73THERMODYNAMICS

THERMODYNAMICS

PROPERTIES OF SINGLE-COMPONENT SYSTEMSNomenclature1. Intensive properties are independent of mass.2. Extensive properties are proportional to mass.3. Specifi c properties are lowercase (extensive/mass).

State Functions (properties)Absolute Pressure, P (lbf/in2 or Pa)Absolute Temperature, T (°R or K)Volume, V (ft3 or m3)Specifi c Volume, v V m= (ft3/lbm or m3/kg)Internal Energy, U (Btu or kJ) Specifi c Internal Energy, u U m= (usually in Btu/lbm or kJ/kg) Enthalpy, H (Btu or KJ)Specifi c Enthalpy, h = u + Pv = H/m (usually in Btu/lbm or kJ/kg)Entropy, S (Btu/°R or kJ/K)Specifi c Entropy, s = S/m [Btu/(lbm-°R) or kJ/(kg•K)] 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 Th

pP2

2= b l

Heat Capacity at Constant Volume, c Tu

vv2

2= b l

Quality x (applies to liquid-vapor systems at saturation) is defi ned as the mass fraction of the vapor phase:

x = mg /(mg + mf), wheremg = mass of vapor, andmf = mass of liquid.

Specifi c volume of a two-phase system can be written:v = xvg + (1 – x)vf or v = vf + xvfg, wherevf = specifi c volume of saturated liquid,vg = specifi c volume of saturated vapor, andvfg = specifi c volume change upon vaporization. = vg – vf

Similar expressions exist for u, h, and s:u = xug + (1 – x) uf or u = uf + xufgh = xhg + (1 – x) hf or h = hf + xhfgs = xsg + (1 – x) sf or s = sf + xsfg

For a simple substance, specifi cation of any two intensive, independent properties is suffi cient to fi x all the rest.

For an ideal gas, Pv = RT or PV = mRT, andP1v1/T1 = P2v2/T2, where

P = pressure,v = specifi c volume,m = mass of gas,R = gas constant, andT = absolute temperature.V = volumeR is specifi c to each gas but can be found from

.,R

mol wtR where=

^ h

R = the universal gas constant = 1,545 ft-lbf/(lbmol-°R) = 8,314 J/(kmol⋅K).

For ideal gases, cp – cv = RAlso, for ideal gases:

Ph

vu0 0

T T22

22

= =b bl l

For cold air standard, heat capacities are assumed to be constant at their room temperature values. In that case, the following are true:

Δu = cvΔT; Δh = cp ΔTΔs = cp ln (T2 /T1) – R ln (P2 /P1); andΔs = cv ln (T2 /T1) + R ln (v2 /v1).

For heat capacities that are temperature dependent, the value to be used in the above equations for Δh is known as the mean heat capacity cp` j and is given by

c T T

c dTp

pT

T

2 1

1

2

=-

#

Also, for constant entropy processes:

;

,

PP

vv

TT

PP

TT

vv

k c cwhere

kk

k

k

p v

1

221

1

2

1

21

1

221

1

= =

= =

-

-

d d

d

n n

n

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:

,

Pva v b RT

a PR T

b PRT

6427

8wherec

c

c

c

2

2 2

+ - =

= =

d ^

b f

n h

l p

where Pc and Tc are the pressure and temperature at the critical point, respectively.

7� THERMODYNAMICS

FIRST LAW OF THERMODYNAMICSThe First Law of Thermodynamics is a statement of conservation of energy in a thermodynamic system. The net energy crossing the system boundary is equal to the change in energy inside the system.Heat Q is energy transferred due to temperature difference and is considered positive if it is inward or added to the system.Closed Thermodynamic SystemNo mass crosses system boundary

Q – W = ∆U + ∆KE + ∆PEwhere∆KE = change in kinetic energy, and∆PE = change in potential energy.Energy can cross the boundary only in the form of heat or work. Work can be boundary work, wb, or other work forms (electrical work, etc.)Work W w m

W=b l is considered positive if it is outward or

work done by the system.Reversible boundary work is given by wb = ∫P dv.

Special Cases of Closed SystemsConstant Pressure (Charles’ Law): wb = P∆v (ideal gas) T/v = constantConstant Volume: wb = 0 (ideal gas) T/P = constantIsentropic (ideal gas): Pvk = constant w = (P2v2 – P1v1)/(1 – k) = R(T2 – T1)/(1 – k)Constant Temperature (Boyle’s Law): (ideal gas) Pv = constant wb = RTln (v2 / v1) = RTln (P1/P2)Polytropic (ideal gas): Pvn = constant w = (P2v2 – P1v1)/(1 – n)Open Thermodynamic SystemMass crosses the system boundaryThere is flow work (Pv) done by mass entering the system.The reversible flow work is given by:

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 _ i

8 8B B

Wneto = rate of net or shaft work transfer,

ms = mass of fluid within the system,

us = specific internal energy of system, andQo = rate of heat transfer (neglecting kinetic and potential

energy of the system).

Special Cases of Open SystemsConstant Volume: wrev = – v (P2 – P1)Constant Pressure: wrev = 0Constant Temperature: (ideal gas) Pv = constant wrev = RT ln (v2 /v1) = RT ln (P1 /P2)Isentropic (ideal gas): Pvk = constant wrev = k (P2v2 – P1v1)/(1 – k) = kR (T2 – T1)/(1 – k)

wk

k RT PP

11

/

rev

k k

11

21

=-

--

d

^

n

h

> H

Polytropic: Pvn = constant wrev = n (P2v2 – P1v1)/(1 – n)Steady-State SystemsThe system does not change state with time. This assumption is 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 = mass flow rate (subscripts i and e refer to inlet and exit states of system),

g = acceleration of gravity,Z = elevation,V = velocity, andWo = rate of work.

Special Cases of Steady-Flow Energy EquationNozzles, Diffusers: Velocity terms are significant. No elevation change, no heat transfer, and no work. Single mass stream.

/ /h V h V2 2i i e e2 2

+ = +

Isentropic Efficiency (nozzle) = ,h h

V V2

wherei es

e i2 2

-

-

_ i

hes = enthalpy at isentropic exit state.

Turbines, Pumps, Compressors: Often considered adiabatic (no heat transfer). Velocity terms usually can be ignored. There are significant work terms and a single mass stream.

hi = he + w

75THERMODYNAMICS

Isentropic Efficiency (turbine) = h hh hi es

i e

--

Isentropic Efficiency (compressor, pump) = h hh h

e i

es i

--

Throttling Valves and Throttling Processes: No work, no heat transfer, and single-mass stream. Velocity terms are often insignificant.

hi = he

Boilers, Condensers, Evaporators, One Side in a HeatExchanger: Heat transfer terms are significant. For a single-mass stream, the following applies:

hi + q = he

Heat Exchangers: No heat or work. Two separate flow rates 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, Open or Closed Feedwater Heaters:mh m h

m m

andi i e e

i e

=

=

R R

R R

o o

o o

BASIC CYCLESHeat engines take in heat QH at a high temperature TH, produce a net amount of work W, and reject heat QL at a low temperature TL. The efficiency η of a heat engine is given by:

η = W/QH = (QH – QL)/QH

The most efficient engine possible is the Carnot Cycle. Its efficiency is given by:

ηc = (TH – TL)/TH, whereTH and TL = absolute temperatures (Kelvin or Rankine).The following heat-engine cycles are plotted on P-v and T-s diagrams (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.CoefficientofPerformance(COP) is defined as:

COP = QH /W for heat pumps, and asCOP = QL/W for refrigerators and air conditioners.

Upper limit of COP is based on reversed Carnot Cycle:COPc = TH /(TH – TL) for heat pumps andCOPc = TL /(TH – TL) 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 = Ni /N; N = Σ Ni; Σ xi = 1where Ni = number of moles of component i.

Mass Fraction: yi = mi /m; m = Σ mi; Σ yi = 1

Molecular Weight: M = m/N = Σ xiMi

Gas Constant: /R R M=

To convert mole fractions xi to mass fractions yi:

yx M

x Mi

i i

i i=R_ i

To convert mass fractions to mole fractions:

xy M

y Mi

i i

i i=R_ i

Partial Pressures: ;P P P VmRT

i ii i= =R

Partial Volumes: ;V V V Pm R T

i ii i= =! , where

P, V, T = the pressure, volume, and temperature of the mixture.

xi = Pi /P = Vi /V

Other Properties:u = Σ (yiui); h = Σ (yihi); s = Σ (yisi)ui and hi are evaluated at T, andsi is evaluated at T and Pi.

PSYCHROMETRICSWe deal here with a mixture of dry air (subscript a) and water vapor (subscript v):

P = Pa + Pv

SpecificHumidity(absolute humidity, humidity ratio) ω:ω= mv /ma, where

mv = mass of water vapor andma = mass of dry air. ω = 0.622Pv /Pa = 0.622Pv /(P – Pv)

Relative Humidity (rh) φ:φ = Pv /Pg

, wherePg = saturation pressure at T.

Enthalpy h: h = ha + ωhv

Dew-Point Temperature Tdp:Tdp = Tsat at Pg = Pv

76 THERMODYNAMICS

Wet-bulb temperature Twb is the temperature indicated by a thermometer covered by a wick saturated with liquid water and in contact with moving air.

Humid Volume: Volume of moist air/mass of dry air.

Psychrometric ChartA plot of specific humidity as a function of dry-bulb temperature plotted for a value of atmospheric pressure.(See chart at end of section.)

PHASE RELATIONSClapeyron Equation for Phase Transitions:

,dTdP

Tvh

vs

wheresat fg

fg

fg

fg= =b l

hfg = enthalpy change for phase transitions,vfg = volume change,sfg = entropy change,T = absolute temperature, and(dP/dT)sat = slope of phase transition (e.g.,vapor-liquid)

saturation line.Clausius-Clapeyron Equation This equation results if it is assumed that (1) the volume change (vfg) can be replaced with the vapor volume (vg), (2) the latter can be replaced with P RT from the ideal gas law, and (3) hfg is independent of the temperature (T).

ln PP

R

hTT

T Te

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 in oxygen:

CH4 + 2 O2 → CO2 + 2 H2O

Combustion in AirFor each mole of oxygen, there will be 3.76 moles of nitrogen. For stoichiometric combustion of methane in air:

CH4 + 2 O2 + 2(3.76) N2 → CO2 + 2 H2O + 7.52 N2

Combustion in Excess AirThe excess oxygen appears as oxygen on the right side of the combustion 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 ratio calculated from the stoichiometric combustion equation.

Percent Theoretical Air = A F

A F100

stoichiometric

actual #_

_

i

i

Percent Excess Air = A F

A F A F100

stoichiometric

actual stoichiometric #-

_

_ _

i

i i

SECOND LAW OF THERMODYNAMICSThermal Energy Reservoirs

∆Sreservoir = Q/Treservoir, whereQ is measured with respect to the reservoir.

Kelvin-Planck Statement of Second LawNo 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 higher efficiency than a Carnot Cycle operating between the same reservoirs.

Clausius’ Statement of Second LawNo refrigeration or heat pump cycle can operate without a net work input.

COROLLARY: No refrigerator or heat pump can have a higher COP than a Carnot Cycle refrigerator or heat pump.

VAPOR-LIQUID MIXTURESHenry’s Law at Constant TemperatureAt equilibrium, the partial pressure of a gas is proportional to its concentration in a liquid. Henry’s Law is valid for low concentrations; i.e., x ≈ 0.

Pi = Pyi = hxi, whereh = Henry’s Law constant,Pi = 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, andP = total pressure.

Raoult’s Law for Vapor-Liquid EquilibriumValid for concentrations near 1; i.e., xi ≈1.

Pi = xi Pi*, where

Pi = partial pressure of component i,xi = mol fraction of component i in the liquid, andPi

* = vapor pressure of pure component i at the temperature of the mixture.

77THERMODYNAMICS

ENTROPYds T Q

s s T Q

1

12 1 1

2

rev

rev

=

- =

d

d

_

_

i

i#

Inequality of Clausius

T Q

T Q s s

1 0

1 2 11

2

rev #

# -

d

d

_

_

i

i#

#

Isothermal, Reversible Process∆s = s2 – s1 = Q/T

Isentropic Process∆s = 0; ds = 0

A reversible adiabatic process is isentropic.

Adiabatic ProcessδQ = 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_ i

Temperature-Entropy (T-s) Diagram

∫= 21 sdTQrev

s

1

2

AREA = HEAT

T

Entropy Change for Solids and Liquidsds = c (dT/T)s2 – s1 = ∫c (dT/T) = cmeanln (T2 /T1),

where c equals the heat capacity of the solid or liquid.

IrreversibilityI = wrev – wactual

EXERGYExergy is the portion of total energy available to do work.

Closed-System Exergy (Availability)(no chemical reactions)

φ= (u – uo) – To (s – so) + po (v – vo)where the subscript o designates environmental conditions

wreversible = φ1 – φ2

Open-System Exergy (Availability)ψ= (h – ho) – To (s – so) + V 2/2 + gzwreversible = ψ1 – ψ2

Gibbs Free Energy, ∆GEnergy released or absorbed in a reaction occurring reversibly at constant pressure and temperature.

Helmholtz Free Energy, ∆AEnergy released or absorbed in a reaction occurring reversibly at constant volume and temperature.

78 THERMODYNAMICS

COMMON THERMODYNAMIC CYCLES Carnot Cycle Reversed Carnot

Otto Cycle (Gasoline Engine)

η = 1 – r 1 – k

r = v 1/v2

Rankine Cycle Refrigeration(Reversed Rankine Cycle)

( ) ( )3 4 2 1

3 2

h h h h

h h

− − −η =

−

p2 = p3

12

32HP

12

41ref hh

hhCOPhhhhCOP

−−

=−−=

p2 = p3

q = 0

q

q

w

w

q

q

T

c

79THERMODYNAMICS

STEAM TABLES Saturated Water - Temperature Table

Specific Volume m3/kg

Internal Energy kJ/kg

EnthalpykJ/kg

Entropy kJ/(kg·K)Temp.

oCT

Sat.Press.kPapsat

Sat.liquid

vf

Sat.vapor

vg

Sat.liquid

uf

Evap.

ufg

Sat.vapor

ug

Sat.liquid

hf

Evap.

hfg

Sat.vapor

hg

Sat.liquid

sf

Evap.

sfg

Sat.vapor

sg

0.015

101520253035404550556065707580859095

0.61130.87211.22761.70512.3393.1694.2465.6287.3849.593

12.349 15.758 19.940 25.03 31.1938.58 47.39 57.83 70.14 84.55

0.001 000 0.001 000 0.001 000 0.001 001 0.001 0020.001 003 0.001 004 0.001 006 0.001 008 0.001 0100.001 012 0.001 015 0.001 017 0.001 020 0.001 0230.001 026 0.001 029 0.001 033 0.001 036 0.001 040

206.14147.12106.3877.93 57.7943.36 32.89 25.22 19.52 15.2612.03

9.5687.6716.1975.0424.1313.4072.8282.3611.982

0.0020.97 42.00 62.99 83.95

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

0.0120.98 42.01 62.99 83.96

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

MPa100105110115120125130135140145150155160165170175180185190195200205210215220225230235240245250255260265270275280285290295300305310315320330340350360370374.14

0.101 35 0.120 82 0.143 27 0.169 06 0.198 530.23210.27010.31300.36130.41540.47580.54310.61780.70050.79170.89201.00211.12271.25441.39781.55381.72301.90622.1042.3182.5482.7953.0603.3443.6483.9734.3194.6885.0815.4995.9426.4126.9097.4367.9938.5819.2029.856

10.547 11.27412.845 14.586 16.513 18.651 21.0322.09

0.001 044 0.001 048 0.001 052 0.001 056 0.001 0600.001 065 0.001 070 0.001 075 0.001 080 0.001 0850.001 091 0.001 096 0.001 102 0.001 108 0.001 1140.001 121 0.001 127 0.001 134 0.001 141 0.001 1490.001 157 0.001 164 0.001 173 0.001 181 0.001 1900.001 199 0.001 209 0.001 219 0.001 229 0.001 2400.001 251 0.001 263 0.001 276 0.001 289 0.001 3020.001 317 0.001 332 0.001 348 0.001 366 0.001 3840.001 404 0.001 425 0.001 447 0.001 472 0.001 4990.001 561 0.001 638 0.001 740 0.001 893 0.002 2130.003 155

1.67291.41941.21021.03660.89190.77060.66850.58220.50890.44630.39280.34680.30710.27270.24280.21680.194 05 0.174 09 0.156 54 0.141 050.127 36 0.115 21 0.104 41 0.094 79 0.086 190.078 49 0.071 58 0.065 37 0.059 76 0.054 710.050 13 0.045 98 0.042 21 0.038 77 0.035 640.032 79 0.030 17 0.027 77 0.025 57 0.023 540.021 67 0.019 948 0.018 350 0.016 867 0.015 4880.012 996 0.010 797 0.008 813 0.006 945 0.004 9250.003 155

418.94440.02461.14482.30503.50524.74546.02567.35588.74610.18631.68653.24674.87696.56718.33740.17762.09784.10806.19828.37850.65873.04895.53918.14940.87963.73986.74

1009.891033.211056.711080.391104.281128.391152.741177.361202.251227.461253.001278.921305.21332.01359.31387.11415.51444.61505.31570.31641.91725.21844.02029.6

2087.62072.32057.02041.42025.82009.91993.91977.71961.31944.71927.91910.81893.51876.01858.11840.01821.61802.91783.81764.41744.71724.51703.91682.91661.51639.61617.21594.21570.81546.71522.01596.71470.61443.91416.31387.91358.71328.41297.11264.71231.01195.91159.41121.11080.9993.7894.3776.6626.3384.5

0

2506.52512.42518.12523.72529.32534.62539.92545.02550.02554.92559.52564.12568.42572.52576.52580.22583.72587.02590.02592.82595.32597.52599.52601.12602.42603.32603.92604.12604.02603.42602.42600.92599.02596.62593.72590.22586.12581.42576.02569.92563.02555.22546.42536.62525.52498.92464.62418.42351.52228.52029.6

419.04440.15461.30482.48503.71524.99546.31567.69589.13610.63632.20653.84675.55697.34719.21741.17763.22785.37807.62829.98852.45875.04897.76920.62943.62966.78990.12

1013.621037.321061.231085.361109.731134.371159.281184.511210.071235.991262.311289.071316.31344.01372.41401.31431.01461.51525.31594.21670.61760.51890.52099.3

2257.02243.72230.22216.52202.62188.52174.22159.62144.72129.62114.32098.62082.62066.22049.52032.42015.01997.11978.81960.01940.71921.01900.71879.91858.51836.51813.81790.51766.51741.71716.21689.81662.51634.41605.21574.91543.61511.01477.11441.81404.91366.41326.01283.51238.61140.61027.9893.4720.3441.6

0

2676.12683.82691.52699.02706.32713.52720.52727.32733.92740.32746.52752.42758.12763.52768.72773.62778.22782.42786.42790.02793.22796.02798.52800.52802.12803.32804.02804.22803.82803.02801.52799.52796.92793.62789.72785.02779.62773.32766.22758.12749.02738.72727.32714.52700.12665.92622.02563.92481.02332.12099.3

1.30691.36301.41851.47341.52761.58131.63441.68701.73911.79071.84181.89251.94271.99252.04192.09092.13962.18792.23592.28352.33092.37802.42482.47142.51782.56392.60992.65582.70152.74722.79272.83832.88382.92942.97513.02083.06683.11303.15943.20623.25343.30103.34933.39823.44803.55073.65943.77773.91474.11064.4298

6.04805.93285.82025.71005.60205.49625.39255.29075.19085.09264.99604.90104.80754.71534.62444.53474.44614.35864.27204.18634.10144.01723.93373.85073.76833.68633.60473.52333.44223.36123.28023.19923.11813.03682.95512.87302.79032.70702.62272.53752.45112.36332.27372.18212.08821.89091.67631.43351.13790.68650

7.35497.29587.23877.18337.12967.07757.02696.97776.92996.88336.83796.79356.75026.70786.66636.62566.58576.54656.50796.46986.43236.39526.35856.32216.28616.25036.21466.17916.14376.10836.07306.03756.00195.96625.93015.89385.85715.81995.78215.74375.70455.66435.62305.58045.53625.44175.33575.21125.05264.79714.4298

80 THERMODYNAMICS

Superheated Water Tables v

m3/kgu

kJ/kgh

kJ/kgs

kJ/(kg⋅K)v

m3/kgu

kJ/kgh

kJ/kgs

kJ/(kg⋅K)T

Temp.oC p = 0.01 MPa (45.81oC) p = 0.05 MPa (81.33oC)

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 (99.63oC) p = 0.20 MPa (120.23oC)Sat.100150200250300400500600700800900

1000110012001300

1.69401.69581.93642.1722.4062.6393.1033.5654.0284.4904.9525.4145.8756.3376.7997.260

2506.12506.72582.82658.12733.72810.42967.93131.63301.93479.23663.53854.84052.84257.34467.74683.5

2675.52676.22776.42875.32974.33074.33278.23488.13704.43928.24158.64396.14640.34891.05147.65409.5

7.35947.36147.61347.83438.03338.21588.54358.83429.09769.33989.56529.77679.9764

10.165910.346310.5183

0.8857

0.95961.08031.19881.31621.54931.78142.0132.2442.4752.7052.9373.1683.3993.630

2529.5

2576.92654.42731.22808.62966.73130.83301.43478.83663.13854.54052.54257.04467.54683.2

2706.7

2768.82870.52971.03071.83276.63487.13704.03927.64158.24395.84640.04890.75147.55409.3

7.1272

7.27957.50667.70867.89268.22188.51338.77709.01949.24499.45669.65639.8458

10.026210.1982

p = 0.40 MPa (143.63oC) p = 0.60 MPa (158.85oC)Sat.150200250300350400500600700800900

1000110012001300

0.46250.47080.53420.59510.6548

0.77260.88931.00551.12151.23721.35291.46851.58401.69961.8151

2553.62564.52646.82726.12804.8

2964.43129.23300.23477.93662.43853.94052.04256.54467.04682.8

2738.62752.82860.52964.23066.8

3273.43484.93702.43926.54157.34395.14639.44890.25146.85408.8

6.89596.92997.17067.37897.5662

7.89858.19138.45588.69878.92449.13629.33609.52569.70609.8780

0.3157

0.35200.39380.43440.47420.51370.59200.66970.74720.82450.90170.97881.05591.13301.2101

2567.4

2638.92720.92801.02881.22962.13127.63299.13477.03661.83853.44051.54256.14466.54682.3

2756.8

2850.12957.23061.63165.73270.33482.83700.93925.34156.54394.44638.84889.65146.35408.3

6.7600

6.96657.18167.37247.54647.70798.00218.26748.51078.73678.94869.14859.33819.51859.6906

p = 0.80 MPa (170.43oC) p = 1.00 MPa (179.91oC)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 44 0.20600.23270.25790.28250.30660.35410.40110.44780.49430.54070.58710.63350.67980.7261

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

81THERMODYNAMICS

P-h DIAGRAM FOR REFRIGERANT HFC-134a(metric units)

(Reproduced by permission of the DuPont Company)

82 THERMODYNAMICS

ASHRAE PSYCHROMETRIC CHART NO. 1(metric units)

(Reproduced by permission of ASHRAE)

83THERMODYNAMICS

THERMAL AND PHYSICAL PROPERTY TABLES(at room temperature)

GASES

cp cvSubstance Mol

wt kJ/(kg·K) Btu/(lbm-°R) kJ/(kg·K) Btu/(lbm-°R)k

GasesAirArgonButaneCarbon dioxide Carbon monoxide

EthaneHeliumHydrogenMethaneNeon

NitrogenOctane vapor OxygenPropaneSteam

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/(kg·K)

SELECTED LIQUIDS AND SOLIDS

cp DensitySubstance

kJ/(kg·K) Btu/(lbm-°R) kg/m3 lbm/ft3

Liquids

AmmoniaMercuryWater

4.80 0.139 4.18

1.146 0.033 1.000

60213,560

997

3884762.4

Solids

AluminumCopperIce (0°C; 32°F)

IronLead

0.900 0.386 2.11 0.450 0.128

0.215 0.092 0.502 0.107 0.030

2,7008,900

9177,840

11,310

17055557.2

490705