psychrometrics - wordpress.com · 09/04/2015 · psychrometrics abstract. this chapter includes...

Psychrometrics

Abstract. This chapter includes basic coverage of psychrometric properties and psychrometric processes. Emphasis is upon properties and processes relative to the environment and to processing of biological materials. The chapter also includes a discussion of steam properties and use of steam tables.

Keywords. Cooling, drying, dew point temperature, enthalpy, heating, humidity ra-tio, psychrometrics, steam quality, relative humidity, wet bulb temperature, steam, steam-air mixtures, steam tables.

9.1 Introduction Air is a mixture of many different gases (a mixture we call dry air) and water va-

por. If pressures do not greatly exceed atmospheric pressure, the perfect gas relation-ships are valid for these air-water vapor mixtures. These ideal gas relationships are used to evaluate thermodynamic properties of the mixtures. This field of study is called psychrometrics.

An understanding of psychrometrics is important in the drying and storage of se-lected food products. Proper drying conditions are necessary to control the drying rate and resulting quality of dried product. In addition, specific psychrometric conditions have been identified for optimum storage of many fresh and dried products. These are further discussed in other chapters. Psychrometric properties are also important in as-sessing environmental conditions relative to plant and animal health.

9.2 Relationships Derived from the Perfect Gas Law The properties of air/water vapor mixtures are based upon ideal gas relationships.

Thus, we will review the basic relationships needed to define important psychrometric properties. The perfect gas law may be written in different forms as:

PV = N Ru T (9.01)

PV = N M R T (9.02)

Pv = R T (9.03)

PV = m R T (9.04)

where: m = mass of the gas, kg M = molecular weight of the gas, kg/kmol N = number of moles of the gas P = pressure, kPa

mccann

Wilhelm, Luther R., Dwayne A. Suter, and Gerald H. Brusewitz. 2004. Psychrometrics. Chapter 9 in Food & Process Engineering Technology, 213-257. St. Joseph, Michigan: ASAE. © American Society of Agricultural Engineers. (Rev. Aug. 2005.)

214 Food & Process Engineering Technology

R = gas constant for a particular gas, Ru /M, kPa m3/kg K Ru = universal gas constant, Ru = 8.314 kPa m3/kmol K (or 8.314 kJ/kmol K) T = absolute temperature, K v = specific volume of the gas, m3/kg V = total volume of the gas, m3

Units for the gas constants R and Ru can be expressed in several different forms. The units given above for Ru are probably the most descriptive; however, using unit factors to convert units, we can also obtain units of kN m/kmol K without affecting the numeric value of 8.314. Similarly, R may be expressed in units of kPa m3/kg K, kN m/kg K, or kJ/kg K without affecting the numeric value. Molecular weights and gas constants for air and water vapor (using the units given above) are: Ma = 28.96, Ra = 0.28706, Mw = 18.015, and Rw = 0.46152.

For a mixture of several gases, Equations 9.01 to 9.04 may be written separately for each gas. If Equation 9.01 is used, the equation for the total mixture becomes:

P = (N1 + N2 + N3 + ...) Ru T/V (9.05)

For air containing water vapor, the total pressure is given by:

P = Pa + Pw (9.06)

where Pa is the partial pressure of the dry air (including all its component gases) and Pw is the partial pressure of the water vapor. These two partial pressures may be writ-ten (using Equation 9.01) as:

Pa = Na Ru T/V (9.07)

Pw = Nw Ru T/V (9.08)

The partial pressure of water vapor is a very important parameter in psychromet-rics. It is frequently used to calculate other psychrometric properties. For example, relative humidity (φ) is defined as the ratio of the amount of water vapor in the air (Nw) to the amount the air will hold when saturated at the same temperature (Nws). Thus:

ws

w

NN

=φ (9.09)

Using Equation 9.08, we can rewrite Equation 9.09 as:

ws

w

uws

uw

PP

TRVP

TRVP

==φ (9. 10)

The partial pressure of water vapor at saturation (Pws) is a function only of tempera-ture. However, this relationship is complex, involving multiple exponential and loga-rithmic terms (Wilhelm, 1976).

Chapter 9 Psychrometrics 215 Another psychrometric parameter of interest is the humidity ratio (W). The humid-

ity ratio is the ratio of the mass of water vapor in the air to the mass of the dry air:

a

w

mmW = (9.11)

Referring to the ideal gas equation in the form of Equation 9.04, we can write:

a

w

a

w

aw

wa

aa

ww

a

w

PP

PP

PRPR

TRVP

TRVP

mmW 622.0

46152.028706.0

===== (9.12)

The partial pressure of the dry air (Pa) is the difference between atmospheric pres-sure and the partial pressure of the water vapor, also called vapor pressure:

wa PPP −= (9.13)

Thus:

w

w

PPPW−

= 622.0 (9.14)

or, solving for Pw:

W

WPPw +=

622.0 (9.15)

The degree of saturation (µ) is another psychrometric parameter that is sometimes used. It is the humidity ratio divided by the humidity ratio at saturation:

sW

W=µ (9.16)

A final parameter that can be determined from the perfect gas law is the specific volume (ν) of the moist air. The specific volume is defined in terms of a unit mass of dry air. Thus, using Equations 9.04 and 9.13:

w

a

a

a

a

aaa

a PPTR

PTR

mPTRm

mVv

−==== (9.17)

Substituting from Equation 9.15 for Pw:

( )WP

TR

WWPP

TRv aa 608.11

622.0

+=

+−

= (9.18)


9.3 Other Important Parameters The dew point temperature (tdp) is the temperature at which moisture begins to

condense if air is cooled at constant pressure. The dew point temperature is directly related to partial pressure of the water vapor (Pw); however, that relationship is com-plex, involving several logarithmic terms (ASHRAE, 1997). Since Pw is also related to the humidity ratio W, this means that specifying any one of the three parameters tdp, Pw, and W specifies all three.

The wet-bulb temperature (twb) is the temperature measured by a sensor (origi-nally the bulb of a thermometer) that has been wetted with water and exposed to air movement that removes the evaporating moisture. The evaporating water creates a cooling effect. When equilibrium is reached, the wet-bulb temperature will be lower than the ambient temperature. The difference between the two (the wet bulb depres-sion) depends upon the rate at which moisture evaporates from the wet bulb. The evaporation rate, in turn, depends upon the moisture content of the air. The evapora-tion rate decreases as the air moisture content increases. Thus, a small wet bulb de-pression indicates high relative humidity, while a large wet bulb depression is indica-tive of low relative humidity.

The enthalpy (h) of moist air is one of the most frequently used psychrometric pa-rameters. It is a measure of the energy content of the air and depends upon both the temperature and the moisture content of the air. It is determined by adding the en-thalpy of the moisture in the air (W hw) to the enthalpy of the dry air (ha):

( )tchWtchWhh pwfgpawa ++=+= (9.19)

or:

( )tWth 805.12501006.1 ++= (9.20)

Equation 9.20 is based upon a specific heat for air of 1.006 kJ/kg K and a zero value of h at t = 0°C. The enthalpy of water is based upon: a zero value of h at 0°C (liquid state); hfg = 2501 kJ/kg at 0°C; and an average specific heat for water vapor of 1.805 kJ/kg K. Equation 9.20 provides a good approximation for the enthalpy of moist air over a wide range of temperatures; however, the error increases rapidly at tempera-tures above 100°C. Empirical relationships, charts, or tables must then be used to de-termine h.

9.4 Psychrometric Charts If two independent psychrometric parameters are known, all the psychrometric pa-

rameters previously discussed can be computed numerically. However, numerical cal-culation is practical only if the calculation method is computerized. The fastest and easiest method of evaluating psychrometric properties is often the use of a psy-chrometric chart. The psychrometric chart shows selected psychrometric properties as a function of each other. Properties shown on most psychrometric charts are dry-bulb, wet-bulb, and dew point temperatures; relative humidity; humidity ratio; en-thalpy; and specific volume. Figure 9.01 is a typical psychrometric chart. It covers the

Chapter 9 Psychrometrics 217

Figure 9.01. Psychrometric chart for normal temperatures (SI units).

(Courtesy of the American Society of Heating, Refrigerating and Air-Conditioning Engineers.)


“normal temperature” range at standard atmospheric pressure. Other charts are avail-able for higher and lower temperature ranges and for pressures above and below one atmosphere. In addition, different chart versions are available for these common psy-chrometric ranges. The general arrangement of all charts is the same; however, differ-ences in appearance are obvious. The procedure for reading the psychrometric pa-rameters differs little among the charts—except for the enthalpy and (occasionally) the wet-bulb temperature. We will use Figure 9.01 to gain an understanding of psy-chrometric charts. Before reading further, you should examine this figure closely. Identify the lines representing parameters such as dew point, wet-bulb and dry-bulb temperatures, humidity ratio, etc.

Each position on a psychrometric chart represents a unique state point. Any two in-dependent psychrometric properties define such a state point. We will now use two properties to define a state point and then determine the values of the other psy-chrometric properties. Let us assume that we used a psychrometer, a device that measures wet-bulb and dry-bulb temperatures, and obtained the following measure-ments:

twb = 17.1°C

t = 24°C

To find the state point represented by these values, we follow a vertical line upward from t = 24°C at the bottom of the chart. We then locate the point where this line in-tersects with an imaginary line just above, and parallel to, the dashed line sloping downward to the right from a wet-bulb temperature of 17.0°C. The intersection of the lines (circled on Figure 9.01) represents the desired state point. Note that the tempera-tures on the curved line at the upper left of the chart may represent either dew point (saturation temperature), wet-bulb, or dry-bulb temperatures. A constant wet-bulb temperature is represented by a line sloping downward to the right; a constant dew point temperature is represented by a horizontal line; and a constant dry bulb line is represented by a vertical (or near vertical) line. At saturation (100% relative humid-ity), the dry bulb, wet-bulb and dew point temperatures are equal. At any other condi-tion, they are not equal and follow the order t > twb > tdp.

We have now located the state point (indicated by the center of the circle on Figure 9.01). Moving left horizontally from this point, we find that the dew point is 13.0°C. Also, moving right along this horizontal line we find that the humidity ratio is 9.3 g/kg of dry air. Relative humidity is represented by lines curving upward to the right. Our state point appears to be exactly on the 50% line. Thus, φ = 50%.

Similarly, the specific volume is found by interpolating between the 0.85 and 0.86 constant specific volume lines which slope sharply downward to the right. We find that v = 0.854 m3/kg. The partial pressure of the water vapor can be calculated from Equation 9.15, noting that P = 101.325 kPa and W must be dimensionless (0.0093 kg/kg of dry air, instead of the 9.3 g/kg noted above):

kPa 493.10093.0622.00093.0325.101

=+

×=wP

Chapter 9 Psychrometrics 219 The psychrometric chart shown in Figure 9.01 is only one of several versions of

psychrometric charts available. Two other charts are shown in Figures 9.02 and 9.03. Figure 9.02 covers lower temperature ranges not covered by Figure 9.01. Figure 9.03 is a greatly condensed chart that extends to higher temperatures. All these charts pre-sent the data in SI units. Similar charts are available using US units. Although there are some differences in chart arrangement, the same interpretation procedures apply for all psychrometric charts.

In reading the psychrometric chart, you should keep the following points in mind: 1. Enthalpy, humidity ratio, and specific volume are referenced to a unit mass of

dry air. 2. On charts using US units, the humidity ratio may be given in pounds of moisture

per pound of dry air or in grains of moisture per pound of dry air. Since one pound contains 7000 grains, the two measurements can be converted as needed. In SI units, the humidity ratio is expressed in either grams of water or kilograms of water per kilogram of dry air.

3. Constant enthalpy and constant wet bulb lines are not parallel, although there is only a slight difference in slope. Because of this, most charts do not show both constant wet-bulb and constant enthalpy lines. Only one parameter is usually plotted, although the other may be plotted at wide intervals. In the example used earlier, the enthalpy is 48 kJ/kg dry air. Note the short sloping lines along the right edge and bottom of the chart. These represent constant enthalpy lines cor-responding to similar lines along the enthalpy scale at the upper left. By using a straight edge to align the point in the circle on Figure 9.01 with equal values of enthalpy along the bottom and upper left of the chart, we find that the enthalpy value is 48 kJ/kg dry air. Some charts use an enthalpy correction curve. These curves show the adjustment to correct for deviation between constant enthalpy and constant wet-bulb lines. On these charts, the constant wet-bulb line is fol-lowed to find a value for enthalpy from the enthalpy scale at upper left. That value is then adjusted by subtracting the value of the enthalpy correction.

9.4.1 Psychrometric Tables Tabulated values of psychrometric properties (see Table 9.01) can also be used for

analysis of psychrometric data. However, use of the tables is more time consuming than use of a chart. Use of the table also has limitations. For example, the wet bulb temperature cannot be directly related to any tabulated properties. However, we can use the table to determine other psychrometric properties at t = 24°C and 50% relative humidity. This is the same point used in the chart analysis; however, we can expect the values of some properties to differ slightly from those determined by the chart. Results obtained using the table would normally be considered more accurate than those from a psychrometric chart.

To find the partial pressure (or vapor pressure) of water vapor in the air, we note that relative humidity is defined as φ = Pw /Pws (Equation 9.10). At t = 24°C, the table gives Pws = 2.9852. Solving for Pw = φ Pws = 0.5(2.9852) = 1.4926 kPa. This is essen-tially the same value found from the psychrometric chart. We can now use Equation 9.14 to solve for the humidity ratio (W) at 24°C and 50% relative humidity:


Figure 9.02. Psychrometric chart for low temperatures (SI units). (Courtesy of

the American Society of Heating, Refrigerating and Air-Conditioning Engineers.)


Figure 9.03. Psychrometric chart for high temperatures (SI units). (Courtesy of the American Society of Heating, Refrigerating and Air-Conditioning Engineers.)


DAkgO Hkg00930

49261325101492610622006220 2.

....

PPP

.Ww

w =−

×=−

×=

Since the dew point temperature is defined as the temperature at which 100% rela-tive humidity is reached as the air is cooled, this would be the temperature at which Ws = 0.0093 kg H2O/kg DA. Searching the table for the temperature corresponding to Ws = 0.0093 kg H2O/kg DA, we find that tdp = 13°C at Ws = 0.009370 kg H2O/kg DA. This is slightly above but very close to the look-up value of 0.0093 that we are using. If necessary, we could interpolate to find the temperature corresponding to Ws = 0.0093. Note that this should also be the temperature corresponding to Pws = 1.4926 kPa. Note also that Ws = 0.018963 at 24°C; but since we have only 50% relative hu-midity, that moisture level is never reached.

The remaining two properties, specific volume (v) and enthalpy (h) can be deter-mined from the table by noting that each are made up of an air component and a water component. For example, the energy content (h) of the wet air is the sum of energy from the dry air and energy from the moisture present. The enthalpy columns of the table give values of ha (enthalpy of the dry air), hs (enthalpy of the saturated air), and has (enthalpy added by the moisture to produce saturated air and equal to hs – ha). We can determine h at any moisture content by using these values and the equation:

h = ha + µ has, where sW

W=µ (9.21)

Rewriting the equation, substituting for µ, and inserting values for all the properties, we find:

DAkgkJ8.47239.48

018963.00093.0146.24 =×+=×+= as

sa h

WWhh

This compares to a value of 48 found from the chart. The solution for specific volume follows exactly the same procedure:

DAkgm8542.00256.0

018963.00093.08416.0

3

=×+=×+= ass

a vWWvv

Again, the resulting value is very close to the value determined from the psychromet-ric chart. Typically, use of the tabulated values, while more time consuming, will give more accurate results than use of the psychrometric chart.


Table 9.01. Selected thermodynamic properties of moist air.[a] Condensed Water

Volume Enthalpy (m3/kgda) (kJ/kgda)

Temp (°C)

t

Humidity Ratio

(kgw/kgda)Ws va vas vs ha has hs

Enthalpy (kJ/kg)

h w

Vapor Pressure

(kPa) pws

0 0.003789 0.7734 0.0047 0.7781 0.000 9.473 9.473 0.06 0.61122 0.004381 0.7791 0.0055 0.7845 2.012 10.970 12.982 8.49 0.70604 0.005054 0.7848 0.0064 0.7911 4.024 12.672 16.696 16.91 0.81356 0.005818 0.7904 0.0074 0.7978 6.036 14.608 20.644 25.32 0.93538 0.006683 0.7961 0.0085 0.8046 8.047 16.805 24.852 33.72 1.07299 0.007157 0.7990 0.0092 0.8081 9.053 18.010 27.064 37.92 1.1481

10 0.007661 0.8018 0.0098 0.8116 10.059 19.293 29.352 42.11 1.228011 0.008197 0.8046 0.0106 0.8188 11.065 20.658 31.724 46.31 1.312812 0.008766 0.8075 0.0113 0.8152 12.071 22.108 34.179 50.50 1.402613 0.009370 0.8103 0.0122 0.8225 13.077 23.649 36.726 54.69 1.497914 0.010012 0.8132 0.0131 0.8262 14.084 25.286 39.370 58.88 1.598715 0.010692 0.8160 0.0140 0.8300 15.090 27.023 42.113 63.07 1.705516 0.011413 0.8188 0.0150 0.8338 16.096 28.867 44.963 67.26 1.818517 0.012178 0.8217 0.0160 0.8377 17.102 30.824 47.926 71.44 1.938018 0.012989 0.8245 0.0172 0.8417 18.108 32.900 51.008 75.63 2.064319 0.013848 0.8274 0.0184 0.8457 19.114 35.101 54.216 79.81 2.197920 0.014758 0.8302 0.0196 0.8494 20.121 37.434 57.555 84.00 2.338921 0.015721 0.8330 0.0210 0.8540 21.127 39.908 61.035 88.18 2.487822 0.016741 0.8359 0.0224 0.8583 22.133 42.527 64.660 92.36 2.644823 0.017821 0.8387 0.0240 0.8627 23.140 45.301 68.440 96.55 2.810524 0.018963 0.8416 0.0256 0.8671 24.146 48.239 72.385 100.73 2.985225 0.020170 0.8444 0.0273 0.8717 25.153 51.347 76.500 104.91 3.169326 0.021448 0.8472 0.0291 0.8764 26.159 54.638 80.798 109.09 3.363327 0.022798 0.8501 0.0311 0.8811 27.165 58.120 85.285 113.27 3.567428 0.024226 0.8529 0.0331 0.8860 28.172 61.804 89.976 117.45 3.782329 0.025735 0.8558 0.0353 0.8910 29.179 65.699 94.878 121.63 4.008430 0.027329 0.8586 0.0376 0.8962 30.185 69.820 100.00 125.81 4.246235 0.036756 0.8728 0.0514 0.9242 35.219 94.236 129.455 146.71 5.628040 0.049141 0.8870 0.0698 0.9568 40.253 126.43 166.683 167.61 7.383845 0.065411 0.9012 0.0943 0.9955 45.289 168.87 214.164 188.51 9.593550 0.086858 0.9154 0.1272 1.0425 50.326 225.02 275.345 209.42 12.350355 0.115321 0.9296 0.1713 1.1009 55.365 299.77 355.137 230.33 15.760160 0.15354 0.9438 0.2315 1.1752 60.405 400.46 460.863 251.25 19.943965 0.20579 0.9580 0.3147 1.2726 65.446 538.55 603.995 272.18 25.039770 0.27916 0.9721 0.4328 1.4049 70.489 732.96 803.448 293.13 31.1986

[a]Abridged data taken from ASHRAE. 1997. Handbook of Fundamentals, Chapter 6. Courtesy of the American Society of Heating, Refrigerating and Air-Conditioning Engineers.


9.5 Processes on the Psychrometric Chart The psychrometric chart is used in many applications both within and outside the

food industry. It is used extensively to analyze product drying and air cooling, primar-ily because it is a simple and quick alternative to more costly methods. Drying with air is an extremely cost-effective method to reduce the moisture of a biological material, and the addition of a small amount of heat significantly improves the air’s drying po-tential. Air at a particular temperature and pressure has a limit to its drying capability and so it is useful to understand the changes in its drying potential as moisture is added or removed by the food materials, people, animals, etc. Hot, dry environments for animals, including humans, can be made more comfortable by evaporative cooling, a low-cost method that lowers the air temperature as a trade-off for increasing humid-ity. The addition of moisture to the air is valuable in certain applications as seen in summertime greenhouse evaporative cooling. Fruit and vegetables harvested in hot weather often can be cooled with evaporatively cooled air to reduce respiration.

Large industrial plants, particularly food processing plants, generating waste heat and needing cooling often utilize cooling towers to reduce their refrigeration require-ments. Cooling towers, operating on the evaporative cooling principle, provide a way to cool water by rejecting the unwanted heat to the atmosphere.

In all these applications, we are concerned with following a process that can be de-scribed on the psychrometric chart. By a process we mean moving from one state point to another state point on the chart. We will look at a few simple processes, and display the paths of these processes on small psychrometric charts in Figure 9.04. Se-lected relevant properties are also noted on each chart (Charts I, II, III, IV, V, VI). These are ideal processes assuming no heat transfer from the surroundings. In actual processes, there will always be some heat gain or loss. a. Heating or cooling. These processes follow a constant moisture line (constant hu-

midity ratio). Thus, temperature increases or decreases but moisture content and dew point are unchanged. Process A–B (Chart I) represents a heating process, while process A–B (Chart II) represents cooling. If cooled below the dew point (Chart III), the constant humidity ratio line is followed until the dew point (Point D) is reached. Further cooling follows the saturation (100% relative humidity) line until the final temperature (Point B) is reached. Moisture is condensed during the part of the process that follows the saturation line.

b. Moisture addition (i.e., evaporation) while using only energy from the air (Chart IV). Both drying and evaporative cooling follow this process. It is represented by a constant wet-bulb line (Process A–B.) Temperature, moisture content, etc., change but the wet-bulb temperature remains constant. This can be verified by an energy balance analysis. Note that enthalpy increases slightly in this process. This is due to energy present in the water before it is evaporated.

c. Heating and drying (Chart V). This combination of the processes shown in Charts I and IV is common in drying applications. Air is heated (Process A–B) and passed over the material to be dried (Process B–C). A second stage of heating (C–D) and drying (D–E) is sometimes included.


d. Adiabatic mixing (no heat transfer) of air (Chart VI). Moist air from two sources and at different state points is mixed to produce air at a third state point. Relation-ships among the properties at the three state points are established from mass and energy balances for the air and water components:

aCaBaA mmm =+ air mass balance (9.22)

CaCBaBAaA WmWmWm =+ water mass balance (9.23)

CaCBaBAaA hmhmhm =+ energy balance (9.24)

These equations are usually solved to relate specific properties to the specific masses involved. For example, we can use Equations 9.22 to 9.24 to obtain the fol-lowing relationships:

BA

BC

BA

BC

aC

aA

WWWW

hhhh

mm

−

−=

−

−= (9.25)

Subscripts A and B in the above equations represent entering air streams, while subscript C represents conditions after mixing. Note that this process does not fol-low a constant property line on the psychrometric chart. The position of Point C along the line between Points A and B is determined by the proportion of air at each state point included in the mix. If equal amounts of air are provided from each source, Point C will be at approximately the midpoint of the line. If 90% of the air is from state Point B, Point C will be approximately 90% of the distance from Point A and 10% of the distance from Point B. This scaled approach is useful as a quick estimate of the resulting state point. It is also useful as a quick verification of nu-merical calculations. However, use of the above equations to calculate the state point of mixed air is the preferred approach.

e. Adiabatic Saturation. The drying process was identified earlier as a constant wet-bulb process. While this is the generally accepted approach, a review of the adia-batic saturation process is provided here for added clarification. An adiabatic satu-ration process occurs when the humidity of air is increased as it flows through an insulated chamber as shown below. Water evaporates into the air as it passes through the chamber. If the chamber is long enough for equilibrium to occur, then the exit air will be saturated at an equilibrium temperature t*.

With no heat transfer, the energy balance then becomes:

sfs hhWWh =−+ )( 11

If the water temperature inside the chamber is equal to the exit temperature, the above equation for adiabatic saturation becomes:

**1

*1 )( sfs hhWWh =−+


BA

Sensible Heating

Heating Coil

BA

WA = WB

tBtA

hB

hA

tdp

Sensible Cooling

Cooling Coil

BA WA = WB

tB tA

hA

hB

tdpBA

Sensible Cooling followed bycondensation formation

Cooling Coil with Condensation

tB

B

A

Ah

WA

WB

hBd

tAtd

BA

Chart I

Chart II

Chart III

Figure 9.04. Examples of psychrometric processes (continued next page).


A B

Evaporative Cooling

Evaporative Pad

B

A

hA

tB tA

WB

WA

Sensible Heating-Evaporative Cooling

Evaporative Pad

A B D E

Preheater Reheater

twbC = twbB

hA

hB

twbD E

A B

CD

tCtA tB tD

WE

WC = WD

WA = WB

C

tA

WC

WA

tC tB

hA

hC

hB

WB

A

B

Adiabatic Mixing

Cooling andDehumidification

B

AC

C

Chart IV

Chart V

Chart VI

hB

Figure 9.04 (continued). Examples of psychrometric processes.


where: h1 = enthalpy of entering air *fh = enthalpy of saturated liquid at t* *sh = enthalpy of saturated air at t*

W1 = humidity ratio of entering air *

sW = humidity ratio of saturated air at t* (this is also W2, since t2 = t*)

Air

Watert t

t*1 2W W1 2

The second term of the equation is the amount of energy added to the air as it passes through the chamber. This is energy already present in the liquid water that is evaporated into the air. The temperature, t*, that satisfies the above equation is called the thermodynamic wet-bulb temperature.

The thermodynamic wet-bulb temperature is not quite the same as the wet-bulb temperature. The wet-bulb temperature is obtained by cooling in a combined heat and mass transfer process governed by an equation slightly different from the adia-batic saturation equation. Comparison of the two equations introduces a dimen-sionless Lewis number Le:

pkchLe =

where: h = surface heat transfer coefficient at the wet-bulb temperature (W/m2 K) cp = specific heat of most air (J/kg K) k = air-film coefficient of mass transfer (kg/m2 s)

If this Lewis number is exactly equal to one, then the wet-bulb and thermody-namic wet-bulb temperatures are equal. Fortunately, for air-water vapor mixtures the Lewis number is very close to one. Thus, the wet-bulb temperature is normally considered the same as the adiabatic saturation, or thermodynamic wet-bulb tem-perature. This relationship is valid only for air and water vapor mixtures. It is not valid with other materials (e.g., air and alcohol) where the Lewis number may sub-stantially deviate from one.

Most real processes do not occur along a constant property line. A number of fac-tors influence each process such that, for example, a constant wet-bulb process is very difficult to attain. In such cases, we may not be able to follow the process on the chart. Instead, we identify the initial and final state points and determine the changes in properties between the two. The following examples will show how psychrometric charts may be used to evaluate processes.

Example 9.1

Air at 30°C and 10% relative humidity enters an evaporative cooler where mois-ture is evaporated until the temperature reaches 21°C. What is the relative hu-midity of the air as it leaves?


Solution: The initial conditions (at t1 = 30°C and φ1 = 10%) are (using Figure 9.01): twb = 13.3°C h1 = 37 kJ/kg dry air w1 = 2.6 g/kg dry air This method of moisture addition is a constant wet-bulb process (Chart IV of Figure 9.04.). By following a constant wet-bulb line to t2 = 21°C, we find: φ2 = 41% ANSWER

Example 9.2

Steam is added to air at 30°C and 10% relative humidity until the temperature reaches 38°C and the humidity ratio (W) is 18 g water/kg dry air. How much wa-ter is added to one kilogram of air? Solution: This process does not follow a constant property line. Instead, we define state point one (Example 9.1) and state point two from the given information. Thus, state point two has the following properties: t2 = 38°C (given) W2 = 18 g/kg dry air (given) φ2 = 43% twb = 26.9°C tdp = 23.2°C h2 = 84.5 kJ/kg dry air The moisture added is W2 – W1 = 18 – 2.6 = 15.4g/kg dry air ANSWER

Example 9.3

Air at 20°C, 50% relative humidity (State 1) is heated to 55°C (State 2). The heated air passes through a dryer and exits at a relative humidity of 90% (State 3). How much water is removed for each cubic meter of air entering the heater? How much heat is added during the heating process? Solution: The processes followed for the heating and drying are: (1) constant humidity ra-


tio (or dew point) for heating, and (2) constant wet-bulb temperature for drying. This is represented by processes A–B and B–C shown on Chart V of Figure 9.04. From Figure 9.01, the properties at each state point are:

Property State 1 State 2 State 3 t (°C) 20[a] 55[a] 26.1

twb (°C) 13.7 24.8 24.8 [b] tdp (°C) 9.0 9.0 [b] 24.3 φ (%) 50[a] 7 90[a]

h (kJ/kg) 38.4 74.7 75.6 W (g H2O/kg dry air) 7.3 7.3 19.5

v (m3/kg dry air) 0.84 0.93 0.87 [a] Properties given in the problem statement. [b] Properties unchanged from previous state point

From the table:

Wrem = W3 – W2 = 19.5 – 7.3 = 12.2 g H2O/kg DA •

Q = h2 – h1 = 74.7 – 38.4 = 36.3 kJ/kg DA

We must now convert to volumetric values based upon the entering air:

32

3

2

mO Hg

514

DAkgm840

DAkgO Hg212

..

.Wrem == ANSWER

mkJ243

DAkgm840

DAkgkJ336

3 ..

.Q ==•

ANSWER

Example 9.4

Air at State Point 3 of Example 9.3 is cooled to 20°C. (1) How much water is removed from the air? (2) How much heat is removed? Solution: From Example 9.3, Point 3 is defined as: t = 26.1°C; tdp = 24.3°C; φ = 90%; and h = 75.6 kJ/kg. (These values are given in the table for the previous example.) Using Figure 9.01, we find W=19.5 g H2O/kg DA.

Chapter 9 Psychrometrics 231 From this point, the cooling process follows a horizontal line (constant W) to 100% relative humidity. Air is now at the dew point temperature (24.3°C). The process then follows the saturation (φ =100%) line to t=twb=tdp=20°C. The en-thalpy and humidity ratio at this point are 57.2 kJ/kg DA and 14.75 g H2O/kg DA. Thus the answers are: ∆W = 19.5 – 14.75 = 4.75 g H2O/kg DA ANSWER 1

•

Q = ∆h = 75.1 – 57.2 = 17.9 kJ/kg DA ANSWER 2

Example 9.5

If the exit flow rate for the air of Example 9.4 is 800 L/s, what are the rates of water and heat removal? Solution: At the exit conditions, v = 0.85 m3/kg DA. Thus, the mass flow rate is:

s DAkg941.0

mL1000

DAkgm85.0

sL800

3

3 =

×

=•

am

s

O Hg474s DAkg9410

DAkgO Hg754 22 ...W =×=∆ ANSWER

kW 8516skJ8516

s DAkg9410

DAkgkJ917 ....Q ==×=

• ANSWER

Example 9.6

Air at 80°C and φ = 4% (Point A) is mixed with air at 40°C and φ = 50% (Point B). The ratio is 60% of air at 80°C to 40% at 40°C. What is the state point of the resulting mix (Point C)? Solution: We can use Equation 9.24 to find properties of the mixed air, but we must first use psychrometric charts to find the enthalpy and humidity ratios for Points A and B.


We must use the high temperature chart (Figure 9.03) for Point A. At t = 80°C and φ = 4%, we find:

WA = 12 g/kg DA hA = 115 kJ/kg DA

For Point B, we may use either Figure 9.03 or 9.01; however, it is easier to read the property values from Figure 9.01. Using that figure, we find at t = 40°C and φ = 50%:

WB = 23.5 g/kg DA hB = 101 kJ/kg DA

Air at properties of Point A represents 60% of the mix. Thus 6.0=aC

aA

mm .

Using Equation 9.24, we can solve for hc (or Wc) as ( )BAaC

aABC hh

mmhh −+=

or: hC = 101 + 0.6 (115 – 101) = 101 + 8.4 = 109.4 kJ/kg DA ANSWER

WC = 23.5 + 0.6 (12 – 23.5) = 23.5 – 6.9 = 16.6 g/kg DA ANSWER

Example 9.7

Air at 30°C and 60% relative humidity is cooled to 18°C. (1) How much energy is removed from the air? (2) Is any water removed? If so, how much? Solution: This process follows the path A–d–B shown on Chart III of Figure 9.04. Initial conditions at point A from Figure 9.01 are:

t = 30°C W = 16 g/kg DA φ = 60% h = 70.8 KJ/kg DA

As the air is cooled, the temperature drops until the air is saturated. At this point (Point d):

t = twb = tdp = 21.3°C and φ = 100%

Continued cooling follows the saturation line to Point B where the properties are: t = twb = tdp = 18°C W = 13 g/kg DA φ = 100% h = 51 KJ/kg DA

The energy removed from the air is: •

Q = hA – hB = 70.8 – 51 = 19.8 KJ/kg DA Similarly, the water removed is: ∆W = WA – WB = 16 – 13 = 3 g/kg DA ANSWERS


Example 9.8

Air at 50°C and a wet-bulb temperature of 30°C (Point A) is mixed with air at 24°C and 50% relative humidity (Point B) in proportions of 70% hot air and 30% cooler air. What are the properties of the air after mixing? Solution: The properties at Point C, the mixed air state point, can be computed using Equation 9.24.

Relevant properties at Points A and B are: WA = 18.7 g/kg DA WB = 9.3 g/kg DA hA = 98.9 KJ/kg DA hB =47.8 KJ/kg DA

Solving Equation 9.24, noting that maA is 70% of the total mixture, maC, we have:

3.97.183.97.0and

8.479.988.477.0

−

−=

−

−= CC Wh

and: hC = 0.7(98.9 – 47.8) + 47.8 WC = 0.7(18.7 – 9.3) + 9.3

hC = 83.6 KJ/kg DA WC = 15.9 g/kg DA

Locating Point C from the values of h and W gives other property values as: φC = 30% t = 42.4°C ANSWER

Example 9.9

Water is often cooled by evaporation into the air, using a cooling tower. Incom-ing hot water is sprayed into the air where a portion is evaporated, lowering the temperature of the remaining water by 10° to15°C. (Evaporation of 1 kg of wa-ter provides sufficient cooling to lower the temperature of approximately 56 kg of liquid water by 10°C.) Consider water entering a cooling tower at 40°C and leaving at 30°C. Air enters at 25°C with a relative humidity of 40% and exits at 34°C with 90% rh. For a water flow rate of 50 kg/s, and sufficient evaporation to meet the above conditions, determine the required air flow rate (kg/s) through the cooling tower. Solution: The solution of cooling tower problems consists of a combination of the evapo-rative cooling process on the psychrometric chart and an energy balance be-tween air and water streams. The process describing the air humidification along


a constant wet-bulb line is needed to determine the enthalpy at the two state points. Read from psychrometric chart at 25°C dry bulb temperature and 40% rh, the enthalpy is 45.5 kJ/kg, and at 34°C and 90% rh the enthalpy is 113.5 kJ/kg. The energy lost by the cooling of water must equal energy gained by air. Thus:

aawpww hmtcm ∆∆••

=

a

wpwwa

htcmm

∆∆••

=

( )( )

−

−×=

•

kgkJ5.455.113

C 3040C kg

kJ18.4s

kg50am

s

kg730.ma =•

of air ANSWER

Note: This solution assumed a constant mw, ignoring the approximately 2% of water that was evaporated. This approach greatly simplifies the solution and has little effect upon the computed air flow.

9.6 Ice-Water-Steam Water in its three forms (solid, liquid, gas) is used extensively in food, agricultural,

and other applications. The properties of water, in all three forms, make it well suited for many processing applications. In many applications we are concerned with the use of water in one or more of its forms for heating or cooling. To understand this use, we must first understand certain water properties that are relevant to these applications.

If ice at –20°C (or any other sub-freezing temperature) and atmospheric pressure is heated very slowly, its temperature would increase until the melting point (0°C, 32°F) is reached (Figure 9.05). It would then melt at that temperature. If additional heat is added after the ice is melted, the water temperature will increase until it reaches 100°C (212°F). At 100°C, the water will evaporate (boil) into gas (steam). Any further addi-tion of heat will cause an increase in steam temperature. This process of heating and change of state is shown in Figure 9.05. The comparative energy requirements for heating (average specific heats) and change of state (latent heats) are also shown.


2800

2400

2000

1600

1200

800

400

0

-400

-8000 20 40 60 80 100 120

c’p = 1.97 kJkg K

.

.

hsf = 335 kJ kg

cp = 4.187 kJkg K

hfg = 2257 kJ kg

Temperature (°C)

Figure 9.05. Heat content (enthalpy) of water at a pressure of one atmosphere as a function of temperature and state (solid, liquid, or gas).


0 100 200 300 400 500 600 700 800 1000 1100900

170

190

030

50

70

90

110

130

150

Absolute Pressure (kPa)

100° C

101.33 kPa

Figure 9.06. Boiling point temperature as a function of pressure for water.

The above example assumes that the water is held at atmospheric pressure. How-ever, steam is usually produced and used at pressures higher than atmospheric. Thus, temperature, pressure, and energy content of the steam are all important factors to be considered. A key consideration here is the effect of pressure upon the boiling point temperature of water. This change in the boiling point of water with pressure is shown in Figure 9.06.

The energy required to melt the ice (latent heat of fusion) and to evaporate the wa-ter (latent heat of vaporization) are important considerations in the use of water for processing and environmental control applications. However, in this unit, we will be concerned exclusively with the properties of steam—either as pure steam (“dry steam”) or a mixture of steam and liquid water droplets (“wet steam”). Figure 9.07 is a temperature enthalpy diagram for steam. By following heating processes on the chart we can get a better picture of the water-steam system. If we begin with liquid water at 25°C and heat it slowly (at atmospheric pressure) to 100°C, the enthalpy of the water would follow line A–B. At 100°C, the water would begin to evaporate (at constant pressure) until all the liquid is converted to steam (point C). Further heating will su-perheat the steam (line C–D). Similarly, heating water at a higher pressure of 600 kPa would produce line A–B–H–I–J. The curved dome containing points A, B, H, X, I and C is commonly called the vapor dome. To the left of the dome, liquid water is pre-sent. To the right of the dome is superheated (dry) steam. The curved line forming the left half of the dome represents saturated liquid; that on the right represents saturated vapor. Between these two lines is “wet” steam progressing from all liquid on the left


to all vapor on the right. Note that above point X, there is no distinct change from liq-uid to gas. Point X is the critical point (22 120 kPa, 374.15°C). Above the critical point, the change from liquid to gas is gradual and cannot be identified as occurring at a specific point.

Note: Strictly speaking, we do not follow the saturated liquid line during the heating process described above. The saturation line represents values of enthalpy at saturated temperature and pressure. The pressures along that saturation line and below Points B and H are less than 101.3 kPa and 600 kPa, respectively; and we are applying heat at a constant pressure of 101.3 or 600 kPa, respectively. However, the effect of pressure upon enthalpy is small. On the graph shown, we would be unable to detect any deviation from the saturated liquid line.

Beneath the vapor dome, a line of constant temperature is also a line of constant pressure. Thus, if either property is specified, the other is also known. In the superheat areas, this is not true. Both temperature and pressure must be specified to identify a specific state point in the superheated region. Figure 9.07 presents a good visual image of the pressure, temperature, enthalpy relationships. However, accurate values of these properties cannot be readily obtained from this figure. Tabulations of these properties, commonly called steam tables, are used to obtain accurate property values.

D

0 500 1000 1500 2000 2500 3000 3500 40000

100

200

300

400 Critical Point

600 kPa

101.3 kPa

H

B

I

C

JX

A

STEAM

Heat Content (Enthalpy) kJkg

LIQUID

Figure 9.07. Temperature-Enthalpy diagram for water. The curve

A–B–H–X–I–C is called a vapor dome. The region beneath the vapor dome represents a condition of wet steam.


9.7 Steam Tables Tables 9.02, 9.03, and 9.04 are the three types of steam tables normally used. The

first two tables show properties as a function of temperature (Table 9.02) and pressure (Table 9.03). Both tables give the same type of information; thus, the table to be used depends upon the known property (temperature or pressure). These tables represent conditions within the vapor dome. Table 9.04 gives properties for superheated steam. The choice of which table to use depends upon the conditions given. Any given com-bination of temperature and pressure may represent either wet steam (Tables 9.02 or 9.03) or superheated steam (Table 9.04). It may be necessary to look at each table be-fore you find the correct state point. However, a notation that the steam is saturated or statement of a value for steam quality (see below) reveals that the wet steam tables (Table 9.02 or 9.03) should be used. For all tables, the properties of interest are tem-perature (t), pressure (P), enthalpy (h), and specific volume (v). Entropy (s) is an addi-tional property often used in steam calculations. The commonly used subscripts are f for fluid properties, g for gaseous properties, and fg for the difference between fluid and gaseous properties. Use of the superheated steam tables is simply a matter of find-ing the appropriate state point given any two of the properties p, t, v, h, or s. Tempera-ture and pressure are most commonly used.

To use Tables 9.02 and 9.03, it is often necessary to know the quality of the steam. Quality is an indication of how much of the wet steam is vapor. It is defined as the mass of the vapor divided by the total mass (liquid plus vapor). Quality is usually identified by the symbol x. At x = 0, we have saturated liquid. At x = 1, we have satu-rated vapor. For x between 0 and 1, we have a mixture of liquid and vapor (wet steam). If we know the enthalpy or specific volume for a given state point under the vapor dome, we can determine the quality, x:

fg

f

fg

f

hhh

xv

vvx

−=

−= or (9.26)

Conversely, the quality (x) can be used to determine the enthalpy or specific vol-ume of wet steam. We shall make all calculations based upon a unit mass of water. Noting that the enthalpy of evaporated water (steam) is hg and the enthalpy of liquid water is hf, we find the enthalpy as follows:

1. Saturated steam (x = 1) (since we have only saturated vapor, the enthalpy is hg): h = x hg = 1 hg = hg 2. Saturated liquid (x = 0): h = (1 – x) hf = (1 – 0) hf = hf 3. Mixture (here we must take the amounts of liquid and vapor into account):

h = hliquid+ hvapor = x hg + (1 – x) hf = x (hg – hf) + hf

h = x hfg + hf = hf + x hfg (9.27)

The above example was for enthalpy. For specific volume, the same rule applies, e.g.:

v = x (vg – vf) + vf = x vfg + vf = vf + x vfg (9.28)


Example 9.10

Find the enthalpy, specific volume, and pressure for steam at 175°C and a qual-ity of 0.5. Locate the approximate position of this state point on Figure 9.07. Solution: We know the pressure and, with a quality of 0.5, we know that the steam is “wet.” Thus, we choose Table 9.02, the table for wet steam properties as a func-tion of temperature. From the table, at 175°C, P = 892.4 kPa ANSWER vf = 0.0011209 m3/kg vfg = 0.21542 m3/kg hf = 741.07 kJ/kg hfg = 2030.7 kJ/kg Solving for v and h: v = vf + x vfg = 0.0011209 + 0.5 (0.21542) = 0.1088 m3/kg ANSWER h = hf + x hfg = 741.07 + 0.5 (2030.7) = 1756.4 kJ/kg ANSWER At 175°C and an enthalpy of 1756.4 kJ/kg, the approximate state point location on Figure 9.07 is near the letter “P” of 600 kPa along line H–I. ANSWER

Example 9.11

Find the temperature and enthalpy of steam at 300 kPa and 0.6506 m3/kg. Locate the approximate position of the state point on Figure 9.07. Solution: From Table 9.03 at 300 kPa, we see that vg = 0.6056 m3/kg. vg is the volume of saturated vapor at the given pressure. This value of vg = 0.6056 is less than the specific volume given (0.6506). Since the specific volume of the steam is greater than that of saturated vapor, the steam must be superheated. Using Table 9.04, at 300 kPa and the specific volume given, we find: t = 160°C h = 2781.8 kJ/kg ANSWER For 160°C, 300 kPa, and 2781.8 kJ/kg, the state point location on Figure 9.07 is below, and to the right of Point I, between lines I–J and C–D. ANSWER Note: (1) If the value of v had not been given exactly in Table 9.04, it would have been necessary for us to interpolate between values in the table. (2) If the value of v had been less than vg = 0.6056, this would indicate that

we have wet steam and we would have used Table 9.03 to find t (at 300 kPa), solve for the quality (x), and compute the enthalpy (h).


9.8 Steam -Air Mixtures In this unit, we have examined systems involving steam (100% water vapor) and

typical air and water vapor mixtures (low levels of water vapor.) We will now exam-ine steam-air mixtures involving high water vapor concentrations. The issue of steam air mixtures in food processing is important because the temperature of a mixture of air and steam at any pressure is lower than the temperature of pure steam at the same pressure. Thus, the first step in batch processing with a retort, home canner, or pres-sure cooker is to vent until a steady stream of steam is produced. Failure to vent and purge the container of air will result in a mixture of air and water vapor, causing lower processing temperatures and, possibly, inadequate sterilization.

Our examination will make the simplifying assumption that ideal gas relationships apply. While not necessarily valid for all conditions, this assumption is a good ap-proximation; and it will allow us to view the effect of increasing amounts of air in a steam environment. The trends we see will be valid even though the numeric values we calculate may differ slightly from the correct values.

Equations 9.05, 9.07, and 9.08 relate total and partial pressures, respectively, to the number of moles of gas present, the temperature, and the total volume. Using this rela-tionship, we can solve for the partial pressure of water vapor in a steam-air mixture. We note that this mixture will be at a uniform temperature and that it occupies a fixed volume. Applying the above referenced equations, we find:

( )air of fraction mole//

==== aaa

u

uaa yyNN

VTNRVTRN

PP

(9.29)

or PyP aa = (9.30)

Using the above information we can solve for the partial pressure of water vapor (steam) at any mass ratio of water vapor. First, we note that the molecular weights of air and water are 28.96 and 18.015, respectively. We need these values to calculate the moles of air and water present in a given mixture.

If we assume a mixture of unit mass, at 200 kPa, containing a mass ratio of 0.2 air (20% air, by mass), we can compute Pw by the following steps.

The moles of air and water are:

04441.0015.188.0and00690.0

96.282.0

======w

ww

a

aa M

mNMmN

This results in a total of 0.05131 moles (0.00690 + 0.04441) in the system. The mole fractions of air and water in the system are then:

1345.05131.00069.0and8655.0

05131.004441.0

======t

aa

t

ww N

NyNNy

The partial pressure of water vapor (steam) for this mixture is then:

kPa 1.1732008655.0 =×=×= tww PyP


0

20

40

60

80

100

120

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Mass Fraction of Air

Tem

pera

ture

(C)

0

40

80

120

160

200

240

Stea

m P

ress

ure

(kPa

)

Temp Pres

Figure 9.08. Effect of air upon steam partial pressure and temperature

in steam-air mixtures at 200 kPa total pressure.

From the steam tables, the boiling points at 200 kPa and 173.1 kPa are 121.23°C and 115.6°C, respectively. Thus, the result of mixing air and steam in a ratio of 2 : 8 by mass results in almost a 6°C drop in the boiling point temperature at a total pres-sure of 200 kPa. This temperature drop could significantly affect a thermal processing operation. While a steam-air mixture containing 20% air is probably extreme, this does illustrate the effect of air in the mixture. Figure 9.08 shows the effect of differing air-steam mixtures (at 200 kPa) upon the steam partial pressure and boiling point tem-perature.

Example 9.12

We will consider the effect of failure to vent by examining the use (or misuse) of a home canner. A typical home canner is approximately 320 mm in diameter and 270 mm deep with a slightly domed lid. Figure 9.09 shows a cross-section representing a typical home canner containing several cans. The typical operating procedure is to add hot water to a depth of about 25 mm, insert the cans to be processed, install the lid, heat, vent until continuous pure steam is observed, seal, and process for the required time. We will assume the following conditions for our example:


STEAM

WATER Figure 9.09. Sketch of home canner showing approximate proportions of

water and steam.

• canner volume (Vt) = 21.7 L = 0.0217 m3 • water volume (Vw) = 2.0 L = 0.0020 m3 (for a depth of about 25 mm) • three cans with a total volume (Vc) = 2.8 L = 0.0028 m3 • initial temperature of all components (ti) = 25°C • processing pressure (Pr) = 200 kPa (“retort” processing pressure) • canner immediately sealed without venting and heated until the pressure reaches

200 kPa (Except for the initial temperatures and the small number of cans, all values above are realistic. In actual conditions, the water and can temperatures would probably be well above 25°C. However, we will make this assumption to sim-plify the problem.)

If the canner had been properly vented to insure pure steam inside, the inside temperature would be 120.2°C at 200 kPa. What is the temperature without the venting? Solution: We must first determine the mass and mole fractions of water and air in the con-tainer. Water: From Table 9.05 at 25°C, we find ρw = 997.1 kg/m3. Thus:

kg 9942.1m 002.0mkg1.997 3

3 =×=×= www Vm ρ

Chapter 9 Psychrometrics 243 Air: From Table 9.01 at 25°C, va = 0.8444 m3/kg, thus ρa = 1.184 kg/m3

(We could also determine va, but with less precision, from Figure 9.01 at 25°C and W = 0.) The volume of air in the canner (Va) is that space not occupied by the cans or the water:

3m 0169.0 L9.168.227.21 ==−−=−−= cwta VVVV

kg 020014.0m 0169.0mkg184.1 3

3 =×== aaa Vm ρ

We can now determine the number of moles of water and air present:

1107.0015.18

9942.1and0006911.096.28

20014.0======

w

ww

a

aa M

mN

Mm

N

and Nt = Na + Nw = 0.0006911 + 0.1107 = 0.1114 Moles

The mole fraction of water vapor and the resulting partial pressure of water va-por are:

kPa76.1982009938.0and9938.01114.01107.0

=×===== wwwt

ww PyP

NN

y

Interpolating from Table 9.03, the temperature corresponding to a pressure of 198.76 kPa is 120.02°C. This is approximately 0.2° below the value for pure steam at 200 kPa (120.23°C). A difference of only 0.2° seems small; however, at the high temperatures used for processing, it can affect the required processing time. Thus, venting is important to insure that processing conditions are known.

Tab

le 9

.02.

Pro

pert

ies o

f sat

urat

ed st

eam

and

satu

rate

d w

ater

(tem

pera

ture

).

Com

pute

d us

ing

ASM

E so

ftw

are

acco

mpa

nyin

g A

SME

Ste

am T

able

s (A

SME

, 199

3).

Tem

pera

ture

Pr

essu

reV

olum

e (m

3 /kg)

En

thal

py (k

J/kg

) En

tropy

(kJ/

kg K

) (°

C)

(K)

(kPa

) W

ater

Ev

ap.

Stea

m

W

ater

Ev

ap.

Stea

m

Wat

er

Evap

. St

eam

t

T p

v f v fg

v g

h f

h f

g h g

s f

s fg

s g

100.

0 10

5.0

110.

0 11

5.0

120.

0

373.

15

378.

15

383.

15

388.

15

393.

15

101.

33

120.

80

143.

27

169.

06

198.

54

0.00

1043

7 0.

0010

477

0.00

1051

9 0.

0010

562

0.00

1060

6

1.67

20

1.41

82

1.20

89

1.03

52

0.89

05

1.67

30

1.41

93

1.20

99

1.03

63

0.89

15

419.

06

440.

17

461.

32

482.

50

503.

72

2256

.9

2243

.6

2230

.0

2216

.2

2202

.2

2676

.0

2683

.7

2691

.3

2698

.7

2706

.0

1.30

69

1.36

30

1.41

85

1.47

33

1.52

76

6.04

85

5.93

32

5.82

03

5.70

99

5.60

17

7.35

54

7.29

62

7.23

88

7.18

32

7.12

93

125.

0 13

0.0

135.

0 14

0.0

145.

0

398.

15

403.

15

408.

15

413.

15

418.

15

232.

1 27

0.1

313.

1 36

1.4

415.

5

0.00

1065

2 0.

0010

700

0.00

1075

0 0.

0010

801

0.00

1085

3

0.76

92

0.66

71

0.58

07

0.50

74

0.44

49

0.77

02

0.66

81

0.58

18

0.50

85

0.44

60

524.

99

546.

31

567.

68

589.

10

610.

59

2188

.0

2173

.6

2158

.9

2144

.0

2128

.7

2713

.0

2719

.9

2726

.6

2733

.1

2739

.3

1.58

13

1.63

44

1.68

69

1.73

90

1.79

06

5.49

57

5.39

17

5.28

97

5.18

95

5.09

10

7.07

69

7.02

61

6.97

66

6.92

84

6.88

15

150.

0 15

5.0

160.

0 16

5.0

170.

0

423.

15

428.

15

433.

15

438.

15

443.

15

476.

0 54

3.3

618.

1 70

0.8

792.

0

0.00

1090

8 0.

0010

964

0.00

1102

2 0.

0011

082

0.00

1114

5

0.39

14

0.34

53

0.30

57

0.27

13

0.24

14

0.39

24

0.34

64

0.30

68

0.27

24

0.24

26

632.

15

653.

77

675.

47

697.

25

719.

12

2113

.2

2097

.4

2081

.3

2064

.8

2047

.9

2745

.4

2751

.2

2756

.7

2762

.0

2767

.1

1.84

16

1.89

23

1.94

25

1.99

23

2.04

16

4.99

41

4.89

89

4.80

50

4.71

26

4.62

14

6.83

58

6.79

11

6.74

75

6.70

48

6.66

30

175.

0 18

0.0

185.

0 19

0.0

195.

0

448.

15

453.

15

458.

15

463.

15

468.

15

892.

4 10

02.7

11

23.3

12

55.1

13

98.7

0.00

1120

9 0.

0011

275

0.00

1134

4 0.

0011

415

0.00

1148

9

0.21

542

0.19

267

0.17

272

0.15

517

0.13

969

0.21

654

0.19

380

0.17

386

0.15

632

0.14

084

741.

07

763.

12

785.

26

807.

52

829.

88

2030

.7

2013

.2

1995

.2

1976

.7

1957

.9

2771

.8

2776

.3

2780

.4

2784

.3

2787

.8

2.09

06

2.13

93

2.18

76

2.23

56

2.28

33

4.53

14

4.44

26

4.35

48

4.26

80

4.18

22

6.62

21

6.58

19

6.54

24

6.50

36

6.46

54

200.

0 20

5.0

210.

0 21

5.0

220.

0

473.

15

478.

15

483.

15

488.

15

493.

15

1554

.9

1724

.3

1907

.7

2106

.0

2319

.8

0.00

1156

5 0.

0011

644

0.00

1172

6 0.

0011

811

0.00

1190

0

0.12

600

0.11

386

0.10

307

0.09

344

0.08

485

0.12

716

0.11

503

0.10

424

0.09

463

0.08

604

852.

37

874.

99

897.

73

920.

63

943.

67

1938

.6

1918

.8

1898

.5

1877

.6

1856

.2

2790

.9

2793

.8

2796

.2

2798

.3

2799

.9

2.33

07

2.37

78

2.42

47

2.47

13

2.51

78

4.09

71

4.01

28

3.92

93

3.84

63

3.76

39

6.42

78

6.39

06

6.35

39

6.31

77

6.28

17

225.

0 23

0.0

235.

0 24

0.0

245.

0

498.

15

503.

15

508.

15

513.

15

518.

15

2550

. 27

98.

3063

. 33

48.

3652

.

0.00

1199

2 0.

0012

087

0.00

1218

7 0.

0012

291

0.00

1239

9

0.07

715

0.07

024

0.06

403

0.05

843

0.05

337

0.07

835

0.07

145

0.06

525

0.05

965

0.05

461

966.

88

990.

27

1013

.83

1037

.60

1061

.58

1834

.3

1811

.7

1788

.5

1764

.6

1740

.0

2801

.2

2802

.0

2802

.3

2802

.2

2801

.6

2.56

41

2.61

02

2.65

61

2.70

20

2.74

78

3.68

20

3.60

06

3.51

95

3.43

86

3.35

79

6.24

61

6.21

07

6.17

56

6.14

06

6.10

57


Tem

pera

ture

Pr

essu

reV

olum

e (m

3 /kg)

En

thal

py (k

J/kg

) En

tropy

(kJ/

kg K

) (°

C)

(K)

(kPa

) W

ater

Ev

ap.

Stea

m

W

ater

Ev

ap.

Stea

m

Wat

er

Evap

. St

eam

t

T p

v f v fg

v g

h f

h f

g h g

s f

s fg

s g

250.

0 25

5.0

260.

0 26

5.0

270.

0

523.

15

528.

15

533.

15

538.

15

543.

15

3978

. 43

25.

4694

. 50

88.

5506

.

0.00

1251

3 0.

0012

632

0.00

1275

6 0.

0012

887

0.00

1302

5

0.04

879

0.04

463

0.04

086

0.03

742

0.03

429

0.05

004

0.04

590

0.04

213

0.03

871

0.03

559

1085

.78

1110

.23

1134

.94

1159

.93

1185

.23

1714

.7

1688

.5

1661

.5

1633

.5

1604

.6

2800

.4

2798

.7

2796

.4

2793

.5

2789

.9

2.79

35

2.83

92

2.88

49

2.93

06

2.97

64

3.27

74

3.19

68

3.11

61

3.03

53

2.95

41

6.07

08

6.03

59

6.00

10

5.96

58

5.93

05

275.

0 28

0.0

285.

0 29

0.0

295.

0

548.

15

553.

15

558.

15

563.

15

568.

15

5950

. 64

20.

6919

. 74

46.

8004

.

0.00

1317

0 0.

0013

324

0.00

1348

7 0.

0013

659

0.00

1384

4

0.03

142

0.02

879

0.02

638

0.02

417

0.02

213

0.03

274

0.03

013

0.02

773

0.02

554

0.02

351

1210

.86

1236

.84

1263

.21

1290

.01

1317

.27

1574

.7

1543

.6

1511

.3

1477

.6

1442

.6

2785

.5

2780

.4

2774

.5

2767

.6

2759

.8

3.02

23

3.06

83

3.11

46

3.16

11

3.20

79

2.87

25

2.79

03

2.70

74

2.62

37

2.53

89

5.89

47

5.85

86

5.82

20

5.78

48

5.74

69

300.

0 30

5.0

310.

0 31

5.0

320.

0

573.

15

578.

15

583.

15

588.

15

593.

15

8593

. 92

14.

9870

. 10

561.

11

289.

0.00

1404

1 0.

0014

252

0.00

1448

0 0.

0014

726

0.00

1499

5

0.02

0245

0.

0185

02

0.01

6886

0.

0153

83

0.01

3980

0.02

1649

0.

0199

27

0.01

8334

0.

0168

56

0.01

5480

1345

.05

1373

.40

1402

.39

1432

.09

1462

.60

1406

.0

1367

.7

1327

.6

1285

.5

1241

.1

2751

.0

2741

.1

2730

.0

2717

.6

2703

.7

3.25

52

3.30

29

3.35

12

3.40

02

3.45

00

2.45

30

2.36

56

2.27

66

2.18

56

2.09

23

5.70

81

5.66

85

5.62

78

5.58

58

5.54

23

325.

0 33

0.0

335.

0 34

0.0

345.

0

598.

15

603.

15

608.

15

613.

15

618.

15

1205

6.

1286

3.

1371

2.

1460

5.

1554

5.

0.00

1528

9 0.

0015

615

0.00

1597

8 0.

0016

387

0.00

1685

8

0.01

2666

0.

0114

28

0.01

0256

0.

0091

42

0.00

8077

0.01

4195

0.

0129

89

0.01

1854

0.

0107

80

0.00

9763

1494

.03

1526

.52

1560

.25

1595

.47

1632

.52

1194

.0

1143

.6

1089

.5

1030

.7

966.

4

2688

.0

2670

.2

2649

.7

2626

.2

2598

.9

3.50

08

3.55

28

3.60

63

3.66

16

3.71

93

1.99

61

1.89

62

1.79

16

1.68

11

1.56

36

5.49

69

5.44

90

5.39

79

5.34

27

5.28

28

350.

0 35

5.0

360.

0 36

5.0

370.

0

623.

15

628.

15

633.

15

638.

15

643.

15

1653

5.

1757

7.

1867

5.

1983

3.

2105

4.

0.00

1741

1 0.

0018

085

0.00

1895

9 0.

0020

160

0.00

2213

6

0.00

7058

0.

0060

51

0.00

5044

0.

0039

96

0.00

2759

0.00

8799

0.

0078

59

0.00

6940

0.

0060

12

0.00

4973

1671

.94

1716

.63

1764

.17

1817

.96

1890

.21

895.

7 81

3.8

721.

3 61

0.0

452.

6

2567

.7

2530

.4

2485

.4

2428

.0

2342

.8

3.78

00

3.84

89

3.92

10

4.00

21

4.11

08

1.43

76

1.29

53

1.13

90

0.95

58

0.70

36

5.21

77

5.14

42

5.06

00

4.95

79

4.81

44

371.

0 37

2.0

373.

0 37

4.0

374.

15

644.

15

645.

15

646.

15

647.

15

647.

30

2130

6.

2156

2.

2182

0.

2208

1.

2212

0.

0.00

2277

8 0.

0023

636

0.00

2496

3 0.

0028

427

0.00

317

0.00

2446

0.

0020

75

0.00

1588

0.

0006

23

0.0

0.00

4723

0.

0044

39

0.00

4084

0.

0034

66

0.00

317

1910

.50

1935

.57

1970

.50

2046

.72

2107

.37

407.

4 35

1.4

273.

5 10

9.5

0.0

2317

.9

2287

.0

2244

.0

2156

.2

2107

.4

4.14

14

4.17

94

4.23

26

4.34

93

4.44

29

0.63

24

0.54

46

0.42

33

0.16

92

0.0

4.77

38

4.72

40

4.65

59

4.51

85

4.44

29


Tab

le 9

.03.

Pro

pert

ies o

f sat

urat

ed st

eam

and

satu

rate

d w

ater

(pre

ssur

e).

Pre

ss.

Tem

p.

Vol

ume

(m3 /k

g)

Enth

alpy

(kJ/

kg)

Entro

py (k

J/kg

K)

(kPa

) (°

C)

Wat

er

Evap

. St

eam

Wat

er

Evap

. St

eam

W

ater

Ev

ap.

Stea

m

p t

v f v fg

v g

h f

h f

g h g

s f

s fg

s g

1.0

10.0

20

.0

100.

0 11

0.0

120.

0 13

0.0

140.

0

6.98

3 45

.833

60

.086

99

.632

10

2.31

7 10

4.80

8 10

7.13

3 10

9.31

5

0.00

1000

1 0.

0010

102

0.00

1017

2 0.

0010

434

0.00

1045

5 0.

0010

476

0.00

1049

5 0.

0010

513

129.

21

14.6

74

7.64

9 1.

6927

1.

5482

1.

4271

1.

3240

1.

2353

129.

21

14.6

75

7.65

0 1.

6937

1.

5492

1.

4281

1.

3251

1.

2363

29.3

4 19

1.83

25

1.45

41

7.51

42

8.84

43

9.36

44

9.19

45

8.42

2485

.0

2392

.9

2358

.4

2257

.9

2250

.8

2244

.1

2237

.8

2231

.9

2514

.4

2584

.8

2609

.9

2675

.4

2679

.6

2683

.4

2687

.0

2690

.3

0.10

60

0.64

93

0.83

21

1.30

27

1.33

30

1.36

09

1.38

68

1.41

09

8.87

06

7.50

18

7.07

74

6.05

71

5.99

47

5.93

75

5.88

47

5.83

56

8.97

67

8.15

11

7.90

94

7.35

98

7.32

77

7.29

84

7.27

15

7.24

65

150.

0 16

0.0

180.

0 20

0.0

220.

0

111.

37

113.

32

116.

93

120.

23

123.

27

0.00

1053

0 0.

0010

547

0.00

1057

9 0.

0010

608

0.00

1063

6

1.15

80

1.09

01

0.97

62

0.88

44

0.80

88

1.15

90

1.09

11

0.99

72

0.88

54

0.80

98

467.

13

475.

38

490.

70

504.

70

517.

62

2226

.2

2220

.9

2210

.8

2201

.6

2193

.0

2693

.4

2696

.2

2701

.5

2706

.3

2710

.6

1.43

36

1.45

50

1.49

44

1.53

01

1.56

27

5.78

98

5.74

67

5.66

78

5.59

67

5.53

21

7.22

34

7.20

17

7.16

22

7.12

68

7.09

49

240.

0 26

0.0

280.

0 30

0.0

350.

0

126.

09

128.

73

131.

20

133.

54

138.

87

0.00

1066

3 0.

0010

688

0.00

1071

2 0.

0010

735

0.00

1078

9

0.74

54

0.69

14

0.64

50

0.60

45

0.52

29

0.74

65

0.69

25

0.64

60

0.60

56

0.52

40

529.

6 54

0.9

551.

4 56

1.4

584.

3

2184

.9

2177

.3

2170

.1

2163

.2

2147

.4

2714

.5

2718

.2

2721

.5

2724

.7

2731

.6

1.59

29

1.62

09

1.64

71

1.67

16

1.72

73

5.47

28

5.41

80

5.36

70

5.31

93

5.21

19

7.06

57

7.03

89

7.01

40

6.99

09

6.93

92

400.

0 45

0.0

500.

0 55

0.0

600.

0

143.

62

147.

92

151.

84

155.

47

158.

84

0.00

1083

9 0.

0010

885

0.00

1092

8 0.

0010

969

0.00

1100

9

0.46

11

0.41

27

0.37

36

0.34

14

0.31

44

0.46

22

0.41

38

0.37

47

0.34

25

0.31

55

604.

7 62

3.2

640.

1 65

5.8

670.

4

2133

.0

2119

.7

2107

.4

2095

.9

2085

.0

2737

.6

2742

.9

2747

.5

2751

.7

2755

.5

1.77

64

1.82

04

1.86

04

1.89

70

1.93

08

5.11

79

5.03

43

4.95

88

4.89

00

4.82

67

6.89

43

6.85

47

6.81

92

6.78

70

6.75

75

650.

0 70

0.0

750.

0 80

0.0

900.

0

161.

99

164.

96

167.

76

170.

41

175.

36

0.00

1104

6 0.

0011

082

0.00

1111

6 0.

0011

150

0.00

1121

3

0.29

138

0.27

157

0.25

431

0.23

914

0.21

369

0.29

249

0.27

268

0.25

543

0.24

026

0.21

481

684.

1 69

7.1

709.

3 72

0.9

742.

6

2074

.7

2064

.9

2055

.5

2046

.5

2029

.5

2758

.9

2762

.0

2764

.8

2767

.5

2772

.1

1.96

23

1.99

18

2.01

95

2.04

57

2.09

41

4.76

81

4.71

34

4.66

21

4.61

39

4.52

50

6.73

04

6.70

52

6.68

17

6.65

96

6.61

92

1000

. 11

00.

1200

. 13

00.

1400

.

179.

88

184.

07

187.

96

191.

61

195.

04

0.00

1127

4 0.

0011

331

0.00

1138

0.

0011

438

0.00

1148

9

0.19

317

0.17

625

0.16

206

0.14

998

0.13

957

0.19

429

0.17

738

0.16

320

0.15

113

0.14

072

762.

6 78

1.1

798.

4 81

4.7

830.

1

2013

.6

1998

.5

1984

.3

1970

.7

1957

.7

2776

.2

2779

.7

2782

.7

2785

.4

2787

.8

2.13

82

2.17

86

2.21

61

2.25

10

2.28

37

4.44

46

4.37

11

4.30

33

4.24

03

4.18

14

6.58

28

6.54

97

6.51

94

6.49

13

6.46

51


Pre

ss.

Tem

p.

Vol

ume

(m3 /k

g)

Enth

alpy

(kJ/

kg)

Entro

py (k

J/kg

K)

(kPa

) (°

C)

Wat

er

Evap

. St

eam

Wat

er

Evap

. St

eam

W

ater

Ev

ap.

Stea

m

p t

v f v fg

v g

h f

h f

g h g

s f

s fg

s g

1500

. 16

00.

1800

. 20

00.

2200

.

198.

29

201.

37

207.

11

212.

37

217.

24

0.00

1153

9 0.

0011

586

0.00

1167

8 0.

0011

766

0.00

1185

0

0.13

050

0.12

253

0.10

915

0.09

836

0.08

947

0.13

166

0.12

369

0.11

032

0.09

954

0.09

065

844.

7 85

8.6

884.

6 90

8.6

931.

0

1945

.2

1933

.2

1910

.3

1888

.6

1868

.1

2789

.9

2791

.7

2794

.8

2797

.2

2799

.1

2.31

45

2.34

36

2.39

76

2.44

69

2.49

22

4.12

61

4.07

39

3.97

75

3.88

98

3.80

93

6.44

06

6.41

75

6.37

51

6.33

67

6.30

15

2400

. 26

00.

2800

. 30

00.

3500

.

221.

78

226.

04

230.

05

233.

84

242.

54

0.00

1193

2 0.

0012

011

0.00

1208

8 0.

0012

163

0.00

1234

5

0.08

201

0.07

565

0.07

018

0.06

541

0.05

579

0.08

320

0.07

686

0.07

139

0.06

663

0.05

703

951.

9 97

1.7

990.

5 10

08.4

10

49.8

1848

.5

1829

.6

1811

.5

1793

.9

1752

.2

2800

.4

2801

.4

2802

.0

2802

.3

2802

.0

2.53

43

2.57

36

2.61

06

2.64

55

2.72

53

3.73

47

3.66

51

3.59

98

3.53

82

3.39

76

6.26

90

6.23

87

6.21

04

6.18

37

6.12

28

4000

. 45

00.

5000

. 55

00.

6000

.

250.

33

257.

41

263.

91

269.

93

275.

55

0.00

1252

1 0.

0012

691

0.00

1285

8 0.

0013

023

0.00

1318

7

0.04

850

0.04

277

0.03

814

0.03

433

0.03

112

0.04

975

0.04

404

0.03

943

0.03

563

0.03

244

1087

.4

1122

.1

1154

.5

1184

.9

1213

.7

1712

.9

1675

.6

1639

.7

1605

.0

1571

.3

2800

.3

2797

.7

2794

.2

2789

.9

2785

.0

2.79

65

2.86

12

2.92

06

2.97

57

3.02

73

3.27

20

3.15

79

3.05

29

2.95

52

2.86

35

6.06

85

6.01

91

5.97

35

5.93

09

5.89

08

6500

. 70

00.

7500

. 80

00.

9000

.

280.

82

285.

79

290.

50

294.

97

303.

31

0.00

1335

0 0.

0013

513

0.00

1367

7 0.

0013

842

0.00

1417

9

0.02

8384

0.

0260

22

0.02

3959

0.

0221

41

0.01

9078

0.02

9719

0.

0273

73

0.02

5327

0.

0235

25

0.02

0495

1241

.1

1267

.4

1292

.7

1317

.1

1363

.7

1538

.4

1506

.0

1474

.2

1442

.8

1380

.9

2779

.5

2773

.5

2766

.9

2759

.9

2744

.6

3.07

59

3.12

19

3.16

57

3.20

76

3.28

67

2.77

68

2.69

43

2.61

53

2.53

95

2.39

53

5.85

27

5.81

62

5.78

11

5.74

71

5.68

20

1000

0.

1100

0.

1200

0.

1300

0.

1400

0.

310.

96

318.

05

324.

65

330.

83

336.

64

0.00

1452

6 0.

0014

887

0.00

1526

8 0.

0015

672

0.00

1610

6

0.01

6589

0.

0145

17

0.01

2756

0.

0112

30

0.00

9884

0.01

8041

0.

0160

06

0.01

4283

0.

0127

97

0.01

1495

1408

.0

1450

.6

1491

.8

1532

.0

1571

.6

1319

.7

1258

.7

1197

.4

1135

.0

1070

.7

2727

.7

2709

.3

2689

.2

2667

.0

2642

.4

3.36

05

3.43

04

3.49

72

3.56

16

3.62

42

2.25

93

2.12

91

2.00

30

1.87

92

1.75

60

5.61

98

5.55

95

5.50

02

5.44

08

5.38

03

1500

0.

1600

0.

1700

0.

1800

0.

1900

0.

342.

13

347.

33

352.

26

356.

96

361.

43

0.00

1657

9 0.

0017

103

0.00

1769

6 0.

0018

399

0.00

1926

0

0.00

8682

0.

0075

97

0.00

6601

0.

0056

58

0.00

4751

0.01

0340

0.

0093

08

0.00

8371

0.

0074

98

0.00

6678

1611

.0

1650

.5

1691

.7

1734

.8

1778

.7

1004

.0

934.

3 85

9.9

779.

1 69

2.0

2615

.0

2584

.9

2551

.6

2513

.9

2470

.6

3.68

59

3.74

71

3.81

07

3.87

65

3.94

29

1.63

20

1.50

60

1.37

48

1.23

62

1.09

03

5.31

78

5.25

31

5.18

55

5.11

28

5.03

32

2000

0.

2100

0 22

000.

22

120.

365.

70

369.

78

373.

69

374.

15

0.00

2037

0 0.

0022

015

0.00

2671

4 0.

0031

7

0.00

3840

0.

0028

22

0.00

1056

0.

0

0.00

5877

0.

0050

23

0.00

3728

0.

0031

7

1826

.5

1886

.3

2011

.1

2107

.4

591.

9 46

1.3

184.

5 0.

0

2418

.4

2347

.6

2195

.6

2107

.4

4.01

49

4.10

48

4.29

47

4.44

29

0.92

63

0.71

75

0.28

52

0.0

4.94

12

4.82

23

4.57

99

4.44

29


Tab

le 9

.04.

Pro

pert

ies o

f sup

erhe

ated

stea

m (t

empe

ratu

re a

nd p

ress

ure)

. C

ompu

ted

usin

g A

SME

soft

war

e ac

com

pany

ing

ASM

E S

team

Tab

les (

ASM

E, 1

993)

. T

empe

ratu

re, t

(°C

) Pr

essu

rep

(kPa

)

60

80

100

120

140

160

180

200

220

1.0

v h s

153.

71

2613

.3

9.30

01

162.

95

2650

.9

9.40

96

172.

19

2688

.6

9.51

36

181.

42

2726

.5

9.61

25

190.

66

2764

.6

9.70

70

199.

89

2802

.9

9.79

75

209.

12

2841

.4

9.88

43

218.

35

2880

.1

9.96

79

227.

58

2919

.0

10.0

48

5.0

v h s

30.7

11

2612

.6

8.55

55

32.5

65

2650

.3

8.66

55

34.4

17

2688

.1

8.76

98

36.2

67

2726

.1

8.86

90

38.1

17

2764

.3

8.96

36

39.9

66

2802

.6

9.05

42

41.8

14

2841

.2

9.14

12

43.6

62

2879

.9

9.22

48

45.5

09

2918

.8

9.30

54

10.0

v h s

15.3

36

2611

.6

8.23

34

16.2

66

2649

.5

8.34

39

17.1

95

2687

.5

8.44

86

18.1

23

2725

.6

8.54

81

19.0

50

2763

.9

8.64

30

19.9

75

2802

.3

8.73

38

20.9

00

2840

.9

8.82

08

21.8

25

2879

.6

8.90

45

22.7

50

2918

.6

8.98

52

20.0

v h s

8.

1172

26

48.0

8.

0206

8.58

47

2686

.3

8.12

61

9.05

08

2724

.6

8.22

62

9.51

6 27

63.1

8.

3215

9.98

0 28

01.6

8.

4127

10.4

44

2840

.3

8.50

00

10.9

07

2879

.2

8.58

39

11.3

70

2918

.2

8.66

47

40.0

v h s

4.

0424

26

44.9

7.

6937

4.27

92

2683

.8

7.80

09

4.51

46

2722

.6

7.90

23

4.74

89

2761

.4

7.99

85

4.98

25

2800

.3

8.09

03

5.21

54

2839

.2

8.17

82

5.44

78

2878

.2

8.26

25

5.68

00

2917

.4

8.34

35

60.0

v h s

2.84

40

2681

.3

7.60

85

3.00

25

2720

.6

7.71

11

3.15

99

2759

.8

7.80

83

3.31

66

2798

.9

7.90

08

3.47

26

2838

.1

7.98

91

3.62

81

2877

.3

8.07

38

3.78

33

2916

.6

8.15

52

80.0

v h s

2.12

62

2678

.8

7.47

03

2.24

64

2718

.6

7.57

42

2.36

54

2758

.1

7.67

23

2.48

36

2797

.6

7.76

55

2.60

11

2836

.9

7.85

44

2.71

83

2876

.3

7.93

95

2.83

50

2915

.8

8.02

12

100.

0 v h s

1.69

55

2676

.2

7.36

18

1.79

27

2716

.5

7.46

70

1.88

86

2756

.4

7.56

62

1.98

38

2796

.2

7.66

01

2.07

83

2835

.8

7.74

95

2.17

23

2875

.4

7.83

50

2.26

60

2915

.0

7.91

69

150.

0 v h s

1.

1876

27

11.2

7.

2693

1.25

29

2752

.2

7.37

09

1.31

73

2792

.7

7.46

67

1.38

11

2832

.9

7.55

74

1.44

44

2872

.9

7.64

39

1.50

73

2912

.9

7.72

66


Tem

pera

ture

, t (°

C)

Pres

sure

p (k

Pa)

60

80

10

0 12

0 14

0 16

0 18

0 20

0 22

0 20

0.0

v h s

0.93

49

2747

.8

7.22

98

0.98

40

2789

.1

7.32

75

1.03

25

2830

.0

7.41

96

1.08

04

2870

.5

7.50

72

1.12

80

2910

.8

7.59

07

300.

0 v h s

0.61

67

2738

.8

7.02

54

0.65

06

2781

.8

7.12

71

0.68

37

2824

.0

7.22

22

0.71

64

2865

.5

7.31

19

0.74

86

2906

.6

7.39

71

400.

0 v h s

0.

4837

27

74.2

6.

9805

0.50

93

2817

.8

7.07

88

0.53

43

2860

.4

7.17

08

0.55

89

2902

.3

7.25

76

500.

0 v h s

0.

3835

27

66.4

6.

8631

0.40

45

2811

.4

6.96

47

0.42

50

2855

.1

7.05

92

0.44

50

2890

.0

7.14

78

600.

0 v h s

0.

3166

27

58.2

6.

7640

0.33

46

2804

.8

6.86

91

0.35

20

2849

.7

6.96

62

0.36

90

2893

.5

7.05

67

800.

0 v h s

0.24

71

2791

.1

6.71

22

0.26

08

2838

.6

6.81

48

0.27

40

2884

.2

6.90

94

1000

.0

v h s

0.19

44

2776

.5

6.58

35

0.20

59

2826

.8

6.69

22

0.21

69

2874

.6

6.79

11

2000

.0

v h s

0.10

20

2819

.9

6.38

29

3000

.0

v h s

5000

.0

v h s


Tem

pera

ture

, t (°

C)

Pres

sure

p (k

Pa)

24

0.

260.

28

0.

300.

40

0.

500.

60

0.

700.

80

0.

1.0

v h s

236.

82

2958

.1

10.1

262

246.

05

2997

.4

10.2

014

255.

28

3037

.0

10.2

743

264.

51

3076

.8

10.3

450

310.

66

3279

.7

10.6

71

356.

81

3489

.2

10.9

61

402.

97

3705

.6

11.2

243

449.

12

3928

.9

11.4

663

495.

27

4158

.7

11.6

911

10.0

v h s

23.6

74

2957

.8

9.06

30

24.5

98

2997

.2

9.13

83

25.5

21

3036

.8

9.21

13

26.4

45

3076

.6

9.28

20

31.0

62

3279

.6

9.60

83

35.6

79

3489

.1

9.89

84

40.2

95

3705

.5

10.1

616

44.9

10

3928

.8

10.4

036

49.5

26

4158

.7

10.6

284

20.0

v h s

11.8

32

2957

.4

8.74

26

12.2

95

2996

.9

8.81

80

12.7

57

3036

.5

8.89

10

13.2

19

3076

.4

8.96

18

15.5

29

3279

.4

9.28

82

17.8

38

3489

.0

9.57

84

20.1

46

3705

.4

9.84

16

22.4

55

3928

.7

10.0

836

24.7

62

4158

.7

10.3

085

40.0

v h s

5.91

18

2956

.7

8.42

17

6.14

35

2996

.3

8.49

73

6.37

51

3036

.0

8.57

04

6.60

65

3075

.9

8.64

13

7.76

25

3279

.1

8.96

80

8.91

76

3488

.8

9.25

83

10.0

72

3705

.3

9.52

16

11.2

27

3928

.6

9.76

36

12.3

81

4158

.6

9.98

85

60.0

v h s

3.93

83

2956

.0

8.23

36

4.09

31

2995

.6

8.30

93

4.24

77

3035

.4

8.38

26

4.40

22

3075

.4

8.45

36

5.17

36

3278

.8

8.78

06

5.94

41

3488

.6

9.07

10

6.71

41

3705

.1

9.33

43

7.48

39

3928

.5

9.57

64

8.25

35

4158

.5

9.80

13

80.0

v h s

2.95

15

2955

.3

8.09

98

3.06

78

2995

.0

8.17

57

3.18

40

3034

.9

8.24

91

3.30

00

3075

.0

8.32

02

3.87

92

3278

.5

8.64

75

4.45

74

3488

.4

8.93

80

5.03

51

3705

.0

9.20

14

5.61

26

3928

.4

9.44

36

6.18

99

4158

.4

9.66

85

100.

0 v h s

2.35

95

2954

.6

7.99

58

2.45

27

2994

.4

8.07

19

2.54

58

3034

.4

8.14

54

2.63

87

3074

.5

8.21

66

3.10

25

3278

.2

8.54

42

3.56

53

3488

.1

8.83

48

4.02

77

3704

.8

9.09

82

4.48

98

3928

.2

9.34

05

4.95

17

4158

.3

9.56

54

150.

0 v h s

1.57

00

2952

.9

7.80

61

1.63

25

2992

.9

7.88

26

1.69

48

3033

.0

7.95

65

1.75

70

3073

.3

8.02

80

2.06

69

3277

.5

8.35

62

2.37

59

3487

.6

8.64

72

2.68

45

3704

.4

8.91

08

2.99

27

3927

.9

9.15

31

3.30

08

4158

.0

9.37

81

200.

0 v h s

1.17

53

2951

.1

7.67

07

1.22

24

2991

.4

7.74

77

1.26

93

3031

.7

7.82

19

1.31

62

3072

.1

7.89

37

1.54

92

3276

.7

8.22

26

1.78

12

3487

.0

8.51

39

2.01

29

3704

.0

8.77

76

2.24

42

3927

.6

9.02

01

2.47

54

4157

.8

9.24

52


Tem

pera

ture

, t (°

C)

Pres

sure

p (k

Pa)

24

0.

260.

28

0.

300.

40

0.

500.

60

0.

700.

80

0.

300.

0 v h s

0.78

05

2947

.5

7.47

83

0.81

23

2988

.2

7.55

62

0.84

38

3028

.9

7.63

11

0.87

53

3069

.7

7.70

34

1.03

14

3275

.2

8.03

38

1.18

65

3486

.0

8.32

57

1.34

12

3703

.2

8.58

98

1.49

57

3927

.0

8.83

25

1.64

99

4157

.3

9.05

77

400.

0 v h s

0.58

31

2943

.9

7.34

02

0.60

72

2985

.1

7.41

90

0.63

11

3026

.2

7.49

47

0.65

49

3067

.2

7.56

75

0.77

25

3273

.6

7.89

94

0.88

92

3484

.9

8.19

19

1.00

54

3702

.3

8.45

63

1.12

14

3926

.4

8.69

92

1.23

72

4156

.9

8.92

46

500.

0 v h s

0.46

47

2940

.1

7.23

17

0.48

41

2981

.9

7.31

15

0.50

34

3023

.4

7.38

79

0.52

26

3064

.8

7.46

14

0.61

72

3272

.1

7.79

48

0.71

08

3483

.8

8.08

79

0.80

39

3701

.5

8.35

26

.089

68

3925

.8

8.59

57

0.98

96

4156

.4

8.82

13

600.

0 v h s

0.38

57

2936

.4

7.14

19

0.40

21

2978

.7

7.22

28

0.41

83

3020

.6

7.30

00

0.43

44

3062

.3

7.37

40

0.51

36

3270

.6

7.70

90

0.59

18

3482

.7

8.00

27

0.66

96

3700

.7

8.26

78

0.74

71

3925

.1

8.51

11

0.82

45

4155

.9

8.73

68

800.

0 v h s

0.28

69

2928

.6

6.99

76

0.29

95

2972

.1

7.08

07

0.31

19

3014

.9

7.15

95

0.32

41

3057

.3

7.23

48

0.38

42

3267

.5

7.57

29

0.44

32

3480

.5

7.86

78

0.50

17

3699

.1

8.13

36

0.56

00

3923

.9

8.37

73

0.61

81

4155

.0

8.60

33

1000

.0

v h s

0.22

76

2920

.6

6.88

25

0.27

39

2965

.2

6.96

80

0.24

80

3009

.0

7.04

85

0.25

80

3052

.1

7.12

51

0.30

65

3264

.4

7.46

65

0.35

40

3478

.3

7.76

27

0.40

10

3697

.4

8.02

92

0.44

77

3922

.7

8.27

34

0.49

43

4154

.1

8.49

97

2000

.0

v h s

0.10

84

2875

.9

6.49

43

0.11

44

2928

.1

6.59

41

0.12

00

2977

.5

6.68

52

0.12

55

3025

.0

6.76

96

0.15

11

3248

.7

7.12

96

0.17

56

3467

.3

7.43

23

0.19

95

3689

.2

7.70

22

0.22

32

3916

.5

7.94

85

0.24

67

4149

.4

8.17

63

3000

.0

v h s

0.06

82

2822

.9

6.22

41

0.07

28

2885

.1

6.34

32

0.07

71

2942

.0

6.44

79

0.08

12

2995

.1

6.54

22

0.09

93

3232

.5

6.92

46

0.11

61

3456

.2

7.23

45

0.13

23

3681

.0

7.50

79

0.14

83

3910

.3

7.75

64

0.16

41

4144

.7

7.98

57

5000

.0

v h s

0.04

22

2856

.9

6.08

86

0.04

53

2925

.5

6.21

05

0.05

78

3198

.3

6.65

08

0.06

85

3433

.7

6.97

70

0.07

86

3664

.5

7.25

78

0.08

84

3897

.9

7.51

08

0.09

81

4135

.3

7.74

31

1000

0.0

v h s

0.02

64

3099

.9

6.21

82

0.03

28

3374

.6

6.59

94

0.03

83

3622

.7

6.90

13

0.04

36

3866

.8

7.16

60

0.04

86

4112

.0

7.40

58


Tab

le 9

.05.

The

rmod

ynam

ic p

rope

rtie

s of w

ater

at t

he sa

tura

tion

pres

sure

.[a]

Tem

pera

ture

(°C

) t

(K) T

Den

sity

(k

g/m

3 ) ρ

Spec

ific

Hea

t (k

J/kg

K)

Cp

Ther

mal

C

ondu

ctiv

ity (W

/m K

) k

Ther

mal

D

iffus

ivity

(m

2 /s)

α

Abs

olut

e

Vis

cosi

ty

(N s/

m2 )

µ

Kin

emat

ic

Vis

cosi

ty

(m2 /s

) ν

Pran

dtl

num

ber

Pr

0 27

3.15

99

9.9

4.22

6 0.

558

0.13

1 ×

10-6

1.

7936

× 1

0-3

1.78

9 ×

10-6

13

.7

5 27

8.15

100

0.0

4.20

6 0.

568

0.13

5 ×

10-6

1.

5347

× 1

0-3

1.5

35 ×

10-6

11

.4

10

283.

15

999.

7 4.

195

0.57

7 0.

137

× 10

-6

1.29

64 ×

10-3

1.

300

× 10

-6

9.43

15

28

8.15

99

9.1

4.18

7 0.

587

0.14

1 ×

10-6

1.

1356

× 1

0-3

1.14

6 ×

10-6

8.

10

20

293.

15

998.

2 4.

182

0.59

7 0.

143

× 10

-6

0.99

34 ×

10-3

1.

006

× 10

-6

6.96

25

29

8.15

99

7.1

4.17

8 0.

606

0.14

6 ×

10-6

0.

8806

× 1

0-3

0.88

4 ×

10-6

6.

07

30

303.

15

995.

7 4.

176

0.61

5 0.

149

× 10

-6

0.79

24 ×

10-3

0.

805

× 10

-6

5.38

35

30

8.15

99

4.1

4.17

5 0.

624

0.15

0 ×

10-6

0.

7198

× 1

0-3

0.72

5 ×

10-6

4.

82

40

313.

15

992.

2 4.

175

0.63

3 0.

151

× 10

-6

0.65

80 ×

10-3

0.

658

× 10

-6

4.34

45

31

8.15

99

0.2

4.17

6 0.

640

0.15

5 ×

10-6

0.

6051

× 1

0-3

0.61

1 ×

10-6

3.

95

50

323.

15

988.

1 4.

178

0.64

7 0.

157

× 10

-6

0.55

50 ×

10-3

0.

556

× 10

-6

3.55

55

32

8.15

98

5.7

4.17

9 0.

652

0.15

8 ×

10-6

0.

5099

× 1

0-3

0.51

7 ×

10-6

3.

27

60

333.

15

983.

2 4.

181

0.65

8 0.

159

× 10

-6

0.47

17 ×

10-3

0.

478

× 10

-6

3.00

65

33

8.15

98

0.6

4.18

4 0.

663

0.16

1 ×

10-6

0.

4354

× 1

0-3

0.44

4 ×

10-6

2.

76

70

343.

15

977.

8 4.

187

0.66

8 0.

163

× 10

-6

0.40

40 ×

10-3

0.

415

× 10

-6

2.55

75

34

8.15

97

4.9

4.19

0 0.

671

0.16

4 ×

10-6

0.

3766

× 1

0-3

0.36

6 ×

10-6

2.

23

80

353.

15

971.

8 4.

194

0.67

3 0.

165

× 10

-6

0.35

20 ×

10-3

0.

364

× 10

-6

2.25

85

35

8.15

96

8.7

4.19

8 0.

676

0.16

6 ×

10-6

0.

3285

× 1

0-3

0.33

9 ×

10-6

2.

04

90

363.

15

965.

3 4.

202

0.67

8 0.

167

× 10

-6

0.30

89 ×

10-3

0.

326

× 10

-6

1.95

95

36

8.15

96

1.9

4.20

6 0.

680

0.16

8 ×

10-6

0.

2922

× 1

0-3

0.31

0 ×

10-6

1.

84

100

373.

15

958.

4 4.

211

0.68

2 0.

169

× 10

-6

0.27

75 ×

10-3

0.

294

× 10

-6

1.75

12

0 39

3.15

94

3.5

4.23

2 0.

685

0.17

1 ×

10-6

0.

2354

× 1

0-3

0.24

4 ×

10-6

1.

43

140

413.

15

926.

3 4.

257

0.68

4 0.

172

× 10

-6

0.20

10 ×

10-3

0.

212

× 10

-6

1.23

16

0 43

3.15

90

7.6

4.28

5 0.

680

0.17

3 ×

10-6

0.

1716

× 1

0-3

0.19

1 ×

10-6

1.

10

180

453.

15

886.

6 4.

396

0.67

3 0.

172

× 10

-6

0.15

20 ×

10-3

0.

173

× 10

-6

1.01

20

0 47

3.15

86

2.8

4.50

1 0.

665

0.17

0 ×

10-6

0.

1392

× 1

0-3

0.16

0 ×

10-6

0.

95

[a] B

ased

upo

n da

ta fr

om R

aznj

evic

(197

6).



List of Symbols cp specific heat capacity at constant pressure, J/(kg K) or kJ/(kg K) h enthalpy, kJ/kg has (hs – ha), enthalpy difference between saturated and dry air, kJ/kg hf enthalpy of saturated liquid, kJ/kg hfg (hg – hf), latent heat of vaporization, kJ/kg hg enthalpy of saturated vapor, kJ/kg Le Lewis Number, dimensionless m mass, kg M molecular weight, kg/kmol N number of moles P pressure, Pa R gas constant for a particular gas, kPa m3/(kg K) Ru gas constant, universal, 8.314 kJ/(kmol K) s entropy, kJ/(kg K) t temperature, °C T absolute temperature, K ν specific volume, m3/kg V volume, m3 W humidity ratio, g H2O/kg DA or kg H2O/kg DA x steam quality, kg vapor/kg total y mole fraction θ time, s µ degree of saturation, dimensionless φ relative humidity, percent or decimal

Subscripts 1, 2 position identification a air (or dry air) dp dew point f fluid state fg difference between properties at fluid and gaseous states g gaseous state rem removed s steam, or saturated t total w water wb wet-bulb ws water at saturation

Superscript * a property at the thermodynamic wet-bulb temperature as saturated air


References 1. ASHRAE. 1977. ASHRAE Brochure on Psychrometry. ASHRAE, Atlanta, GA. 2. ASHRAE. 1997. Handbook of Fundamentals, Chapter 6: Psychrometrics.

ASHRAE, Inc., Atlanta, GA. 3. ASME. 1993. Steam Tables. 6th ed. with software for calculating steam properties.

ASME, New York, NY. 4. Cengel, Yunus A., and Michael A. Boles. 1989. Thermodynamics: An Engineering

Approach. McGraw-Hill Book Company, New York, NY. 5. Raznjevic, Kuzman. 1976. Handbook of Thermodynamic Tables and Charts.

Hemisphere Publishing Corp., Washington, DC. 6. Van Wylen, Gordon J., and Richard E. Sonntag. 1986. Fundamentals of Classical

Thermodynamics. John Wiley & Sons, New York, NY. 7. Wilhelm, Luther R. 1976. Numerical calculations of psychrometric properties in SI

units. Transactions of the ASAE 19(2): 318-321, 325.

Problems 9.1. Use a psychrometric chart to complete the following table.

tdb (°C)

twb

(°C) tdp

(°C) φ

(%) h

(kJ)/(kg) v

(m3/(kg) W

(g H2O)/(g air)21 17 21 17 21 30

18 81 27 18 10 20

9.2. A psychrometer measures wet bulb and dry bulb temperatures of 20°C and 30°C, respectively. What is:

a. the dew point temperature? c. the relative humidity? b. the humidity ratio? d. the enthalpy? 9.3. For a dew point of 24°C and dry bulb of 30°C, find: a. relative humidity c. humidity ratio b. enthalpy d. vapor pressure 9.4. Air inside a room is at 20°C with a twb = 15°C. Will condensation occur if the air

contacts a surface at 10°C? 9.5. A 4m × 7m × 2.5m room contains air at 27°C and atmospheric pressure. The

partial pressure of the water vapor in the air is 1.5 kPa. Find: a. the wet bulb temperature d. the dew point b. the humidity ratio e. the enthalpy per kg of dry air c. the specific volume


9.6. One kilogram of air at 20°C and 70% relative humidity is heated to 40°C with no moisture added or removed.

a. What is the relative humidity of the heated air? b. If this air is maintained at a pressure of 1 atmosphere (101.325 kPa) during

the heating process, what is the percentage change in volume due to the heating? 9.7. Air at 25°C and a relative humidity of 40% is to be cooled until condensation

begins. a. How low can it be cooled? b. What happens if the initial relative humidity is 90%? 9.8. A large balloon contains air at 44°C and 10% relative humidity. The contents are

slowly cooled. a. How much heat must be removed to cool the air to 15°C? b. To what temperature must the air be cooled before condensation begins? 9.9. Evaporative cooling by forcing air through trailer loads of snap beans is some-

times used during shipments. Assume the following conditions: Air enters at 27°C and 70% relative humidity. It leaves at 27°C and 95% relative humidity. a. How much heat is removed per 1000 m3 of air entering the trailer? b. How much water is removed per 1000 m3 of air? 9.10. In hot, dry areas evaporative cooling is often very effective. Consider a system

where water for evaporation is added by spraying into a duct containing air at 45°C and 20% relative humidity.

a. If the resulting air-vapor mixture must not exceed 60% relative humidity, how much can the temperature be lowered by evaporative cooling?

b. If the air flow rate is 0.50 m3/s, what must be the flow rate of the water added for evaporation?

c. Show this process on a psychrometric chart. 9.11. In a building heating/cooling system, air flows over cooling coils for moisture

removal and is then reheated as necessary to maintain a cooling air temperature of 21°C. If the air temperature as it crosses the coils is 13°C, what will be the relative humidity of the cooling air?

9.12. Air at 55°C and a wet-bulb temperature of 26°C passes through a humidifier and exits at 80% relative humidity. For this process, find:

a. the change in temperature of the air b. the change in moisture content of the air c. the change in specific volume d. the change in dew point temperature e. the change in enthalpy


9.13. Air at 15°C and 50% relative humidity is mixed with an equal amount of air at 35°C and 50% relative humidity. Determine the temperature and relative humid-ity of the mixed air. Repeat for a mixture containing 80% of the 15°C air and 20% of the 35°C air.

9.14. Ambient air at 15°C and 50% relative humidity is heated to 50°C. This heated air is than mixed with an equal amount of ambient air (at 15°C and 50% relative humidity). Determine the temperature and relative humidity of the mixed air. Repeat for a mixture containing 80% of the heated air and 20% of the ambient air.

9.15. Air at 22°C and 90% relative humidity (Point 1) is passed over cooling coils and cooled to 5°C (Point 2). It is then heated to 45°C (Point 3). The heated air is forced through a drier, exiting at 80% relative humidity (Point 4).

a. Give the values of the following properties at State Point 2: twb, tdp, h, v, W. b. How much water per unit mass of dry air is removed by the drying air in the

drying process? c. How much heat, per unit mass of dry air, is removed from the air in the cool-

ing process? 9.16. Show that each term of Equation 9.19 can be written in units of kJ/kg DA. 9.17. Using the latent heat of fusion of water, calculate the amount of energy needed

to melt 50 kg of ice at 0°C. If the ice is initially at –15°C, how much energy would be needed?

9.18. Use the steam tables to find the enthalpy of steam under the following condi-tions.

State P (kPa) t (°C) h (kJ/kg) Liquid 300 133.5 Liquid 10 45.8 Vapor 300 133.5 Vapor 200 300 Vapor 400 800

9.19. What is the enthalpy of 1 kg of “wet” steam in a 0.2 m3 container at: a. 100°C c. 800 kPa b. 4000 kPa d. 175°C Note: First determine the quality (x). Since 0 < x < 1, any computed value of x >

1 indicates a physically impossible condition. 9.20. What is the enthalpy of an 80% vapor and 20% liquid mixture at 100°C? 9.21. Superheated steam at 200 kPa and 160°C is cooled at constant pressure a. What are the initial values of t, h, and v? b. What are the values of t, h, and v when the steam is cooled to saturated va-

por?


c. What are the values of t, h, and v when it is cooled to a quality of 0.5? d. What are the values of t, h, and v when it is cooled to saturated liquid? e. If additional cooling occurs, will the temperature change? If so, how? 9.22. Plot enthalpy (h) as a function of quality (x) for steam at: a. 100°C c. 130°C b. 120 kPa d. 400 kPa 9.23. Complete the following table of steam properties.

Item t (°C) P (kPa) v (m3/kg) h (kJ/kg) x State A 170 792 2047.9 B 400 200 C 140 0.9 D 140 150 E 140 SL F 140 0.5 G 121 0.1

State codes: SL = saturated liquid SV = saturated vapor SH = superheated vapor WS = wet steam

9.24. Calculate the partial pressure of water vapor and the corresponding temperature for a steam air mixture that is 10% air by mass with a total pressure of 400 kPa.

9.25. Repeat the previous problem for a mixture that is 20% air by mass.

psychrometrics - wordpress.com · 09/04/2015 · psychrometrics abstract. this chapter includes...

Documents