Fe Thermodynamics Reference Handbook1

8/10/2019 Fe Thermodynamics Reference Handbook1

1/117

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


2/1174

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.


6/1178

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


7/1179

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


8/1180

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


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


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


9/118

THERMODYNAMICS

P- h DIAGRAM FOR REFRIGERANT HFC-134a


10/1182

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


11/118

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

Fe Thermodynamics Reference Handbook1

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