Pressure-enthalpy Diagrams

Chapter 9

Pressure-enthalpy
Diagrams
One diagnostic tool that is available to everyone but seldom used is the
pressure-enthalpy (P-H) diagram, sometimes called the Mollier diagram.
This tool is used by most design engineers, but unfortunately it is over-
looked by service technicians.

The important thing to remember about the P-H diagram is that it cannot
be used to plot every system that is serviced. However, just learning the
chart provides a new and fresh insight on what is happening inside the
system.

The P-H diagram is a simple, graphic way to plot a system cycle and ob-
serve its characteristics. No two systems are exactly alike. Each one has its
own personality. When using the diagram, a single pound of refrigerant is
followed completely around the system in order to learn when and where
it changes states and what those changes mean. Since only one pound of
refrigerant is followed, the diagram may be applied to any size system. The
pounds per minute circulated will determine the total system capacity . To
better understand this process, some basics must be reviewed, starting with
diagram construction.

SATURATION, SUBCOOLING, AND SUPERHEAT

In order to become a proficient technician, you must learn about the three
conditions in which a refrigerant can exist while it is traveling around the
system. These conditions are: saturation, subcooling, and superheat. To
pinpoint which condition the refrigerant is in at any given point, both a
temperature reading and a pressure reading must be taken. Taking only one
of these readings will not be sufficient.

A good method for learning about the three conditions is to study water,
which is something most people are familiar with. W
ater and refrigerant are

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 similar, except that at atmospheric pressure (0 psig) water boils at 212 °F,
whereas R-22, for example, boils at -41 °F at the same pressure. The boiling
point is called the saturation temperature.

The diagram in Figure 9-1, plots the heat content of water in Btu/lb along
the horizontal axis versus the temperature in °F along the vertical axis.
There are two types of heat involved in the process depicted in Figure 9-1:
sensible heat and latent heat. Sensible heat involves a change in temperature,
and latent heat involves a change of state (at a constant temperature). The
diagram is plotted at 0 psig (atmospheric) pressure. As the water is warmed
from 52°F to 212 °F, only sensible heat is used. This is because the only
change experienced is a change in temperature. Since subcooling is defined
as the number of degrees the liquid temperature is below its saturation
temperature, the liquid is in the subcooling state. At 52°F, the subcooling is
160 °F (212 °F – 160 °F = 52 °F). At 212°F, the subcooling is 0 °, because it has
reached the saturation point.

When the water reaches its saturation point of 212 °F at atmospheric pres-
sure, boiling will start at a constant temperature as long as the pressure
remains constant. During this change of state from a liquid to a vapor, the
water absorbs approximately 1000 Btu for each pound of water evaporated.
This is called the latent heat of evaporation.

Figure 9-1. Sensible and latent heat

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 When all of the liquid has boiled off and more heat is added to the vapor,
the vapor temperature rises above the saturation temperature of 212 °F.
Since the temperature of the vapor changes, sensible heat is again experi-
enced. The water now exists as a vapor and is in the superheated state.
Superheat is defined as the amount of degrees the vapor temperature is
above the saturation temperature at a given pressure. If the temperature of
the superheated vapor is measured at 232 °F, then the amount of superheat
would be 20°F, because it is 20 °F above the saturation temperature of 212 °F.

Note the tremendous amount of heat required to boil a fluid or cause it to

go through a change of state (latent heat of evaporation) when compared to
the amount of heat it takes to simply change its temperature. For this rea-
son, the evaporator should be kept as full of liquid refrigerant as possible
without flooding back to the compressor in order to get the maximum
amount of heat transfer.

Since all of the conditions shown on the diagram occur at one pressure (0
psig), it is obvious that just taking a pressure reading will not indicate what
the system is doing. In order to determine if the refrigerant is subcooled,
saturated, or superheated, the temperature at a given point must also be
known. Whenever the pressure reading is taken, immediately check a pres-
sure-temperature (p-t) chart to see what the saturation temperature is for
the refrigerant at that pressure. When the temperature at that point is
known, it can then be determined if the refrigerant is subcooled, saturated,
or superheated. If the temperature is above the saturation temperature, then
it is superheated. If the temperature is below the saturation temperature,
then it is subcooled. If the temperature is the same as the p-t chart indicates,
then both saturated liquid and saturated vapor are present.

THE THREE ZONES

The P-H diagram is divided into three zones: saturated, subcooled, and
superheated, Figure 9-2. As the refrigerant travels around the system, it
exists in one of the three zones indicated on the diagram. The refrigerant is
always changing conditions and never exists in any two zones at the same
time. The refrigerant is saturated, subcooled, or superheated. If technicians
do not have an understanding of these basic principles, they will never
thoroughly understand how refrigeration systems operate.

Saturated Zone
Any time the refrigerant is inside the envelope or dome, it is in thesaturated
zone. When a refrigerant is saturated, it contains both liquid and vapor. The
right-hand curve of the saturated zone is the 100% saturated vapor line, and
the curve on the left-hand side of the zone is the 100% saturated liquid line.
Some P-H charts have a series of vertical lines within the saturated zone.
These lines indicate the percentage of vapor along each line. Saturation
occurs in the evaporator, where the refrigerant changes state from a liquid

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 Figure 9-2. P-H diagram zones

to a vapor (boiling), and in the condenser, where the refrigerant changes

state from a vapor to a liquid (condensing). As previously noted, the tem-
peratures and pressures shown on the pressure-temperature chart are all in
the saturated state.

Superheated Zone
To the right of the 100% saturated vapor line is the superheated vapor zone,
where the refrigerant is above the saturation temperature. The superheated
condition should exist from within the outlet of the evaporator to within the
inlet portion of the condenser. The superheat measurement is the tempera-
ture of the vapor minus the saturation temperature at a given pressure.

Subcooled Zone
To the left of the 100% saturated liquid line is the subcooled liquid zone. The
refrigerant is in the liquid state, and its temperature is below the saturated
temperature at a given pressure. The subcooled condition should exist from
the outlet of the condenser to the inlet of the expansion device. The amount
of subcooling is found by subtracting the temperature of the liquid from the
condensing temperature at a given pressure.

Critical Point
The critical point on the P-H diagram is located where the saturated liquid
curve and the saturated vapor curve converge. At any temperature above
this point, the refrigerant may exist in the vapor condition only
.

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 FIVE REFRIGERANT PROPERTIES
The following five refrigerant properties are graphically depicted in Figures
9-3 through 9-7: absolute pressure, enthalpy , constant temperature, entropy,
and constant volume.

Most refrigeration gauges read in pounds per square inch gauge (psig)
above atmospheric pressure. At sea level, or 0 pounds gauge, the pressure
would be 14.7 pounds of atmospheric pressure. Pressures below 0 psig are
considered a partial vacuum and read in inches of mercury (Hg). A perfect
vacuum is defined as 0 pounds per square inch absolute (psia). The P-H
diagram in Figure 9-3 is scaled for absolute pressure.

Most computations use psia. To obtain absolute pressure simply add 14.7
psi to the gauge reading in psig. For example, to convert a gauge pressure
reading of 10 psig to psia, add 10 psig + 14.7 psi. This gives an absolute
pressure reading of 24.7 psia. Many people forget to make this conversion
when reading the P-H diagram. Always convert pressures to absolute for
this use.

Enthalpy represents the total heat content in Btu per pound. The enthalpy
scale shown in Figure 9-4 is usually shown at both the top and bottom of
the diagram, and the lines of constant enthalpy run vertically.

In Figure 9-5, please note that the lines of constant temperature run almost
vertically in the superheated zone, horizontally in the saturated zone, and
vertically in the subcooled zone.

Entropy is defined as the heat available measured in Btu/lb per degree of

change for a substance. The lines of constant entropy extend diagonally up

Figure 9-3. Absolute pressure diagram (psia)

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 Figure 9-4. Enthalpy diagram (Btu/lb)

Figure 9-5. Constant temperature (°F)

to the right from the saturated vapor line, Figure 9-6. Entropy is used
mainly for engineering calculations. The main concern of the service tech-
nician is that when the refrigerant is compressed, it follows up the line of
constant entropy,

The lines of constant volume extend out from the saturated vapor line into
the superheated zone, Figure 9-7. These values indicate how much space
(cu ft) is taken up by each pound of refrigerant vapor.

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 Figure 9-6. Entropy

THE IDEAL CYCLE

Usually, the refrigeration cycle is shown as an ideal cycle. This is generally
an illustration of a cycle, but it does not show superheating in the evapo-
rator, suction line, heat exchangers, vapor-cooled compressors, etc. Also,
subcooling of the liquid and pressure losses are not shown.

Figure 9-7. Constant volume (cu ft/lb)

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 These things are important to the service technician, but to understand the
basic cycle, the ideal cycle will be discussed first.

The four functions of the refrigeration cycle are: compressing, condensing,

expanding, and evaporating. The following is a discussion of these four
functions.

To draw a simple ideal cycle, only two pressures are required: the evapo-
ration pressure and the condensing pressure. They are also called the high
side and low side pressures. Do not forget to add 14.7 psi to the gauge read-
ings to obtain the absolute pressure required for the diagram. Figure 9-8
shows the condensing and evaporating horizontal pressure lines.

Next, drop the expansion line down from the intersection of the condensa-
tion line and the saturated liquid line to intersect with the horizontal evapo-
ration line, Figures 9-9 and 9-10.

Finally, complete the cycle by extending the compression line up to the

superheated zone, parallel with the constant entropy lines, until it intersects
the condensation line, Figure 9-11.

Figure 9-12 shows a pound of refrigerant as it travels around the ideal cycle.
The refrigerant leaves the compressor as high pressure vapor in a highly
superheated condition (line a to b). The refrigerant vapor is compressed and
thereby condensed into a liquid with such cooling media as air or water. It
is then reused for another cycle. As the pound of refrigerant moves left,
horizontally along the condensing pressure line, the condenser must re-
move the superheat before it reaches the 100% saturated vapor line (line b
to c).

CONDENSATION LINE

Figure 9-8. Condensation line

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 EXPANSION

Figure 9-9. Expansion line

EVAPORATION LINE

Figure 9-10. Evaporation line

Condensation starts when the refrigerant crosses the saturated vapor line
(point c) into the saturated zone. Note that as the refrigerant moves along
the constant pressure line in the saturated zone, the temperature remains
constant. When the pound of refrigerant reaches the 100% saturated liquid
line (point e), all of the vapor has condensed to a liquid.

The next step is the expansion process, during which the pressure is
dropped suddenly from high pressure to low pressure within the expansion

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 COMPRESSION

Figure 9-11. Compression line

CONDENSATION
EXPANSION

N
O
SI
ES
PR
M
O
C

EVAPORATION

Figure 9-12. The ideal cycle

device (and refrigerant distributor and tubes if used).There is no external

transfer of heat into or out of the refrigerant in the ideal cycle process;
therefore, the refrigerant flows vertically down the line of constant enthalpy
(line e to d). Since it is crossing the horizontal lines of temperature while in
the saturated zone, there is a temperature drop in the mixture. This is due
to the latent heat of vaporization as a portion of the refrigerant flashes into
a vapor. The refrigerant is now ready to enter the evaporator (point d).

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 The refrigerant enters the evaporator at the evaporator pressure in the satu-
rated zone. It passes along the constant pressure line in the saturated zone
to the 100% saturated vapor line (point a). As previously mentioned, some
P-H diagrams have vertical lines in the saturated zone which represent the
percentage of vapor in the mixture. As the refrigerant passes through the
evaporator, it gains heat as it boils from a liquid to a vapor. When the re-
frigerant reaches the 100% saturated vapor line, all the heat absorbed is
contained in the vapor. It is now ready to be compressed again.

Do not forget, this is just the ideal cycle. A more realistic cycle will be dis-
cussed later in the chapter .

PERFORMANCE OF THE CYCLE

With the help of the P-H diagram, certain quantities of the cycle may be
obtained. The engineer who wants more exact figures should use the vari-
ous refrigerant tables. The P-H diagram, remember, is made up from the
values in these tables. However, it is much simpler to use the P-H diagram.

The quantities that can be obtained are the heat of rejection, the refrigerat-
ing effect, the circulation rate, the compression ratio, the work of compres-
sion, the coef ficient of performance, the volume rate of flow per ton, and
the power per ton. The purpose of this presentation is to help the technician
better understand the refrigeration cycle through the study of the P-H dia-
gram and not to confuse things with a lot of mathematical formulas; there-
fore, we will just discuss the first four points mentioned above. For the
clarification of these points, we will consider an R-22 system that develops
10 tons of refrigeration while operating with a 90°F condensing temperature
and 20 °F evaporating temperature.

Heat of Rejection
The heat of rejection is the heat given up by the condenser , Figure 9-13. If the
one pound of refrigerant has an enthalpy (total heat content) entering the
condenser of 1 18 Btu/lb (h3) and an enthalpy leaving the condenser of 38
Btu/lb (h1), the difference is the heat given up by the condenser . Note that
the condenser is rejecting the heat picked up by the evaporator plus the
heat of compression. The heat of compression is the heat added to the refrig-
erant by the work done by the compressor. Use the following formula to
find the heat of rejection:

Heat of rejection = h3 – h1 = 118 Btu/lb – 38 Btu/lb = 80 Btu/lb

where: h = enthalpy

Refrigerating Effect
Refrigerating effect is the heat absorbed by the evaporator , as indicated by h2

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 and h1 in Figure 9-14. Since the total heat content is 38 Btu/lb entering and
107 Btu/lb leaving, then the heat picked up in the evaporator is:

Refrigerating effect = h2 - h1 = 107 Btu/lb - 38 Btu/lb = 69 Btu/lb

Circulation Rate
If the refrigerating capacity is known, we can then determine the total cir-
culation rate in lb/min by dividing the capacity in Btu/min by the refriger-
ating effect of 69 Btu/lb.

80 Btu/lb

h1 38 Btu/lb h3 118 Btu/lb

Figure 9-13. Heat of rejection

69 Btu/lb

h1 38 Btu/lb h2 107 Btu/lb

Figure 9-14. Refrigerating effect

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 Refrigerant flow = 10 tons × 200 Btu/min/ton = 28.98 lb/min
69 Btu/lb

Compression Ratio
The compression ratio is the absolute discharge pressure divided by the ab-
solute suction pressure, Figure 9-15. Consequently , the higher the suction
pressure the lower the compression ratio at a given discharge pressure.
Also, the lower the discharge pressure the lower the compression ratio.

While maintaining operating temperatures to satisfy the product require-

ments, try to keep the compression ratio as low as possible. The lower the
compression ratio the higher the volumetric efficiency. The higher the volu-
metric efficiency the more mass flow of refrigerant pumped by the com-
pressor. The more mass flow pumped by the compressor the greater the
system capacity, and less running time is required. The less running time
required, the more money saved.

As strange as it may seem, keeping the suction pressure up has a greater

effect in lowering the compression ratio than lowering the discharge pres-
sure by an equal amount. An added benefit of a lower compression ratio is
lower discharge temperatures, which in turn result in less refrigerant-oil
breakdown and less contaminants formed by high operating temperatures.

THE ACTUAL REFRIGERATION CYCLE

Remember that the ideal cycle discussed earlier in the chapter did not have
pressure drops, subcooling, or evaporator superheat. Such a system does

211 psia

58 psia

211 psia Compression

= 3.6
58 psia Ratio

Figure 9-15. Compression ratio

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 not exist except on paper. Without evaporator superheat in the refrigeration
cycle, there would be liquid slugging the compressor; without pressure
drops, there would be no refrigerant flow . However, the
ideal cycle is an excellent place to start when attempting to understand the
basic P-H diagram and the refrigeration cycle.

To begin, consider a simple system with the following basic components:

evaporator, compressor, and expansion device. The other components can
be added later. This section will illustrate some of the horrors that can
happen in the field and show how your knowledge of the P-H diagram can
be used to provide a solution to these problems.

Low Pressure Line

Certain assumptions have to be made to illustrate the difference between
the ideal cycle and the actual cycle. Let’ s start with the low pressure line.
Notice that it is no longer called the evaporator line, because it now in-
volves more than just the evaporator. There is a pressure drop through the
evaporator tubes and suction line, superheat is developed in the evaporator,
and additional superheat occurs in the suction line. Also, assume that this
is a semi-hermetic, vapor-cooled type compressor. There is also additional
superheat in the compressor body before the compression begins.

As shown in Figure 9-16, there is quite a difference in the discharge tem-

perature between the two plots. Also, notice the “spike” in the actual cycle
discharge temperature at the peak of its plot. This illustrates the high tem-
perature experienced at the discharge valve of the compressor . Compressor
engineers indicate that this temperature is approximately 75°F higher than
the temperature measured about 6" down the discharge line from the dis-

Effect of
Subcooling Liquid
Actual
Operating Cycle Pressure loss
in Compressor
Discharge Valves

Pressure loss
in High Side
Piping

Ideal
Saturated Pressure loss
in Low Side
Cycle Piping

Pressure loss
in Compressor
Suction Valves

Figure 9-16. Plotting the actual refrigeration cycle on a P-H, diagram

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 charge service valve. Consequently , if the oil-refrigerant mixture starts to
breakdown at about 300°F, then the temperature of the discharge vapor
should be limited to about 225°F.

By observing the diagram, it is evident that moving the point where com-
pression starts toward the left decreases the chances of running excessively
high discharge temperatures, which result in refrigerant-oil breakdown.
The following are some ideas to reduce the discharge temperature:

1. Check to see if the evaporator superheat is too high.

2. Re-route the suction line if possible to a cooler location.
3. Check to see if a liquid-suction heat exchanger is used unnecessarily .
4. Inject liquid into the suction line (consult theTXV manufacturer).

The idea behind all of these steps is to move the compression line further
to the left by decreasing the superheat and the discharge gas temperature.
Also, if the superheat in the evaporator is too high, lowering it to the rec-
ommended amount increases the evaporator capacity, because it contains
more refrigerant. This also raises the suction pressure, which results in a
lower compression ratio, which in turn increases system capacity.

Some people equate frost with liquid refrigerant presence. Do not adjust
the superheat to a frost line. Admittedly
, there could possibly be some liq-
uid present when frost is present, but not always. It depends on the oper-
ating pressures and temperatures of the system.

Suppose we had an ice cream case operating at a -40 °F evaporator satura-

tion temperature, and we adjusted to a frost line at the suction service
valve. This means the temperature at the service valve would be about 32 °F.
Since superheat is defined as the vapor temperature minus the evaporator
saturation temperature, this would result in a 72°F superheat at the suction
service valve (32 °F – 42 °F = 72 °F). This is excessive. Generally , case manu-
facturers recommend a 7 °F superheat in the evaporator. With the valve
adjusted properly and assuming a 20°F rise in the suction line, the tempera-
ture at the suction service valve would be –13 °F. There would certainly be
frost at this temperature. However, there would be no liquid refrigerant
present. This type of adjustment also makes quite a difference in the oper-
ating efficiency of the system.

High Pressure Line

The high pressure line consists of the discharge line, condenser , receiver (if
used), and the liquid line. Since the refrigerant is still superheated when it
enters the condenser and is subcooled when it leaves the condenser , the
condenser is the only component in which all three states (superheat, satu-
ration, and subcooling) exist simultaneously. There are some systems that
have the liquid line subcooled below the evaporator saturation tempera-
ture. This would produce all three states in the evaporator, but these sys-
tems are the exception rather than the rule.

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 If a liquid-to-suction heat exchanger is used, about 10 °F of subcooling is
possible, and the vertical expansion line will move to the left. Now there is
a smaller value of enthalpy entering the evaporator, which produces a
greater capacity. Remember that while adding a heat exchanger increases
the capacity on the low side, it causes the opposite ef fect on the high side
of the system. About 15°F can be added to the suction gas temperature
entering the compressor, which, as we discussed, results in a higher dis-
charge temperature. Before arbitrarily adding a heat exchanger, determine
that this is a step that needs to be made. Sometimes a heat exchanger is
required to subcool the liquid to ensure 100% liquid at the expansion device
inlet. This would justify the use of a heat exchanger.

Suppose the subcooling at the receiver is only 2 °F, and there is a 10 ft lift
in the liquid line to the expansion device. There would be a minimum 5 psi
pressure drop, because there is a 1/2 lb drop for every foot of lift. Add to
this the line loss drop due to friction, plus the drop through the accessories.
As shown in Figure 9-16, the pressure drop could carry the refrigerant
down into the saturation zone where vapor would exist.The challenge is to
move the vertical line to the left by subcooling or to elevate the horizontal
pressure line so that even with the pressure drops there will still be
subcooled liquid in the subcooled zone.

The following are some suggested methods to increase the subcooling and
move the vertical line to the left:

1. Liquid-to-suction line heat exchanger

2. Liquid-to-expansion device outlet heat exchanger
3. Mechanical subcooling
4. Water-cooled subcooler
5. Surge receiver

Expansion Line
Most P-H diagrams show the expansion line as the pressure drop only
through the expansion device. This is true is some cases, but over the years
there has been a tremendous increase in the use of refrigerant distributors.
For this reason, a distributor has been added to the example. The drop from
the thermostatic expansion valve (TXV) inlet to the evaporator inlet in-
cludes both the TXV and distributor. If a system were operating under full
load (200 psig at the TXV inlet and 70 psig at the evaporator inlet), the total
pressure drop would be 130 psig. However, the drop across the TXV would
be about 100 psig, and the distributor tubes would be approximately 30
psig. This must be considered when selecting the TXV.

Today, mechanical subcooling is a design concept used by many engineers.

As shown in Figure 9-16, with an increase in subcooling, the pressure drops
lower before the expansion line crosses into the saturated zone. This means
that not only is system capacity increased because of lowering the entering
heat content, or enthalpy, but a greater mass flow through the expansion

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 device is experienced, because the vapor is formed during the expansion
process. This is important to know when sizing the expansion device. Many
systems are operating with oversized TXVs because of a high degree of
subcooling. This sometimes results in liquid floodback to the compressor.
Expansion valve manufacturers provide subcooling capacity factors in their
catalogs. Remember that subcooling also increases distributor and tube
capacities and should be checked for proper sizing. Quite often, extensive
mechanical subcooling is used on a system although the TXV and distribu-
tor sizing have not been considered. This results in poor system perfor-
mance and poor refrigerant distribution and floodback.

Plotting The EPR Valve

The evaporator pressure regulating (EPR) valve can be easily plotted on the
P-H diagram. If the system has a single evaporator and a single compressor ,
there would not be much change in the plot, because they are selected at a
low pressure drop of 2 psi or less. This small amount would not show much
on the diagram. However, if there is a supermarket system that has a high
temperature evaporator, then there could be as much as a 20 psi or more
pressure drop across the valve. The reason for mentioning the EPR is that
many people expect a high temperature drop to accompany the pressure
drop.

If the EPR valve is located in the machine room and there is a superheat of
about 40 °F at the EPR location, then the pressure would be dropped down
20 psi from this point. Notice that since the plot is in the superheated zone,
the temperature lines run almost vertically and thus only a slight tempera-
ture change would be detected, if any. If the operation was in the saturation
zone then there would be a dramatic temperature drop.

The P-H diagrams that follow are used by permission of DuPont Suva®
Refrigerants.

©2002 by The Fairmont Press. All rights reserved.

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 ENTHALPY (Btu/lb above Saturated Liquid at –50°F)

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 ENTHALPY (Btu/lb above Saturated Liquid at –50°F)

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©2002 by The Fairmont Press. All rights reserved.
 ENTHALPY, Btu/lb

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