ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
TABLE OF CONTENTS
Page
List of Figures ............................................................................................................................................... ii
Enabling Objectives ..................................................................................................................................... iii
Introduction ................................................................................................................................................ 2-1
Water and Steam Properties ........................................................................................................... 2-1
Steam Tables .................................................................................................................................. 2-1
Saturation Temperature and Pressure ............................................................................................ 2-1
Specific Volume (V) ...................................................................................................................... 2-4
Quality (x) ...................................................................................................................................... 2-6
Wet Steam ...................................................................................................................................... 2-7
Internal Energy (u) ......................................................................................................................... 2-8
Enthalpy (h).................................................................................................................................... 2-9
Entropy......................................................................................................................................... 2-10
Subcooled Liquid ......................................................................................................................... 2-12
Superheated Steam Tables ........................................................................................................... 2-14
Mollier h-s Diagram For Steam ................................................................................................... 2-14
Water Vaporizing to Steam.......................................................................................................... 2-18
Summary .................................................................................................................................................. 2-18
Definitions................................................................................................................................................ 2-19
Exercises .................................................................................................................................................. 2-20
i
ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
LIST OF FIGURES
Page
Figure 2.1
Coffee Pot
2.2
Figure 2.2
Pressure versus Temperature
2.3
Figure 2.3
Specific Volume Relationship at Saturation
2.5
Figure 2.4
Mollier h-s Diagram For Steam
2.15
ii
ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
1.0
Enabling Objectives
1.1
Predict the effects of varying the temperatures on the pressure of a fluid at a constant
volume.
1.2
Explain the terms quality and percent moisture as they apply to saturated water.
1.3
Define the following terms:
1.4
1.5
•
Internal Energy
•
Enthalpy
•
Entropy
Given a Mollier Diagram, identify the following:
•
Saturation Line
•
Constant Pressure Lines
•
Constant Temperature Lines
•
Constant Moisture Lines
•
Constant Enthalpy Lines
•
Constant Entropy Lines
Given the steam tables and the temperature and pressure of water, determine whether the
water is subcooled (compressed), saturated, or superheated.
iii
ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
2.0
Introduction
Steam cannot be considered an idea gas at normal operating temperatures and pressures. For this
reason, the relationships between the thermodynamic properties of steam at any given state must
be experimentally determined and tabulated for reference. The steam tables are our source for this
thermodynamic information.
This chapter deals with the use of the steam tables to determine properties of water.
2.1
Water and Steam Properties
2.1.1 Steam Tables
Steam Tables are based on 32°F. Besides pressure and temperature, the steam tables give other
properties such as volume, enthalpy, entropy, internal energy, etc. To establish these properties it
is necessary to start from some temperature as a base. The base of the steam tables has been
selected as 32°F. This choice was purely arbitrary as any other temperature such as 0°Fm etc.,
might have been selected. However, the properties of steam are not ordinarily needed at such low
temperatures; 32°F, which is the temperature of melting ice at standard atmospheric pressure, is a
temperature that is conveniently reproducible as a starting point.
2.1.2 Saturation Temperature and Pressure
Saturation Temperature is a function of saturation pressure. Consider, as in Figure 2.2, a coffee
pot on a stove open to the atmosphere and at a location where the barometric pressure is that of a
standard atmosphere, 14.7 psia. Consider this coffee pot to be partially filled with cold water at
32°F. If heat is added to the water in the coffee pot, its temperature rises until 212°F is reached.
If additional heat is now added, the temperature of the water no longer rises but some of the water
begins to boil. This temperature at which the water first begins to boil, while under a given
pressure, such as 14.7 psia atmospheric pressure, is known as the saturation temperature. Water
at this temperature is said to be saturated water. The designation saturation arises from the
consideration that the space above the water is saturated with water vapor, and if any more heat is
supplied, the water boiling now creates a visible steam. Thus 212°F is the saturation-temperature
corresponding to a saturation (vapor) pressure of 14.7 psia.
2.1
ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
FIGURE 2.1 COFFEE POT
Suppose the coffee pot is located where the atmospheric pressure is 12 psia. The water rises in
temperature from 32°F to 202°F and then begins to boil. Thus 202°F is the saturation temperature
that corresponds to a saturation pressure of 12 psia.
Similarly, if the coffee pot is enclosed in a partial vacuum of 1 psia, the water boils at a saturation
temperature of 102°F that corresponds to the pressure of 1 psia.
Suppose the outlet of the coffee pot is restricted so that the inside pressure becomes 100 psia. If
heat is added to the water, it does not begin to boil until a temperature of 328°F is reached. Thus,
328°F is the saturation temperature that corresponds to a pressure of 100 psia.
2.2
Chapter 2
ESP100.30 Rev. 4
Properties of Heat Transfer
The conclusion may now be stated: For every pressure there is a corresponding temperature,
called the saturation temperature, at which water boils. The converse is also true. For every
saturation temperature at which boiling occurs, there is a corresponding saturation pressure.
Figure 2.2 shows the unique PT relationship.
FIGURE 2.2 PRESSURE VERSUS TEMPERATURE
The foregoing may be verified by examination in Table 1 in the Steam Tables. For every value of
saturation temperature (T) in degrees (F) in the first column, there is a corresponding saturation
pressure (P) in psia in the second column.
Table 2 differs from the first table, in that the first complete column has pressures (P) in psia and
the second complete column has corresponding values of saturation temperature (T).
2.3
Chapter 2
ESP100.30 Rev. 4
Properties of Heat Transfer
In determining steam properties, either Table 1 or Table 2 may be used. The first table contains
whole-number values of saturation temperature and rounded decimal values of corresponding
pressures, while the second table contains whole-number values of pressure and rounded decimal
values of corresponding saturation temperatures. Using interpolation, values obtained from either
of the two tables are the same. In use, one of the two tables is selected in accordance with
whichever one provides the easiest reading or interpolation.
Steam tables are based on absolute pressure. Pressures tabulated in the steam tables are absolute
pressures, either in psia (lbf per sq in abs) or sometimes in inches Hg abs (inches mercury
absolute). In practice, most pressures above atmospheric pressure are obtained from gages which
give a reading in psig (lb per sq in gage), but sometimes in inches Hg. Gages reading below
atmospheric pressure are normally calibrated in inches Hg vacuum. Before use is made of the
steam tables, these gage readings must be transformed to absolute pressures.
2.1.3 Specific Volume (V)
Values in the steam tables are in engineering units of °F, psia and BTU per lbm. Values of
specific volume are designated small v and are given in cubic feet per lbm (or ft3/lbm). Reference
to the steam table indicates that there is a family o three specific-volume columns in each table.
To understand the significance of these three columns, it is desirable to return to the example of
the coffee pot on the stove in Figure 2.1. Imagine one pound of water in the coffee pot on the
stove initially at 32°F and at atmospheric pressure of 14.7 psia. If sensible heat is supplied by the
stove to the water, the temperature of the water rises until the saturation temperature of 212°F is
reached. The water is now known as a “saturated liquid.”
At this saturation temperature, one pound of water occupies a certain volume designated as the
specific volume of the liquid (at the saturation temperature corresponding to the pressure on the
water). This specific volume of the saturated liquid is the first column in the family group of three
columns under specific volume. Specific volume of a liquid is designated as vf where v indicates
specific volume and f indicates that the fluid is a saturated liquid.
Suppose latent heat is now added to the one pound of water at a saturation temperature of 212°F
in the coffee pot. The temperature does not rise any higher but remains at the saturation
temperature of 212°F, and the water begins to boil. As long as the heat is supplied, the pound of
water continues to boil at the saturation temperature of 212°F until all the water is converted into
steam. Immediately after the last drop of water is boiled into steam, there is no water present so
that the steam is said to be “dry” steam. Because it is still at the saturation temperature of 212°F,
it is sometimes designated as “dry-and-saturated steam,” “dry-saturated steam” or simply
“saturated steam.”
The increase in volume in changing from one pound of water into one pound of dry steam is
known as the specific volume of vaporization, designated as vfg. The designation of vfg in the
steam tables arises from use of the subscript f for fluid (or liquid) and g for gas (or vapor), fg
indicating a change from all liquid to all vapor.
2.4
ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
The specific volume of a pound of dry-steam vapor is designated vg. In the vg designation, the g
indicates that the pound of steam has just reached the vapor (or gaseous) state. The following
equation is then valid. (The same equation is shown expressed in varied notation.)
The relationship between vf, vfg, and vg is illustrated by Figure 2.3
FIGURE 2.3 SPECIFIC VOLUME RELATIONSHIP AT SATURATION
As discussed earlier, vf represents the specific volume of water when the water is saturated (i.e.,
the water is at saturation temperature corresponding to the pressure on the water). If the pressure
on the water is increased above this saturation pressure, the specific volume of the water changes
very little, because water is essentially incompressible. Liquid water expands or contracts more
significantly with changes in temperature. For this reason, the specific volume of liquid water is
determined by using the specific volume corresponding to the temperature (and not the pressure)
of the water. The value of specific volume given in the steam tables for the temperature of the
liquid water is approximately valid for all pressures equal to or above the corresponding saturation
pressure.
2.5
Chapter 2
ESP100.30 Rev. 4
Properties of Heat Transfer
2.1.4 Quality (x)
Let us consider the specific volume of a mixture which is part water and part steam. Such a
mixture is said to have a quality x (or dryness fraction). In the following definition, mass is
numerically equal to weight.
Quality is usually expressed as a percent by multiplying by 100.
The term “percent moisture” or moisture fraction is frequently used instead of percent quality.
Quality is related to moisture by the relationships.
(% moisture) = 100% - (% quality) or moisture fraction = 1 - x
(% quality) = 100% - (% moisture) or quality fraction = x = 1 – moisture fraction.
Referring to Figure 2.3, saturated liquid exists to Point vf, since at this point no steam has been
generated, the quality is 0% and the percent moisture is 100%. As latent heat is added to the
saturated liquid, steam is generated, quality will increase, percent moisture will decrease, and the
position of the water-steam mixture will move toward Point vg. At Point vg, all the water has been
vaporized resulting in saturated steam whose quality is 100% and percent moisture is 0%.
Example A
Determine the quality of a mixture of 0.2 lbm water and 0.8 lbm steam.
Solution
Note that the moisture content of the mixture in this example is 1 – x = 1 – 0.80 = 0.20, or 20%
2.6
Chapter 2
ESP100.30 Rev. 4
Properties of Heat Transfer
2.1.5 Wet Steam
Wet steam is a term frequently used to designate a liquid-vapor mixture at saturated conditions.
Because the steam is mixed with liquid water, it is said to be wet. More specifically, wet steam
(or wet vapor) is a mixture of saturated liquid and saturated vapor. If the wet vapor is static, as it
is in the pressurizer, the saturated vapor will separate from the saturated liquid due to their
difference in density. In a dynamic situation, like the steam generator, saturated liquid droplets
will be entrained in the saturated vapor flow. Wet steam must have a quality x; or conversely, if
steam has a quality <100%, it must be wet steam.
It is now desired to establish an equation for determining the specific volume of wet steam. The
specific volume (v) of the pound of wet steam may be considered to be made up of two parts, the
specific volume of steam in the pound of wet steam xvg plus the specific volume of water in the
pound of wet steam (1-x) vf.
Thus,
or
where
This last form of the equation is most satisfactory for use. The value of vf may be obtained from
the first of the three specific volume columns in the Steam Table. The value of (vfg) during
boiling is obtained from the middle specific volume column. The last specific volume equation is
preferred because only one multiplication and one addition is involved.
Note that the reciprocal of specific volume is density.
2.7
ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
Example B
For steam at 50 psia and 93 percent quality, calculate: (a) specific volume in cu ft. per lbm, (b)
density in lbm per cu ft. (c) temperature in °F
Solution
(a) From Table 2 at 50 psia
(b) Density = 1/v = 1/7.92 = 0.1263 lbm per cu ft
(c) T = 281.02°F (saturation temperature)
21.6
Internal Energy (u)
The internal energy of steam is only required to solve non-flow problems. As a consequence,
internal energy values are given in some steam tables such as the Keenan steam tables, but in
limited fashion in other steam tables such as the ASME steam tables. The CE steam tables do not
give internal energy values at all.
In the Keenan tables, internal energy values appear as three columns to give (uf) = internal energy
of the liquid water, (ufg) = internal energy increase during evaporation, and (ug) = internal energy
of dry or 100 quality steam.
Values of internal energy increase from the 32°F base in the Steam Tables as heat is added. The
internal energy of water is a function of temperature and is nearly independent of pressure.
For the internal energy of wet steam of less than 100 percent quality, the formula is similar to that
for specific volume.
where:
2.8
Chapter 2
ESP100.30 Rev. 4
Properties of Heat Transfer
2.1.7 Enthalpy (h)
Reference to the first two steam tables indicates that there is a family of three columns marked
enthalpy.
Enthalpy has several meanings, but it may be considered to be the heat in BTU added at constant
pressure to a pound of water initially at 32°F, to raise it to some other temperature or to change it
to a water-steam mixture or steam. Values of enthalpy in the steam tables are designated by the
small letter h, having units BTU per lbm.
Reference to the first steam table indicates that at the base, or starting point of the steam tables, the
arbitrary assumption is made that water at 32°F has essentially zero enthalpy. Any other base
might have been taken, but this was a convenient starting point since water ordinarily exists as ice
below this temperature. The first column of the tables gives the enthalpy hf required to be
supplied to the water to change its temperature from 32°F to a higher temperature such as 212°F.
Consider again the example of the pound of water in a coffee pot under at atmospheric pressure of
14.7 psia in Figure 2.1. If this pound of water, initially at 32°F, has heat supplied to it at constant
pressure, there is a consequent increase in enthalpy. Reference to the steam tables indicates that at
212°F, the enthalpy of water is 180BTU per lbm. This means that 180 BTU are added at constant
pressure to raise the temperature of one pound of water from 32°F to 212°F.
Enthalpy is defined as the heat added to the water at constant pressure to change its temperature
from 32°F to some other temperature. Actually, because water is nearly incompressible, the
pressure at which this heat is added is not important. Similar to the specific volume of water, the
enthalpy of water is primarily dependent on temperature rather than pressure.
There is a small correction for pressure but for ordinary pressures the amount of the correction is
negligible. In all of the following calculations, this correction is neglected. If it were desired to
make this slight correction, it would be necessary to use large unabridged steam tables such as
those of Keenan which give tables from which this small correction could be determined.
Thus, the enthalpy of water is determined by finding the enthalpy hf at the saturation temperature
and pressure. The result is approximately valid for all pressures, provided that the temperature of
the water is below the saturation temperature corresponding to the pressure on the water.
Otherwise, the water would not be all water but would be partly water and partly steam or all
steam. Returning to the example, heat is added to the water (considered to be at the constant
atmospheric pressure of 14.7 psia) until the pound of water reaches the temperature of incipientboiling or evaporation at 212°F. Reference to the steam tables indicates that an amount of
enthalpy hf equal to 180.17 BTU per lbm is supplied.
2.9
ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
If more enthalpy or heat at constant pressure (in this case 14.7 psia atmospheric pressure) is
supplied, the water begins to boil and an additional amount of enthalpy of evaporation hfg is
supplied to change the water from all water at the saturation temperature of 212°F to all steam at
the same saturation temperature. Reference to the middle column of the three-column enthalpyfamily indicates that hfg = 970.3 BTU per lbm. The quantity hfg is sometimes referred to as the
heat of vaporization, or latent heat.
The value in the last column of the three enthalpy columns is the enthalpy of 100 percent quality
steam which is all vapor. For the 212°F steam at 14.7 psia it is hg = (1150.5 BTU per lbm), equal
to the sum of hf = (180.17 BTU per lbm) from the first column plus hfg = (970.3 BTU per lbm)
from the second column. Thus, hg = hf + hfg.
By proof similar to that given in the case of specific volume, for wet steam:
where:
This formula should always be used for enthalpy calculations of wet steam. Referring to Steam
Tables 1 or 2, when the pressure reaches 3208.2 psia, the enthalpy-of-evaporation becomes zero,
indicating that water no longer undergoes an evaporation process in changing into steam. At this
pressure, called the critical pressure, and at higher pressures, water has the same specific volume
or density as steam.
Water, as it is heated, gradually rises in temperature and changes into steam without undergoing
an evaporation process. An evaporation process in the usual sense is not present, because an
evaporation process is ordinarily recognized as one in which the water remains constant in
temperature during the change from water to steam.
2.1.8
Entropy
In thermodynamics, the usefulness of energy is rated according to the amount of work that can be
done with it. The chemical energy in the bonds of octane molecules (i.e., automobile gasoline)
can do more work and is more useful than an equal amount of thermal energy in a hot sidewalk or
in the desert sand.
2.10
Chapter 2
ESP100.30 Rev. 4
Properties of Heat Transfer
The usefulness of energy is rated using the quantity called entropy. Entropy, like golf, has an
inverted scale: the lower the score, the better. Entropy quantifies the energy in terms of
usefulness.
Each of the first two Steam Tables contains a family of three columns marked entropy. In the
steam tables entropy (s) is given as BTU per lbm-°R (specific entropy).
The tabulated entropy values are a mathematical evaluation of the function defining entropy.
where:
Heat flow from a high temperature to a low temperature represents a degradation of energy. This
process is directional. Friction represents degradation of work energy into heat energy. A
frictional process is directional and cannot be reversed. The mechanical energy of a rotating shaft
may be transformed into heat energy at the shaft bearing, but heating the shaft bearing will not
cause the shaft to rotate and deliver mechanical energy.
Both non-productive temperature decrease and friction represent the degradation of energy.
Entropy increases as the energy is degraded.
Although entropy is a mathematical property, it is just as definite a property as the more familiar
physical properties: temperature, pressure, etc. Like enthalpy, the base or starting point for
entropy values is taken as zero for water at 32°F.
As heat is added to water, the mathematically calculated value of entropy also increases so that
water at any given temperature has a definite value of entropy. Like specific volume and enthalpy,
the entropy of water is a function of temperature and is nearly independent of pressure. For the
pound of water in the coffee pot at 212°F, reference to the steam tables indicates that sf = 0.3121
BTU per lbm-°R.
To change one pound of water at 212°F into one pound of steam at 212°F requires an entropy of
evaporation sfg = 1.447 units. The resultant steam or vapor has an entropy of sg = 1.7568
BTU/lbm °R.
2.11
Chapter 2
ESP100.30 Rev. 4
Properties of Heat Transfer
By a procedure similar to that used for the discussion of specific volume, it may be shown that for
1 lbm of wet steam, the entropy may be calculated as:
where:
Summary of Wet-Steam Formulas. The preceding wet-steam formulas may now be summarized.
Observe that these equations are similar; the value of the property for wet steam is equal to: (the
value of the property for the saturated liquid) plus (the quality expressed as a decimal) times (the
value of the property-increase during vaporization).
2.1.9 Subcooled Liquid
In the plant, water exists in three (3) different general conditions. We have just defined one of
those conditions: saturated conditions. We have also learned how to completely define the state of
the water under saturated conditions using the Steam Tables to determine the values of all the
thermodynamic properties.
Another general condition of water in our plant is subcooled liquid. Subcooled liquid can be
defined in several ways. First, if the temperature of water is less than the saturation temperature
for the existing pressure, then the water is a subcooled liquid. For example, condensate leaving
the condenser at 100°F and 1 psia is subcooled since 100°F < 101.74°F, which is the saturation
temperature corresponding to 1 psia. Secondly, if the pressure on the water is greater than the
saturation pressure for the existing temperature, then the water is a subcooled liquid. Referring
back to our example of the condensate, since 1 psia > 0.94924 psia, which is the saturation
pressure corresponding to 100°F, the water is subcooled.
2.12
ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
In order to determine the thermodynamics properties of a subcooled liquid, we will need, just as
before, two independent properties (temperature and pressure will do) and some Compressed
Liquid Tables. Since you are not supplied with Compressed Liquid Tables, you cannot determine
the actual values of the thermodynamic properties of the subcooled liquid. However, the Steam
Tables can provide you with a close estimate of these values. This is possible because
pressurizing liquid water, which itself is nearly incompressible, does not radically change its
thermodynamic properties.
Earlier, you learned to determine the specific volume of liquid water by using the Steam Table
value for the specific volume of a saturated liquid at the liquid’s temperature. The same procedure
can be used to estimate the enthalpy and entropy of the subcooled liquid.
Example C
Determine the specific volume, enthalpy, and entropy of water which is at a temperature of 120°F
and a pressure of 2 psia.
Solution
1.
First determine the general condition of the water (i.e., is it subcooled, saturated, or
superheated?)
Since 2.0 psia > 1.6927 psia (Psat for 120°F water), the water is subcooled.
2.
To determine the properties of the subcooled liquid recall that the properties of a saturated
liquid at the same temperature closely approximate the properties of the subcooled liquid.
Therefore:
v for subcooled liquid = vf for 120°F = 0.016204 ft3/lbm
h for subcooled liquid = hf for 120°F = 87.97 BTU/lbm
s for subcooled liquid = sf for 120°F = 0.1646 BTU/lbm ˚R
Another important property associated with a subcooled liquid is subcooling margin (SCM). The
subcooling margin of a subcooled liquid is the temperature difference between the saturation
temperature corresponding to the liquid cover pressure and the liquid’s temperature.
Subcooling Margin (SCM) = Tsat for liquid pressure – Tliq
Subcooling margin is an important Reactor Coolant System (RCS) parameter because it is an
indication of the type of heat removal occurring at the fuel cladding and coolant interface.
2.13
ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
Example D
Calculate the Subcooled Margin for the following two Reactor Coolant Systems:
a)
Pressurizer pressure is 2250 psia, and the highest RCS hot leg temperature is 607°F
b)
Pressurizer pressure is 2100 psia, and the highest RCS hot leg temperature is 575°F.
Solution
a)
b)
2.1.10 Superheated Steam Tables
More heat can be added at constant pressure to dry saturated steam so that the steam rises in
temperature with a resultant increase in specific volume, enthalpy, and entropy.
The increase in temperature of the steam above the saturation temperature corresponding to the
pressure is known as the degree of superheat, or simply the superheat.
The third CE-ASME steam table, Table 3, tabulates the properties of superheated steam. For
various pressures in psia and temperatures in °F, values are listed for degrees of superheat (Sh) in
°F, specific volume(v) in cu ft per lbm, enthalpy (h) in BTU per lbm, and entropy (s) in BTU per
lbm °R.
2.1.11 Mollier h-s Diagram For Steam
The Mollier diagram is an h-s plot and is a graphic representation of the information presented in
the Steam Tables. Figure 2.4 is a simplified facsimile of the Mollier diagram. A Mollier chart
suitable for calculation purposes is given in the back of the CE steam tables.
The saturated steam or 100 percent quality saturation line is the dome-shaped curve across the
chart. Below the saturation line lies the wet steam region with lines of constant percent moisture.
2.14
Chapter 2
ESP100.30 Rev. 4
Properties of Heat Transfer
Constant-pressure lines run upward diagonally across the chart. Below atmospheric pressure, a
complete chart includes two sets of constant-pressure lines for pressures (not shown in Figure 2.4).
One set is measured in inches of mercury. The other set is in lbf per sq. in. absolute. In using the
chart, care must be taken to read these lines with the proper units.
There is still another family of lines that branch off to the right from the saturation line. These are
lines of constant steam temperature, depicted on Figure 2.4. Below the saturation line, constant
steam-temperature lines coincide with constant steam-pressure lines. The chart also includes lines
of constant superheat.
There are no constant-volume lines on the Mollier chart, although there are other types of charts
which include constant-volume lines.
A definite advantage of the Mollier diagram is it allows you to determine the properties of a wet
vapor (x > 44%) without using the wet vapor formulas.
FIGURE 2.4 MOLLIER h-s DIAGRAM FOR STEAM
2.15
ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
The Mollier chart presents as data:
•
Pressure in psia
•
Moisture in percent
•
Steam temperature in degrees F
•
Enthalpy in BTU per lbm
•
Entropy in BTU lbm per degree R
If any two of the above properties are known, any of the remaining three properties may be
obtained.
The major advantage of the Mollier diagram over the steam tables is in analyzing a process where
a thermodynamic property that is presented on the diagram is known to be or can be assumed to be
constant.
As a first example consider 900 psia, saturated steam discharging to the atmosphere through the
main steam dump header. No heat is added to or removed, so this can be considered as a constant
enthalpy (throttling or isenthalpic) process. At 900 psia on the saturation line of the Mollier
Diagram (refer to the chart in the back of the Steam Table), we can see that the temperature is
530°F and enthalpy is 1195 BTU/lbm. If we now follow the 1195 BTU/lbm enthalpy line to
atmospheric pressure, we see that we first pass through the wet steam region under the saturation
line and then emerge into the superheat region. When the 1195 Btu/lbm line arrives at the
atmospheric pressure line, the conditions are: 300°F and 90°F superheat.
As a second example, let us consider a constant entropy (isentropic) process. In the ideal case as
steam is expanded through a turbine the heat is converted to work and entropy remains constant.
If we now take the same initial steam conditions (900 psia, saturation and 1195 BTU/lbm) and
follow a vertical constant entropy line through a high pressure turbine to 180 psia, we have turbine
exhaust conditions of 15% moisture and 1070 BTU/lbm. If we want to know the temperature of
the turbine exhaust steam we follow the 180 psia line to the saturation line and see that the
temperature of 180 psia saturated steam is about 375°F. Utilizing the Steam Pressure Table would
provide an accurate answer of 373.08°F. We can obtain the temperature in this manner because
both the temperature and pressure are constant and/or saturation conditions regardless of steam
quality or moisture content. This leads us to the conclusion that if we have a constant temperature
(isothermal) process that is adding or removing heat under the vapor dome, we can follow the
corresponding constant pressure line to determine the temperature of the water-steam mixture.
The constant enthalpy process and the constant entropy process discussed in the examples above
are common applications of the Mollier Diagram.
2.16
ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
2.1.12 Determining the General State of Water
If the temperature and pressure of water are known, the Steam Tables can be used to determine
whether the water is subcooled (compressed), saturated, or superheated. Recall that a subcooled
liquid is one whose temperature is below the saturation temperature for the existing pressure or
whose pressure is above the saturation pressure for the existing temperature. When water is at
saturation, its temperature is the saturation temperature for the existing pressure; stated another
way, its pressure is the saturation pressure for the existing temperature. Finally, when steam is
superheated, its temperature is above the saturation temperature for the existing pressure;
similarly, its pressure is below the saturation pressure for the existing temperature.
Example E
Water is leaving the condenser at a temperature of 100°F and a pressure of 1 psia. Is the water
subcooled, saturated, or superheated?
Solution
There are two ways to determine the general state of the water:
1)
Go to Steam Table 1 and find 100°F. The corresponding saturation pressure is 0.94924
psia. Since 1 psia > 0.94924 psia, the water is compressed or subcooled.
2)
Go to Steam Table 2 and find 1 psia. The corresponding saturation temperature is
101.74°F. Since 100°F < 100.74°F, the water is subcooled slightly.
Example F
Determine the missing values for water:
T
°F
P
psia
80
v
3
ft /lbm
h
BTU/lbm
s
BTU/lbm°R
General
State
SC, SAT, SH
Quality
(if SAT)
20
Solution
1.
First determine general state.
Since for 80°F, 20 is between the vf and vg values, the water is at saturated conditions (it is
neither saturated liquid nor saturated vapor).
2.17
ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
2.
Choose appropriate Steam Table or Mollier diagram.
Since 80°F is given, Steam Table 1 is best. Properties of a wet vapor are calculated using
wet steam formulas; therefore, quality must be calculated first.
or
2.1.13 Water Vaporizing to Steam
Based on the previous discussions in the chapter up to this point, it becomes obvious that there are
two conditions which can lead to the vaporizing of liquid water to steam. First of all, if heat is
added to saturated liquid, then steam will be generated. This condition occurs in the pressurizer
when it becomes necessary to increase or maintain primary system pressure by energizing heaters.
Secondly, if the pressure of the saturated liquid is reduced, then steam will be generated.
This condition also occurs in the pressurizer. For a power transient, as average RCS temperature
decreases, primary coolant flows out of the pressurizer. As level falls, pressure begins to decrease,
causing saturated liquid at the surface in the pressurizer to flash to steam, restoring pressure.
2.2
Summary
Steam cannot be considered an ideal gas at normal operating temperatures and pressures. For this
reason, the relationships between the thermodynamic properties of steam at any given state must
be experimentally determined and tabulated for reference. The steam tables are our source for this
thermodynamic information.
In this chapter, we dealt with the use of the steam tables to determine properties of water.
2.18
Chapter 2
ESP100.30 Rev. 4
Properties of Heat Transfer
Definitions
Saturated Liquid – liquid at saturation temperature and pressure for which any heat added will
result in vaporization of some of that liquid.
Saturated Steam – steam at saturation temperature and pressure for which any heat removed will
result in condensation of some of that steam.
Wet Steam, Wet Vapor – water coexisitng in liquid and vapor states for saturation temperature and
pressure.
Quality – ratio of the mass of steam to the mass of the steam-water mixture in which it exists.
Subcooled Liquid – water at a temperature less than the saturation temperature for the existing
pressure. See Compressed Liquid.
Compressed Liquid – water at a pressure greater than saturation pressure for the existing
temperature. See Subcooled Liquid.
Superheated Steam – steam at a temperature greater than the saturation temperature for the
existing pressure.
Isothermal – a constant-temperature process
Isobaric – a constant-pressure process
Isenthalpic – a constant-enthalpy process
Isentropic – a constant-entropy process
Adiabatic – a process in which no heat is transferred
Percent Moisture (Moisture Content) – ratio of the mass of water (liquid) to the mass of the steamwater mixture in which it exists.
Subcooled Margin – the difference between the saturation temperature corresponding to a given
pressure and the temperature of the subcooled liquid.
2.19
ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
EXERCISES
2.20
ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
2.1.1
Select the best choice to answer the following:
As the temperature of water increases, the value of vfg (vg-vf) _____________________,
and the latent heat of vaporization ___________________________.
A.
B.
C.
D.
2.2.1
What is the moisture-content of steam at 1,000 psia and 1,145 BTU/lbm?
A.
B.
C.
D.
2.2.2
10.028 ft3/lbm
10.037 ft3/lbm
10.045 ft3/lbm
20.056 ft3/lbm
The amount of energy in a system that is a function of temperature is called:
A.
B.
C.
D.
2.3.2
3%
5%
7%
9%
A steam-water mixture as 228°F has quality of 50%. What is the specific volume?
A.
B.
C.
D.
2.3.1
Increases; remains constant
Increases; decreases
Decreases; decreases
Decreases; increases
Kinetic energy
Potential energy
Internal energy
Total energy
The enthalpy of a working fluid is best described as its:
A.
B.
C.
D.
Potential energy plus kinetic energy
Internal energy plus pressure-volume energy
Pressure-volume energy plus flow energy
Internal energy plus kinetic energy
2.21
ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
2.3.3
Which of the following statements regarding entropy is/are true?
A.
B.
C.
D.
2.4.1
Which of the following is the approximate steam quality of a steam-water mixture at 467°F
with an enthalpy of 1000 BTU/lbm?
A.
B.
C.
D.
2.5.1
557.5 BTU/lbm
631.5 BTU/lbm
1,189.1 BTU/lbm
1,192.9 BTU/lbm
The saturation pressure for water at 328°F is:
A.
B.
C.
D.
2.5.3
25%
27%
73%
75%
A saturated liquid at 1,100 psia has a specific enthalpy of:
A.
B.
C.
D.
2.5.2
Entropy is used to quantify the degree of irreversibility of a process.
In a real process, entropy is always increasing.
Entropy is a thermodynamic property like enthalpy; however, it is a relative, not
absolute property.
All of the above.
85 psig
100 psig
115 psig
130 psig
If a wet vapor is at 130°F and has a quality of 90%, its specific enthalpy is:
A.
B.
C.
D.
1,015.78 BTU/lbm
1,019.80 BTU/lbm
1,117.80 BTU/lbm
1,215.76 BTU/lbm
2.22
ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
2.5.4
If condensate temperature in the hotwell is 4°F subcooled with a temperature of 112°F,
what is the condenser pressure?
A.
B.
C.
D.
2.5.5
The reactor is shutdown with RCS pressure at 1500 psig with decay heat being removed by
the steam generators. What pressure must be maintained in the steam generators to obtain a
100°F subcooling margin in the RCS loops? (Assume a negligible ΔT exists between the
RCS and the steam generators.)
A.
B.
C.
D.
2.5.6
577 psig
592 psig
607 psig
622 psig
Reactor coolant system hot leg temperature is 568°F and reactor coolant system pressure is
decreasing due to a small leak. Which one of the following pressure ranges includes the
pressure at which two-phase flow will first occur in the hot leg?
A.
B.
C.
D.
2.5.7
1.0 psia
1.2 psia
1.5 psia
1.8 psia
1250 to 1201 psig
1200 to 1151 psig
1150 to 1101 psig
1100 to 1051 psig
What is the specific volume of steam at 1000 psia and 100°F superheated?
A.
B.
C.
D.
0.5191 ft3/lbm
0.5582 ft3/lbm
0.5636 ft3/lbm
0.6186 ft3/lbm
2.23
ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
2.5.8
Steam exiting a moisture separator reheater (MSR) is measured at 250 psia and 1255
BTU/lbm. What is the status of the steam at these conditions?
A.
B.
C.
D.
2.5.9
A vendor specifies the below values for operating a feed pump turbine at 200 psia inlet
steam pressure:
•
minimum inlet enthalpy 1050 BTU/lbm
•
maximum inlet enthalpy 1175 BTU/lbm
•
What is the maximum moisture content of the inlet steam allowed?
A.
B.
C.
D.
2.5.10
75°F superheated
80°F superheated
85°F superheated
90°F superheated
2.8%
17.6%
24.5%
42.1%
Select the best choice to answer the following:
For water, the pressure at the triple point is very __________, while the pressure at the
critical point is relatively ___________.
A.
B.
C.
D.
2.5.11
The reactor coolant subcooling margin will be DIRECTLY INCREASED by:
A.
B.
C.
D.
2.5.12
Low, high
High, low
Low, unimportant
High, lower
Increased pressurizer pressure
Decreased reactor coolant flow
Decreased pressurizer level
Increased reactor coolant temperature
Steam at the exhaust of the HP turbine is at 180 psia with a known specific volume of
2.24
ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
2.1291 ft3/lbm. What is the moisture content of the steam at that point?
A.
B.
C.
D.
2.5.13
A steam-water mixture at 100 psia has a specific volume of 2.06 ft3/lbm. What is the
quality?
A.
B.
C.
D.
2.5.14
401°F
449°F
626°F
1251°F
If a wet vapor is at 130°F and has a quality of 90%, its specific enthalpy is:
A.
B.
C.
D.
2.5.17
57u psig
592 psig
607 psig
622 psig
If the steam pressure is 250 psig at a temperature of 850°F, the degree of superheat is:
A.
B.
C.
D.
2.5.16
46.3%
46.7%
46.1%
46.5%
The reactor is shutdown with RCS pressure at 1500 psig with decay heat being removed by
the steam generators. What pressure must be maintained in the steam generators to obtain a
110 degrees F subcooling margin in the RCS loops? (Assume a negligible ΔT exists
between the RCS and the steam generators.)
A.
B.
C.
D.
2.5.15
16%
82%
18%
84%
1,015.78 BTU/lbm
1,019.80 BTU/lbm
1,117.80 BTU/lbm
1,215.76 BTU/lbm
if steam pressure is 230 psia at a temperature of 900°F, the degree of superheat is:
2.25
ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
A.
B.
C.
D.
2.5.18
Which one of the following is the approximate amount of heat required to convert 3 lbm of
water at 100°F and 100 psia to a saturated vapor at 100 psia>
A.
B.
C.
D.
2.5.19
888.6 BTU
1119.2 BTU
2665.8 BTU
3357.6 BTU
A comparison of RCS temperature and RCS pressure may be used to determine:
A.
B.
C.
D.
2.6.1
368.28°F
393.70°F
506.30°F
510.12°F
CHF (critical heat flux)
DNBR (departure from nucleate boiling ratio)
SCM ( subcooling margin)
DNB (departure from nucleate boiling)
As power increases from 0% to 100%, what happens to RCS subcooling margin?
Subcooling margin….
A.
B.
C.
D.
INCREASES
REMAINS THE SAME
DECREASES and the changes linearly with power
DECREASES and the rate change INCREASES as power increases
2.26
ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
2.1.1
Select the best choice to answer the following:
As the temperature of water increases, the value of vfg (vg-vf) _____________________,
and the latent heat of vaporization ___________________________.
A.
B.
C.
D.
2.2.1
What is the moisture-content of steam at 1,000 psia and 1,145 BTU/lbm?
A.
B.
C.
D.
2.2.2
10.028 ft3/lbm
10.037 ft3/lbm
10.045 ft3/lbm
20.056 ft3/lbm
The amount of energy in a system that is a function of temperature is called:
A.
B.
C.
D.
2.3.2
3%
5%
7%
9%
A steam-water mixture as 228°F has quality of 50%. What is the specific volume?
A.
B.
C.
D.
2.3.1
Increases; remains constant
Increases; decreases
Decreases; decreases
Decreases; increases
Kinetic energy
Potential energy
Internal energy
Total energy
The enthalpy of a working fluid is best described as its:
A.
B.
C.
D.
Potential energy plus kinetic energy
Internal energy plus pressure-volume energy
Pressure-volume energy plus flow energy
Internal energy plus kinetic energy
2.27
ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
2.3.3
Which of the following statements regarding entropy is/are true?
A.
B.
C.
D.
2.4.1
Which of the following is the approximate steam quality of a steam-water mixture at 467°F
with an enthalpy of 1000 BTU/lbm?
A.
B.
C.
D.
2.5.1
85 psig
100 psig
115 psig
130 psig
If a wet vapor is at 130°F and has a quality of 90%, its specific enthalpy is:
A.
B.
C.
D.
2.5.4
557.5 BTU/lbm
631.5 BTU/lbm
1,189.1 BTU/lbm
1,192.9 BTU/lbm
The saturation pressure for water at 328°F is:
A.
B.
C.
D.
2.5.3
25%
27%
73%
75%
A saturated liquid at 1,100 psia has a specific enthalpy of:
A.
B.
C.
D.
2.5.2
Entropy is used to quantify the degree of irreversibility of a process.
In a real process, entropy is always increasing.
Entropy is a thermodynamic property like enthalpy; however, it is a relative, not
absolute property.
All of the above
1,015.78 BTU/lbm
1,019.80 BTU/lbm
1,117.80 BTU/lbm
1,215.76 BTU/lbm
If condensate temperature in the hotwell is 4°F subcooled with a temperature of 112°F,
2.28
ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
what is the condenser pressure?
A.
B.
C.
D.
2.5.5
The reactor is shutdown with RCS pressure at 1500 psig with decay heat being removed by
the steam generators. What pressure must be maintained in the steam generators to obtain a
100°F subcooling margin in the RCS loops? (Assume a negligible ΔT exists between the
RCS and the steam generators.)
A.
B.
C.
D.
2.5.6
1250 to 1201 psig
1200 to 1151 psig
1150 to 1101 psig
1100 to 1051 psig
What is the specific volume of steam at 1000 psia and 100°F superheated?
A.
B.
C.
D.
2.5.8
577 psig
592 psig
607 psig
622 psig
Reactor coolant system hot leg temperature is 568°F and reactor coolant system pressure is
decreasing due to a small leak. Which one of the following pressure ranges includes the
pressure at which two-phase flow will first occur in the hot leg?
A.
B.
C.
D.
2.5.7
1.0 psia
1.2 psia
1.5 psia
1.8 psia
0.5191 ft3/lbm
0.5582 ft3/lbm
0.5636 ft3/lbm
0.6186 ft3/lbm
Steam exiting a moisture separator reheater (MSR) is measured at 250 psia and 1255
BTU/lbm. What is the status of the steam at these conditions?
A.
B.
C.
D.
75°F superheated
80°F superheated
85°F superheated
90°F superheated
2.29
ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
2.5.9
A vendor specifies the below values for operating a feed pump turbine at 200 psia inlet
steam pressure:
•
minimum inlet enthalpy 1050 BTU/lbm
•
maximum inlet enthalpy 1175 BTU/lbm
•
What is the maximum moisture content of the inlet steam allowed?
A.
B.
C.
D.
2.5.10
2.8%
17.6%
24.5%
42.1%
Select the best choice to answer the following:
For water, the pressure at the triple point is very __________, while the pressure at the
critical point is relatively ___________.
A.
B.
C.
D.
2.5.11
The reactor coolant subcooling margin will be DIRECTLY INCREASED by:
A.
B.
C.
D.
2.5.12
Increased pressurizer pressure
Decreased reactor coolant flow
Decreased pressurizer level
Increased reactor coolant temperature
Steam at the exhaust of the HP turbine is at 180 psia with a known specific volume of
2.1291 ft3/lbm. What is the moisture content of the steam at that point?
A.
B.
C.
D.
2.5.13
Low, high
High, low
Low, unimportant
High, lower
16%
82%
18%
84%
A steam-water mixture at 100 psia has a specific volume of 2.06 ft3/lbm. What is the
quality?
2.30
ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
A.
B.
C.
D.
2.5.14
The reactor is shutdown with RCS pressure at 1500 psig with decay heat being removed by
the steam generators. What pressure must be maintained in the steam generators to obtain a
110 degrees F subcooling margin in the RCS loops? (Assume a negligible ΔT exists
between the RCS and the steam generators.)
A.
B.
C.
D.
2.5.15
1,015.78 BTU/lbm
1,019.80 BTU/lbm
1,117.80 BTU/lbm
1,215.76 BTU/lbm
if steam pressure is 230 psia at a temperature of 900°F, the degree of superheat is:
A.
B.
C.
D.
2.5.18
401°F
449°F
626°F
1251°F
If a wet vapor is at 130°F and has a quality of 90%, its specific enthalpy is:
A.
B.
C.
D.
2.5.17
57u psig
592 psig
607 psig
622 psig
If the steam pressure is 250 psig at a temperature of 850°F, the degree of superheat is:
A.
B.
C.
D.
2.5.16
46.3%
46.7%
46.1%
46.5%
368.28°F
393.70°F
506.30°F
510.12°F
Which one of the following is the approximate amount of heat required to convert 3 lbm of
water at 100°F and 100 psia to a saturated vapor at 100 psia>
A.
888.6 BTU
2.31
ESP100.30 Rev. 4
Properties of Heat Transfer
Chapter 2
B.
C.
D.
2.5.19
A comparison of RCS temperature and RCS pressure may be used to determine:
A.
B.
C.
D.
2.6.1
1119.2 BTU
2665.8 BTU
3357.6 BTU
CHF (critical heat flux)
DNBR (departure from nucleate boiling ratio)
SCM ( subcooling margin)
DNB (departure from nucleate boiling)
As power increases from 0% to 100%, what happens to RCS subcooling margin?
Subcooling margin….
A.
B.
C.
D.
INCREASES
REMAINS THE SAME
DECREASES and the changes linearly with power
DECREASES and the rate change INCREASES as power increases
2.32