1. Operator Generic Fundamentals Thermodynamic Properties of Steam
K1.01 Define energy and work.
K1.02 Describe effects of pressure and temperature on density or specific volume of a liquid.
K1.03 Describe the effects of pressure and temperature on density or specific volume of a gas.
K1.04 Define the following terms: Latent heat of vaporization
K1.05 Define the following terms: Vaporization line
K1.06 Define the following terms: Critical point
K1.07 Define the following terms: Vapor dome
K1.08 Define the following terms: Saturated liquid
K1.09 Define the following terms: Wet vapor
K1.10 Define the following terms: Saturated vapor
K1.11 Define the following terms: Vapor pressure
K1.12 Define the following terms: Moisture content
K1.13 Define the following terms: Quality
K1.14 Define the following terms: Superheated vapor
K1.15 Define the following terms: Supersaturated vapor
K1.16 Define the following terms: Subcooled and compressed liquids
K1.17 Define the following terms: Subcooling
K1.18 Define the following terms: Specific heat
K1.19 Define the following terms: Enthalpy
K1.20 Identify the following terms on a T-s diagram: Critical point
K1.21 Identify the following terms on a T-s diagram: Saturated liquid line
K1.22 Identify the following terms on a T-s diagram: Saturated vapor line
K1.23 Identify the following terms on a T-s diagram: Solid, liquid, gas, vapor, and fluid regions
K1.24 Explain the usefulness of steam tables to the Control Room operator.
K1.25 Explain and use saturated and superheated steam tables.
K1.26 Apply specific heat in solving heat transfer problems.
Operator Generic Fundamentals Thermodynamic Properties of Steam

2. Thermodynamic Properties of Steam
TLO1 – Use Mollier diagrams and steam tables to determine properties of a fluid.
1.1 Define the following terms:
Critical point
Saturation
Triple point
Subcooled liquid
Sublimation
Saturated liquid
Fusion
Wet vapor
Supersaturated vapor
Saturated vapor
Superheated vapor
Quality
Moisture content
Vapor pressure curve
Vaporization dome
Vaporization
Condensation
ELOs

3. Enabling Learning Objectives for TLO 1
1.2 Predict the effect change of phase will have on plant response.
1.3 Describe the following types of property diagrams:
Pressure-temperature diagram
Pressure-specific volume diagram
Pressure-specific enthalpy diagram
Specific enthalpy-temperature diagram
Temperature-specific entropy diagram
Mollier diagram
1.4 Describe the use of steam tables and Mollier diagrams, and when given sufficient information to indicate the state of the fluid, determine any unknown properties for the fluid.
ELOs

4. Steam Terms
ELO 1.1 – Define the following terms: saturation, subcooled liquid, saturated liquid, wet vapor, saturated vapor, superheated vapor, quality, moisture content, vapor pressure curve, vaporization dome, vaporization, condensation, critical point, triple point, sublimation, fusion, and supersaturated vapor.
Must understand relationship between
Phase change
State change
Many of above terms used in T-s and Mollier diagrams
Some of these terms are minor in nature and rarely used, while others are important to understanding the various states/phases of properties used in our thermodynamic cycle.
The minor ones are presented first. More information about these “minor terms” is available in the Student Guide.
ELO 1.1

5. Saturation
Saturation - condition in which a mixture of vapor and liquid can exist together at a given temperature and pressure
Saturated liquid to saturated steam
Saturation temperature
Temperature at which vaporization (boiling) starts to occur for a given pressure
Saturation pressure
Pressure at which vaporization (boiling) starts to occur for a given temperature
Saturation temperature/pressure for water
14.7 psia and 212°F
ELO 1.1

6. Subcooled Liquid
Subcooled liquid - temperature lower than saturation temperature for given pressure
In secondary cycle – condensate and feedwater
Heat added to subcooled liquid raises temperature until saturated
Called Sensible Heat
ELO 1.1

7. Saturated Liquid
Saturated liquid - temperature equal to saturation temperature for given pressure
No vapor content
Addition of heat causes liquid to vaporize until saturated vapor
No change in temperature
ELO 1.1

8. Wet Vapor
Wet vapor- Substance whose temperature is equal to the saturation temperature for a given pressure
Some combination of liquid/vapor content
Between a saturated liquid and a saturated vapor
Addition/removal of heat causes liquid/vapor content to change
Example:
Turbine exhaust in condenser
ELO 1.1

9. Saturated Vapor
Saturated vapor - substance that exists entirely as a vapor at saturation temperature for a given pressure
Sometimes referred to as:
dry steam or saturated steam
No moisture content
Example:
Steam exiting steam generator is “almost” 100% saturated
Addition of heat to a saturated vapor results in an increase in temperature
ELO 1.1

10. Superheated Vapor
Superheated vapor - vapor at temperature greater than saturation temperature
Sometimes called superheated steam
Example(s):
Reheated steam entering low pressure turbine
Steam leaving B&W once-through steam generator
ELO 1.1

11. Quality
Quality (x) – ratio of mass of vapor to total mass of both vapor and liquid
Applies to a wet vapor
As heat added to wet vapor
Quality increases
If mass of vapor is 0.2 lbm and mass of liquid is 0.8 lbm, quality is 0.2 or 20 percent
𝑥= 𝑚 𝑣𝑎𝑝𝑜𝑟 𝑚 𝑙𝑖𝑞𝑢𝑖𝑑 + 𝑚 𝑣𝑎𝑝𝑜𝑟
Figure: T-s Diagram for Water
ELO 1.1

12. Moisture Content
Moisture (M) is ratio of mass of liquid to total mass of liquid and vapor
Opposite of quality
Moisture of mixture in previous example would be 0.8 or 80 percent
M = 𝑚 𝑙𝑖𝑞𝑢𝑖𝑑 𝑚 𝑙𝑖𝑞𝑢𝑖𝑑 + 𝑚 𝑣𝑎𝑝𝑜𝑟
Relationship of moisture content to quality
𝑀=1−𝑥
𝑥=1−𝑀
ELO 1.1

13. Vapor Pressure Curve
Relationship between saturation pressure and saturation temperature
Higher pressure, higher saturation temperature
Vapor/liquid mixture at saturation when conditions of pressure and temperature fall on curve
Figure: Vapor-Pressure Curve
ELO 1.1

14. Vaporization & Vaporization Dome
Vaporization - process of changing a substance from a saturated liquid to a saturated vapor
Heat added called “latent heat of vaporization”
Value dependent on pressure
Vaporization Dome - the region bounded by the saturated-liquid line and saturated-vapor line
Everything “under the dome” considered a wet vapor
ELO 1.1

15. Condensation
Condensation – process of removing latent heat from a saturated vapor to a saturated liquid
Condensing process actually starts with a wet vapor
Process also called “removal of latent heat of vaporization”
Processes of vaporization and condensation exact opposite of each other
ELO 1.1

16. Minor Steam Terms
Critical point - temperature and pressure at which a gas and liquid cannot exist in equilibrium as distinguishable phases
psia, 705.1oF
No latent heat of vaporization
Triple point - point at which all three phases can exist together
psia, 32.02oF
Sublimation - values of pressure and temperature at which a substance can exist as both a solid and gas in equilibrium
Fusion - change of phase from solid to liquid
For example, addition of heat causes ice to melt to water
Supersaturated vapor - moisture-free gas that results from rapid pressure decrease and expansion where temperature drops below Tsat for existing pressure
ELO 1.1

17. Thermodynamic Properties of Steam
Knowledge Check
Any vapor having a temperature above saturation temperature is a...
saturated vapor.
superheated vapor.
dry saturated vapor.
wet saturated vapor.
Correct answer is B.
Correct Answer is B.
NRC Bank Question – P574
ELO 1.1

18. State and Phase Changes
ELO 1.2 – Predict the effect a change of phase will have on plant response.
Properties of a substance include:
pressure, temperature, specific volume, and internal energy
When two or more properties of a substance fixed, state established
Except between a saturated liquid and a saturated vapor
Need third property, such as specific volume, to define state
When a property changes, a "change of state" has occurred
Every state unique, every property has only one value at that state
Phase change
Saturated liquid to wet vapor or saturated vapor
Wet vapor to saturated liquid or subcooled liquid
Related KAs K1.02 Describe effects of pressure and temperature on density or specific volume of a liquid
Define the following terms: K1.08 Saturated liquid ; K Wet vapor 2.1* 2.1; K Saturated vapor
A phase change is a state change, but a state change is not always a phase change
ELO 1.2

19. State vs Phase Change State A - initial state
State B - saturated liquid line (212°F)
Line AB - liquid heated from subcooled to saturation temperature
Figure: T-v Diagram
ELO 1.2

20. State vs Phase Change Point C - saturated vapor state
Line BC - constant temperature phase change liquid to vapor
Line CD - steam is super- heated at constant pressure
Temperature and volume both increase during the process
Figure: T-v Diagram
ELO 1.2

21. State vs Phase Change Raise process pressure to 100 psia
Point E - initial state
Specific volume being slightly less than psia and 60°F
Point F - new vaporization temperature
327.8°F
Figure: T-v Diagram
ELO 1.2

22. State vs Phase Change Point G - saturated-vapor state
Line GH - constant-pressure process in which steam is superheated
In a similar manner, a constant pressure of 1,000 psia is represented by line IJKL, with the saturation temperature being 544.6°F
Figure: T-v Diagram
ELO 1.2

23. Five States of Water State Definition Characteristics Subcooled Liquid
(Compressed Liquid)
Liquid below its boiling temperature
Heat addition is sensible (fluid is 100% liquid phase)
Saturated Liquid
Liquid at its boiling temperature
Heat addition will cause boiling
Wet Vapor
Liquid and vapor mixture at its boiling temperature
Two phases (liquid and vapor) co-exist simultaneously within the fluid
Saturated Vapor
Vapor (steam) at its boiling temperature
Fluid is 100% vapor (no liquid remains)
Superheated Vapor
Vapor (steam) above its boiling temperature
Heat addition is sensible
ELO 1.2

24. Thermodynamic Properties of Steam
Knowledge Check
A liquid is saturated with 0 percent quality. Assuming pressure remains constant, the addition of a small amount of heat will...
raise the steady-state liquid temperature above the boiling point.
result in a subcooled liquid.
result in some of the liquid vaporizing.
result in a superheated liquid.
Correct answer is C.
Correct answer is C.
NRC Bank Question – P674
Analysis:
Since the liquid was saturated with 0 percent quality, heat addition at a constant pressure will result in the liquid changing phase to a wet vapor with some amount of quality and moisture content. If enough heat is added it will become a saturated vapor. Since the STEM of the question stated that a “small amount of heat is added”, some of the liquid will vaporize.
ELO 1.2

25. Pressurizer Principle of Operation
RCS fluid is relatively incompressible
Pressures applied equally throughout system
Pressure controlled by varying vapor pressure in pressurizer
Connected remotely from RCS piping
Pressurizer temperature will not affect the RCS
Hot leg temperature is subcooled
ELO 1.2

26. Pressurizer System General
This section briefly discusses pressurizer operation with regards to saturated/superheated conditions and how changes in level affects steam volume size and therefore, pressure.
Figure: Typical Westinghouse Pressurizer System
ELO 1.2

27. Pressurizer Operation
Establishes normal operating pressure during startup
Maintaining coolant pressure for a given temperature maintains subcooled liquid in RCS
Subcooling margin
Limits pressure changes caused by thermal expansion
Prevents RCS pressure from exceeding safety limit value
Figure: Typical Westinghouse Pressurizer
ELO 1.2

28. Pressurizer Principle of Operation
Once normal operating temperature reached, RCS operated essentially as a constant mass system
TAvg increases from no load to full load, so pressurizer level will also increase to maintain constant mass
Level control system adjusts pressurizer level
ELO 1.2

29. Pressure Control
Pressurizer provides inherent pressure-control characteristics of a saturated system with liquid-vapor interface
Design pressure control features consisting of immersion heaters and cooling sprays require a control system
Heaters and spray needed for larger volume changes and to establish initial saturated conditions in the pressurizer
ELO 1.2

30. Inherent Pressure Control - Insurge
Coolant expansion caused by an increase in TAvg
Steam bubble compressed
Pressure and temperature rise
Some steam condenses to water (due to PZR Spray)
Steam bubble mass decreases
Minimizes pressure rise
As vapor condenses (latent heat of condensation), it transfers heat to liquid, slightly raising its temperature at the surface
NOTE: In the NRC bank a few questions state that a “10% outsurge or insurge” occurs. Level changes by that much WILL impact system pressure. The system is designed to minimize pressure changes on “small level changes only”.
ELO 1.2

31. Inherent Pressure Control - Outsurge
Decrease in Tavg, due to coolant contraction causes outsurge
Steam bubble expands
Lowers system pressure
Pressure falls below saturation pressure
Some water flashes to steam
Steam bubble mass increases
Minimizes drop in pressure
Water flashing to steam (removing latent heat of vaporization) has a cooling effect on water volume
ELO 1.2

32. Pressurizer Heaters and Sprays
Pressure-control system with heaters and spray is operational requirement
Heaters necessary for raising pressurizer liquid to saturation temperature for desired system pressure
System shutdowns need cooling spray to lower pressurizer temperature corresponding to desired pressure
Figure: Typical Westinghouse Pressurizer
ELO 1.2

33. Pressurizer Heaters and Sprays
Heaters raise pressurizer liquid to saturation temperature
Large insurge
Cooling sprays lower temperature
Corresponding to desired pressure
Process
Cooling sprays lower pressure by condensing steam
Heaters push inherent control process to higher equilibrium pressures
Compensates for errors between actual and desired pressure
ELO 1.2

34. Phase Changes & Pressurizer Operation
Knowledge Check – NRC Question
A pressurizer is operating in a saturated condition at 636°F. If a sudden 10 percent liquid outsurge occurs, pressurizer pressure will __________; and pressurizer temperature will __________.
remain the same; decrease
remain the same; remain the same
decrease; decrease
decrease; remain the same
Correct answer is C.
Correct answer is C.
NRC Question P774
Analysis:
When the outsurge occurs, the vapor bubble (saturated steam region) within the pressurizer expands, causing
pressure to drop.
Because the system is saturated, any reduction in pressure will cause some of the saturated water to flash to steam.
This flashing of water to steam helps mitigate the pressure drop as thermodynamic equilibrium is attained
at a new lower pressure.
The temperature is also lower due to the new lower pressure (saturated system).
ELO 1.2

35. Property Diagrams
ELO 1.3 – Describe the types of property diagrams: pressure- temperature diagram, pressure-specific volume diagram, pressure- specific enthalpy diagram, specific enthalpy-temperature diagram, temperature-specific entropy diagram, and Mollier diagram.
Related KAs Identify the following terms on a T-s diagram: K Critical point 1.9* 2.0* K Saturated liquid line 2.1* 2.1 K Saturated vapor line K Solid, liquid, gas, vapor, and fluid regions 1.9* 1.9*
There are several way to visualize state and phase changes in thermodynamic processes. Our processes mostly use the Temperature-Specific Entropy (T-s) Diagram and the Specific Enthalpy-Specific Entropy (Mollier) Diagrams.
There are not any bank questions that require you to draw or label various diagrams, but understanding the T-s and Mollier diagrams will assist in answering many bank questions.
Figure: T-s Diagram for Water
ELO 1.3

36. Property Diagrams
Property diagrams normally depict relationships between two or more of the following properties of a substance: pressure (P), temperature (T), specific volume (ν), specific enthalpy (h), and specific entropy (s)
In saturated mixtures, quality (x) may also be used
Common property diagrams
Pressure-temperature (P-T) diagrams
Pressure-specific volume (P-ν) diagrams
Pressure-specific enthalpy (P-h) diagrams
Specific enthalpy-temperature (h-T) diagrams
Temperature-specific entropy (T-s) diagrams
Specific enthalpy-specific entropy (h-s) or Mollier diagrams
ELO 1.3

37. Pressure-Temperature Diagram
Sublimation curve separates solid and vapor phases
Fusion curve separates solid and liquid phases
Vaporization line separates liquid and vapor phases
Triple point where three lines meet
Only point where all three phases exist in equilibrium
Critical point where vaporization line ends:
Figure: P-T Diagram for Water
ELO 1.3

38. Pressure-Specific Volume Diagrams
P-ν diagram can be constructed for any pure substance
Different from P-T diagram, there are regions on a P-ν diagram in which two phases exist together
Liquid-vapor region water and steam exist together
Point A water with a specific volume (νf) given by point B exists together with steam with a specific volume (νg), given by point C
Dotted lines are lines of constant temperature
Vapor dome is region bounded by saturated liquid line and saturated vapor line
Figure: P-v Diagram for Water
ELO 1.3

39. Pressure-Specific Volume Diagrams
Quality of mixture at any point in liquid-vapor region can be found because specific volumes of water, steam, and mixture all known
Quality found using:
𝑣=𝑥 𝑣 𝑔 + 1−𝑥 𝑣 𝑓
𝑥= 𝑣− 𝑣 𝑓 𝑣 𝑔 − 𝑣 𝑓 = 𝑣− 𝑣 𝑓 𝑣 𝑓𝑔
Where:
v = specific volume of the mixture (ft3/lbm)
x = quality of the mixture (no units)
vg = specific volume of the vapor (ft3/lbm)
vf = specific volume of the liquid (ft3/lbm)
vfg = specific volume change of vaporization (ft3/lbm) or
𝑣𝑓𝑔=𝑣𝑔−𝑣f
ELO 1.3

40. Pressure-Specific Volume Diagrams
On P-v diagram, triple point becomes a line, which separates solid- liquid, solid-vapor, and liquid-vapor regions, shown in figure:
Triple Point Line
Figure: P-v Diagram for Water
ELO 1.3

41. P-V-T Property Diagram
Relationship of properties when saturated must be looked at using three properties
Diagram shows how specific volume changes while temperature and pressure remain constant
Addition on heat drives mixture to right across liquid and vapor dome at constant temperature and pressure
All three properties required to know where mixture located on saturation line
Figure: Pressure-Temperature-Specific Volume Diagram
ELO 1.3

42. P-V-T Property Diagram
Figure shows a similar three-dimensional representation of a
P-V-T diagram, along with associated two-dimensional P-T and P-v property diagram projections, for clarity
Figure: Pressure–Temperature–Specific Volume Diagram Projections
ELO 1.3

43. Pressure-Specific Enthalpy
A P-h diagram can be constructed for any pure substance and exhibits the same features as a P-ν diagram
Two phases may exist together
Liquid-vapor region water and steam exist together
At point A, water with an enthalpy (hf) given by point B, exists together with steam with an enthalpy (hg) given by point C
Figure: P-h Diagram for Water
ELO 1.3

44. Pressure-Enthalpy Diagrams
Quality of mixture at any point in liquid-vapor region can be found using:
ℎ=𝑥 ℎ 𝑔 + 1−𝑥 ℎ 𝑓
𝑥= ℎ− ℎ 𝑓 ℎ 𝑓𝑔
Where:
h = specific enthalpy of the mixture (BTU/lbm)
x = quality of the mixture (no units)
hg = specific enthalpy of the saturated vapor (BTU/lbm)
hf = specific enthalpy of the saturated liquid (BTU/lbm)
hfg = specific enthalpy change of vaporization (BTU/lbm) or
𝐵𝑇𝑈 𝑙𝑏𝑚
ℎ𝑓𝑔 =ℎ𝑔−ℎ𝑓
ELO 1.3

45. Specific Enthalpy-Temperature
An h-T diagram can be constructed for any pure substance
Two phases may exist together
Region between saturated liquid line and saturated vapor line represents area of two phases existing at same time
Vertical distance between the two saturation lines represents latent heat of vaporization
Figure: h-T Diagram for Water
ELO 1.3

46. Temperature-Specific Enthalpy
Relationship between temperature and specific enthalpy can also be shown with axis rotated on T-h Diagram
32oF
705oF
This graph, even though seldomly used, is a good representation of the specific enthalpy (sensible heat) added to a subcooled liquid to raise the temperature to saturation, then the specific enthalpy (latent heat of vaporization) needed to raise a saturated liquid to a saturated vapor, then the specific enthalpy to raise a saturated vapor to a superheated vapor. Keep in mind that because this is looking at the “intensive” property of specific enthalpy, it is the heat added “per lbm” (BTU/lbm).
Figure: T-h Diagram
ELO 1.3

47. Temperature-Specific Entropy Diagram
T-s - used to analyze energy transfer system cycles
Work done by or on system
heat added to or removed from system
Point B (sf) – specific entropy of saturated liquid (fluid)
Point C (sg) – specific entropy of saturated vapor (gas)
Point A – specific entropy of a wet vapor
Even though it is early in the CYCLE discussion, it might be helpful to draw the T-s diagram on the board and show the four processes in an IDEAL secondary steam system. Noting that the area under the curve for a given process is the change in specific enthalpy (BTU/lbm).
Subcooled FW to 100% saturated steam (SG process)
100% saturated steam to wet vapor (Isentropic single turbine process)
Wet vapor to subcooled condensate (Condensing process)
Subcooled condensate to subcooled feedwater (Pump process)
Figure: T-s Diagram for Water
ELO 1.3

48. Temperature-Entropy Diagram
Quality of the mixture at any point in the liquid-vapor region can be found using:
𝑠=𝑥 𝑠 𝑔 + 1−𝑥 𝑠 𝑓
𝑥= 𝑠− 𝑠 𝑓 𝑠 𝑓𝑔
Where:
s = specific entropy of the mixture (BTU/lbm-°R)
x = quality of the mixture (no units)
sg = specific entropy of the saturated vapor (BTU/lbm-°R)
sf = specific entropy of the saturated liquid (BTU/lbm-°R)
sfg = specific entropy change of vaporization (BTU/lbm-°R) or
𝑠𝑓𝑔 =𝑠𝑔−𝑠𝑓
NOTE: Once QUALITY (X) is found, the quality can be used to find the specific enthalpy of the wet vapor. h = hf + X(hfg). This process will be used several times to find the exhaust specific enthalpy from the turbine (hexh).
ELO 1.3

49. Specific Enthalpy-Specific Entropy
Chart on which enthalpy (h) versus entropy (s) is plotted
Frequently called the Mollier diagram
Contains
constant temperature lines
constant pressure lines
constant moisture or quality lines
constant superheat lines
Used when quality is > 50 percent and for superheated steam
Main process of our thermodynamic cycle used by Mollier Diagram is the – Specific Work/Work of the turbine (hstm – hexh); or (m-dot)x(hstm – hexh).
The various lines of the Mollier diagram is explained in greater detail in the next ELO.
Figure: Mollier Diagram
ELO 1.3

50. Steam Tables and Mollier Diagram
ELO 1.4 – Describe the use of steam tables and Mollier diagrams, and given sufficient information to indicate the state of the fluid, determine any unknown properties for the fluid.
Related KAs –
K1.24 Explain the usefulness of steam tables to the Control Room operator
K1.25 Explain and use saturated and superheated steam tables
Figure: Mollier Diagram
ELO 1.4

51. Steam Tables
Steam tables consist of two sets of tables of energy transfer properties of water and steam:
Saturated steam tables
Table 1 – Temperature Table
Table 2 – Pressure Table
Superheated steam tables (Table 3)
Tables are tabulations of pressure (P), temperature (T), specific volume (ν), specific enthalpy (h), and specific entropy (s)
Appendix E: Engineering Conversion Factors
Rarely used
Conversions provided on NRC Equation Sheet
Notation used in steam tables
Some tables use v for specific volume because there is little possibility of confusing it with velocity
ELO 1.4

52. Steam Tables – Table 1
In order to solve problems in Thermodynamics, information concerning "state" of substance studied must be obtained
Usually, two properties (ν, p, T, h, s) of substance must be known in order to determine other needed properties (Note: temperature and pressure not independent properties in a saturated system; if one is used, another property must be known to solve problem)
These other properties usually obtained utilizing either
Mollier diagram if substance is steam
Saturated and superheated steam tables
Figure: Portion of a Typical Saturated Steam Temperature Table
ELO 1.4

53. Steam Tables – Table 2
Sat.
NOTE: MUST convert from PSIG to PSIA when using this table. ALL values provided in Steam Tables (Table 1 , 2, or 3) are in PSIA!
Figure: Portion of a Typical Saturated Steam Pressure Table
ELO 1.4

54. Steam Tables Definitions
T = temperature (゜F)
P = pressure (psi)
ν = specific volume (ft3/lbm)
νf = specific volume of saturated liquid (ft3/lbm)
νg = specific volume of saturated vapor (ft3/lbm)
νfg = specific volume change of vaporization (ft3/lbm)
h = specific enthalpy (BTU/lbm)
hf = specific enthalpy of saturated liquid (BTU/lbm)
hg = specific enthalpy of saturated vapor (BTU/lbm
hfg = specific enthalpy change of vaporization (BTU/lbm)
s = specific entropy (BTU/lbm-°R)
sf = specific entropy of saturated liquid (BTU/lbm-°R)
sg = specific entropy of saturated vapor (BTU/lbm-°R)
sfg = specific entropy change of vaporization (BTU/lbm-°R)
Sh = number of degrees of superheat (°F)
Sh, number of degrees of superheat, not provided in all versions of the Steam Table. All you have to do is take Tact – Tsat to get Sh
ELO 1.4

55. Steam Tables Practice What is saturation temperature for 225 psig?
What is the specific enthalpy of saturated vapor at 1,420 psia?
What saturation pressure has the highest enthalpy per lbm?
What is the enthalpy of saturated vapor at atmospheric pressure?
How much energy must be added to 2 lbm of saturated water at 552oF to convert it to dry saturated steam at the same temperature?
Answers (may vary slightly based on version of Steam Tables used):
1.) 397oF
2.) BTUs/lbm
3.) 460 psia
4.) BTUs/lbm
5.) hfg= BTUs/lbm but there are 2 lbm so BTUs
ELO 1.4

56. Steam Tables 𝑥= 𝑣− 𝑣 𝑓 𝑣 𝑓𝑔 Key properties of steam-water mixtures:
𝑥= 𝑣− 𝑣 𝑓 𝑣 𝑓𝑔
Key properties of steam-water mixtures:
Steam quality (x) mass of steam present per unit mass of steam-water mixture
Steam moisture content (M) mass of water present per unit mass of steam-water mixture
Relationships are used with saturated steam tables
𝑣= 𝑥 𝑣 𝑔 +𝑀 𝑣 𝑓
𝑥= ℎ− ℎ 𝑓 ℎ 𝑓𝑔
ℎ=𝑥 ℎ 𝑔 +𝑀 ℎ 𝑓
𝑥= 𝑠− 𝑠 𝑓 𝑠 𝑓𝑔
𝑠=𝑥 𝑠 𝑔 + 𝑀𝑠 𝑓
ELO 1.4

57. Steam Tables
Same approach can be used to solve for specific enthalpy or entropy of a mixture
In place of f, g, and f g, just use hf, hg, hfg or sf, sg, sfg
𝑣=𝑥 𝑣 𝑔 + 1−𝑥 𝑣 𝑓
Same as 𝑣= 𝑀𝑣 𝑓 + 𝑋𝑣 𝑔
Same as 𝑣= 𝑣 𝑓 + 𝑥 𝑣 𝑔 − 𝑣 𝑓
Same as 𝑣= 𝑣 𝑓 + 𝑋𝑣 𝐹𝐺
Same as 𝑣= 𝑣 𝑔 − 𝑀𝑣 𝑓𝑔
𝑥= 𝑣− 𝑣 𝑓 𝑣 𝑓𝑔
ELO 1.4

58. Steam Tables Practice Problems
What is hfg for saturated water at 542°F?
Answer:
654.4 BTUs must interpolate between given values
What is hfg for saturated water at 950 psig?
Answer:
~655 BTUs, if you got 650 it is because you read the psia line
Answer: 1.) BTUs Must interpolate between given values.
Answer: 2.) ~655 BTUs, if you got 650 it is because you read the 950 psia line.
ELO 1.4

59. Steam Tables Use – Example 1
What are the specific volume, enthalpy, and entropy of steam having a quality of 90 percent at psig?
From the steam tables at psia
𝑣 𝑓 = 𝑓 𝑡 3 𝑙𝑏𝑚
ℎ 𝑓 = 𝐵𝑇𝑈 𝑙𝑏𝑚
𝑠 𝑓 = 𝐵𝑇𝑈 𝑙𝑏 𝑚 _ °𝑅
𝑣 𝑓𝑔 = 𝑓 𝑡 3 𝑙𝑏𝑚
ℎ 𝑓𝑔 = 𝐵𝑇𝑈 𝑙𝑏𝑚
𝑠 𝑓𝑔 = 𝐵𝑇𝑈 𝑙𝑏 𝑚 _ °𝑅
𝑣= 𝑣 𝑓 +𝑥 𝑣 𝑓𝑔
𝑣= 𝑓 𝑡 3 𝑙𝑏𝑚 𝑓 𝑡 3 𝑙𝑏𝑚 = 𝑓 𝑡 3 𝑙𝑏𝑚
ℎ= ℎ 𝑓 +𝑥 ℎ 𝑓𝑔
ℎ= 𝐵𝑇𝑈 𝑙𝑏𝑚 𝐵𝑇𝑈 𝑙𝑏𝑚 =1, 𝐵𝑇𝑈 𝑙𝑏𝑚
𝑠= 𝑠 𝑓 +𝑥 𝑠 𝑓𝑔
𝑠= 𝐵𝑇𝑈 𝑙𝑏 𝑚 _ °𝑅 𝐵𝑇𝑈 𝑙𝑏 𝑚 _ °𝑅 = 𝐵𝑇𝑈 𝑙𝑏 𝑚 _ °𝑅
ELO 1.4

60. Steam Tables Use – Example 2
Saturated water at 1,100 psia is heated in a steam generator. What is the temperature, pressure and steam quality of the output if BTU/lbm of heat is added?
From steam tables at 1,100 psia
𝑇𝑠𝑎𝑡 = °𝐹
ℎ𝑓 = BTU/lbm
ℎ𝑓𝑔 = BTU/lbm
ℎ𝑔 = 1,188.6 BTU/lbm
ELO 1.4

61. Steam Tables Use – Example 2 Continued
Since 600 BTU/lbm of heat is added, the enthalpy of output is 1, BTU/lbm
This is less than enthalpy of saturated steam at 1,100 psia
Output is a steam-water mixture at 1,100 psia and °F
𝑥 = ℎ− ℎ 𝑓 ℎ 𝑓𝑔
𝑥= 1,157.55𝐵𝑇𝑈 𝑙𝑏𝑚 − 𝐵𝑇𝑈 𝑙𝑏𝑚 𝐵𝑇𝑈 𝑙𝑏𝑚
𝑥= 600 𝐵𝑇𝑈 𝑙𝑏𝑚 𝐵𝑇𝑈 𝑙𝑏𝑚
𝑥=0.95
Therefore, x = 0.95, T = oF, and P = 1,100 psia
ELO 1.4

62. Steam Tables Use – Example 3
Find the specific entropy of 97 percent quality steam at 556°F.
𝑃𝑠𝑎𝑡=1,096.9 𝑝𝑠𝑖𝑎
𝑠𝑓= 𝐵𝑇𝑈 𝑙𝑏𝑚°𝑅
𝑠𝑓𝑔= 𝐵𝑇𝑈 𝑙𝑏𝑚°𝑅
𝑠𝑔= 𝐵𝑇𝑈 𝑙𝑏𝑚°𝑅
ELO 1.4

63. Steam Tables Use – Example 3 Continued
𝑥= 𝑠− 𝑠 𝑓 𝑠 𝑓𝑔 𝑠=𝑋 𝑠 𝑓𝑔 + 𝑠 𝑓 𝑠= 𝐵𝑇𝑈 𝑙𝑏𝑚–°𝑅 𝐵𝑇𝑈 𝑙𝑏𝑚–°𝑅 𝑠=0.603 𝐵𝑇𝑈 𝑙𝑏𝑚–°𝑅 𝐵𝑇𝑈 𝑙𝑏𝑚–°𝑅 𝑠=1.36 𝐵𝑇𝑈 𝑙𝑏𝑚–°𝑅
ELO 1.4

64. Steam Tables - Superheat
Superheat is degrees of temperature above Tsat for a vapor
𝑆ℎ =𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 – 𝑇𝑠𝑎𝑡
Sh = superheat
Temperature = measured temperature of steam
Tsat = temperature of saturated steam at that pressure
Newer version of Steam Tables do not list degrees of superheat.
Figure: Superheat Steam Temperature Table
ELO 1.4

65. Superheated Steam Table Use
Determine the degrees of superheat for steam at 1,200 psia and 1,000°F.
Determine the specific enthalpy of steam at 1,085 psig and 244°F superheat.
Find the specific volume, enthalpy and entropy of superheated steam at 1,000 psia and 660°F. How many degrees of superheat does it have?
439oF superheat
BTUs/lbm
 = h = s = Sh = oF
1.) 433oF superheat
2.) BTUs/lbm
3.) Sh = °F  = h = s =
ELO 1.4

66. Steam Tables - Subcooled
Subcooling is amount of degrees F a liquid is below saturation temperature for given pressure
Subcooled liquid tables not provided
Use “Saturation Fluid” value of Temperature Table
Since liquid essentially incompressible, energy provided to fluid is mostly due to its temperature, not pressure
A simple rule of use for determining a value (like specific enthalpy) for a substance:
Go to Table 2 for the pressure and temperature provided to determine if subcooled, saturated, or superheated.
If subcooled, use hf for the temperature provided
If superheated, use Table 3 for the pressure provided
If saturated, Table 1 OR 2 can be used
ELO 1.4

67. Steam Tables - Subcooled
You may calculate h and s for a subcooled/compressed liquid using the following formulas and data from saturated steam tables:
ℎ= ℎ 𝑓 − 𝑐 𝑝 𝑇 𝑠𝑎𝑡 −𝑇
The above formula is really not necessary since you can use the hf, sf, or vf for the temperature of the subcooled liquid
Since a liquid is essentially incompressible, the additional pressure adds very little to the “approximation” values
This calculation is not necessary because the hf value at the subcooled temperature can be used as the subcooled approximation.
ELO 1.4

68. Steam Tables - Practice
What is the specific enthalpy of a lbm of subcooled water at 1,005 psig and 524°F?
How many degrees of subcooling does the fluid possess?
Answers:
518.4 BTUs/lbm
19.58 degrees of subcooling
BTUs/lbm
23 degrees of subcooling
ELO 1.4

69. Mollier Diagram Specific Entropy vs Specific Enthalpy
Constant enthalpy (blue line)
Used in throttling processes
Constant entropy (red line)
Constant Pressure Line (green line)
Figure: Mollier Diagram
ELO 1.4

70. Mollier Diagram Constant % Moisture line
“Third” property sometimes used to determine state of wet vapor
Recall Quality/Moisture Content relationship
M = 1 – X
X = 1 - M
Figure: Mollier Diagram – Constant Percent Moisture Lines
ELO 1.4

71. Mollier Diagram Superheat Lines Low Pressure Turbine inlet
Heat added at constant pressure to HP exhaust
MSR
Figure: Mollier Diagram - Constant-Superheat Lines
ELO 1.4

72. Mollier Diagram Constant temperature lines called isotherms
At Saturation Line, curve follows pressure line
Wet vapor temperature at Tsat for pressure
Figure: Mollier Diagram - Constant-Temperature Lines
ELO 1.4

73. Mollier Diagram Mollier diagram with: constant temperature
constant superheat
constant percent moisture
constant pressure lines
Figure: Mollier Diagram - Labeled
ELO 1.4

74. Mollier Diagram - Example 1
Using the Mollier diagram, determine the specific enthalpy, specific entropy, and temperature of steam if its quality is 90 percent and its pressure is 1,000 psia.
ELO 1.4

75. Mollier Diagram - Example 1 Solution
Determine the correct isobar (constant-pressure line), below the saturation line.
Quality (x) is provided, although the Mollier diagram provides moisture content (M); therefore, the following conversion must be performed:
𝑀=1−𝑥
𝑀=1−0.90
𝑀=0.10 (𝑜𝑟 10%)
Identify the appropriate moisture-content line (i.e., 10 percent) that corresponds to a quality of 90 percent.
The intersection of the isobar and moisture content line represents the precise state of the saturated mixture.
To determine the specific enthalpy and specific entropy of the mixture, follow a horizontal and vertical line (respectively) from the intersection point to the associated axes; a straightedge is useful in such analyses.
ℎ=1,125 𝐵𝑇𝑈 𝑙𝑏𝑚 , 𝑠=1.324 𝐵𝑇𝑈 𝑙𝑏𝑚–°𝑅
As this is a saturated mixture at 1,000 psia, the saturated temperature is 545°F.
Note that this problem could also be solved using only the steam tables.
ELO 1.4

76. Mollier Diagram - Example 2
An ideal turbine (i.e. a constant-entropy process) expands superheated steam at 700 psia and 680°F to 140 psia. What is the change in enthalpy for this process?
ELO 1.4

77. Mollier Diagram - Example 2 Solution
Using diagram, locate intersection of the 700 psia and the 680°F lines in the superheat region
Read h ~ 1,333 BTU/lbm
Follow a constant-entropy line downward to 140-psia line and read h ~ 1,175 BTU/lbm
Δh = 1,178 -1,333 = BTU/lbm
Δh = 1,178 -1,333 = -155 BTU/lbm
Additional practice problems are provided in the Student Guide.
ELO 1.4

78. NRC Mollier Practice Knowledge Check
A nuclear power plant is maintained at 2,000 psia with a pressurizer temperature of 636oF. A pressurizer relief safety valve is leaking to a collection tank that is being held at 10 psig. With 100 percent quality saturated steam in the pressurizer vapor space, which one of the following is the approximate temperature of the fluid just downstream of the relief valve?
280oF
240oF
190oF
170oF
Correct answer is B.
TOPIC: KNOWLEDGE: K1.15 [2.8/2.8] QID: P76 See next slide - ANSWER: B
NOTE: This is what is called a “constant enthalpy” (isenthalpic) process. This is also related to the problem associated with TMI that initiated GFE training.
ELO 1.4

79. NRC Mollier Solution
Since the PRT (Quench Tank) contains a wet vapor, you can also determine the temperature by looking it up in the Steam Table. It will be the Tsat for the ABSOLUTE pressure provided.
The correct answer: B. 240oF
ELO 1.4

80. Steam Tables and Mollier Diagram
Knowledge Check – NRC Question
Saturated steam undergoes an ideal expansion process in an ideal turbine from 1,000 psia to 28 inches Hg vacuum. Approximately how much specific work is being performed by the turbine?
1,193 Btu/lbm
805 Btu/lbm
418 Btu/lbm
388 Btu/lbm
Correct answer is C.
Correct answer is C.
NRC Question P1875
One VERY important concept to understand in the turbine process is that the secondary system is approximately 33% efficient. Which means if your plant generates 3600 Mwth then it generates approximately 1200 Mwe. Also since the steam entering the turbine is around 1000 psia and its hstm is around 1200 BTU/lbm, it stands to reason that we are only getting about 1/3 of the energy out of that steam. That means the turbine exhaust is around 800 BTU/lbm. That means the “specific work” done by the turbine is about 400 BTU/lbm. That means the answer MUST be “C” or “D”! (1/3 = 400/1200).
Also the better the vacuum, the more work out of the turbine. 28 inHg vacuum equates to about 1 psia on the Mollier Diagram.
Draw the Mollier Diagram on the board showing the data points. Note that since the process is “ideal” the specific entropy at the turbine inlet is the same as the turbine exhaust. That can be used to determine the quality and then the specific enthalpy of the turbine exhaust.
It is always a good idea to back up your MOLLIER work with STEAM TABLE work if possible!
ELO 1.4

81. Module Summary Review Activity
Complete the following table:
Temp (oF)
Pressure (psia)
Moisture Content
Quality
Specific Volume – v (ft3/lbm)
Specific Enthalpy – h (BTU/lbm)
Specific Entropy – s (BTU/lbmoR)
228oF
20.031 4%
96%
19.261
1,117.8
656oF
2300.9 1%
99%
1,107.3
548oF
1027.9
0.5%
99.5%
1,188.3
102oF
1.0092
14%
86%
960.6
364oF
160.89
12%
88%
1092.5
Temp (oF)
Pressure (psia)
Moisture Content
Quality
Specific Volume – v (ft3/lbm)
Specific Enthalpy – h (BTU/lbm)
Specific Entropy – s (BTU/lbmoR)
228oF
96%
656oF 1%
548oF
99.5%
102oF
14%
364oF
88%
The unfilled table is directly behind the filled table and will show in Slide Show mode. Click to see the filled table.
Optional Activity – Have students use steam tables to fill in values for table above, then review results with class, or call on selected students to find a specific table cell answers during module review.
NOTE: These values were calculated from the 2000 steam tables (newer version). Depending on the version of Steam Tables used, these values might vary slightly.
Summary

82. NRC KA to ELO Tie
KA #
KA Statement RO
SRO
ELO
K1.01
Define energy and work.
1.9
2.0
K1.02
Describe effects of pressure and temperature on density or specific volume of a liquid.
2.4
2.5
1.2
K1.03
Describe the effects of pressure and temperature on density or specific volume of a gas.
2.3
K1.04
Define the following terms: Latent heat of vaporization
1.1
K1.05
Define the following terms: Vaporization line
K1.06
Define the following terms: Critical point
K1.07
Define the following terms: Vapor dome
1.8
K1.08
Define the following terms: Saturated liquid
2.8
K1.09
Define the following terms: Wet vapor
2.1
K1.10
Define the following terms: Saturated vapor
K1.11
Define the following terms: Vapor pressure
1.7
K1.12
Define the following terms: Moisture content
K1.13
Define the following terms: Quality
K1.14
Define the following terms: Superheated vapor
K1.15
Define the following terms: Supersaturated vapor
K1.16
Define the following terms: Subcooled and compressed liquids
2.6
2.7
K1.17
Define the following terms: Subcooling
3.0
3.2
K1.18
Define the following terms: Specific heat
K1.19
Define the following terms: Enthalpy
K1.20
Identify the following terms on a T-s diagram: Critical point
1.3
K1.21
Identify the following terms on a T-s diagram: Saturated liquid line
K1.22
Identify the following terms on a T-s diagram: Saturated vapor line
K1.23
Identify the following terms on a T-s diagram: Solid, liquid, gas, vapor, and fluid regions
K1.24
Explain the usefulness of steam tables to the Control Room operator.
3.1
1.4
K1.25
Explain and use saturated and superheated steam tables.
3.3
3.4
K1.26
Apply specific heat in solving heat transfer problems.
K1.01 was covered in ELO 2.3 of the previous topic ( – Units and Properties).