g h
t 1 9 9 2
A M E R I C A N S O C I E T Y O F H E A T I N G
, R E F R I G E R A T I N G A N D A I R - C
O N D I T I O N I N G E N G I N E E R S
, I N
C .
S E A L E V E L
0
1 . 0
1 . 0
-
1 . 5
2 . 0
4 . 0
- 4 . 0
- 2 . 0
- 1 . 0
- 0 . 5
- 0. 2
0 . 1
0 . 2
0 . 3
0 . 4
0 . 5
0 . 6
0 . 7
0 . 8
- 5 . 0
- 2 . 0
0 . 0
1 . 0
2. 0
2 .5
3 .0
4 . 0
5 . 0
1 0 . 0
-
S E N S I B L E H E A T
Q s
T O T A L H E A T
Q t
E N T H A L P Y
H U M I D I T Y R A T I O
h
W
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THERMODYNAMICS
THERMAL AND PHYSICAL PROPERTY TABLES
GASES
c p cvSubstance Molwt kJ/(kgK) Btu/(lbm-
R) kJ/(kgK ) Btu/(lbm-
R)k
Gases
Air ArgonButaneCarbon dioxideCarbon monoxide
EthaneHeliumHydrogenMethane
Neon
NitrogenOctane vaporOxygenPropaneSteam
2940584428
3042
1620
28114
324418
1.000.5201.720.8461.04
1.775.19
14.32.251.03
1.041.710.9181.681.87
0.2400.1250.4150.2030.249
0.4271.253.430.5320.246
0.2480.4090.2190.4070.445
0.7180.3121.570.6570.744
1.493.12
10.21.740.618
0.7431.640.6581.491.41
0.1710.07560.3810.1580.178
0.3610.7532.440.4030.148
0.1770.3920.1570.3620.335
1.401.671.091.291.40
1.181.671.401.301.67
1.401.041.401.121.33
0.28700.20810.14300.18890.2968
0.27652.07694.12400.51820.4119
0.29680.07290.25980.18850.4615
R
kJ/(kgK )
SELECTED LIQUIDS AND SOLIDS
c p DensitySubstance
kJ/(kgK) Btu/(lbm-
R) kg/m 3 lbm/ft 3
Liquids
AmmoniaMercuryWater
4.800.1394.18
1.1460.0331.000
60213,560
997
38847
62.4
Solids
AluminumCopper Ice (0 C; 32 F)IronLead
0.9000.3862.110.4500.128
0.2150.0920.5020.1070.030
2,7008,900
9177,840
11,310
170555
57.2490705