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1.2 · Read property tables and identify phase regions

Learn to read property tables and identify phase regions through clear examples and targeted practice.

University of Alberta MEC E 340: Applied Thermodynamics

Cycle Analysis Foundations

MEC E 340 Applied Thermodynamics study topic 1.2

A property table is a compact record of fluid properties at specified conditions. The key first step is not to search for a number: it is to identify which phase region the state occupies. This lesson considers a pure working fluid in an equilibrium state, labelled state 1 unless a problem gives other state numbers. The system may be a closed component or a control volume, but no cycle or energy balance is needed merely to classify a state. Assume the fluid identity is known and use only the property data supplied by the problem or its named source. The phase tests below rely on saturation properties at the same pressure or temperature as the state.

What you will learn

  • Choose the appropriate property-table section from the known state information.
  • Distinguish compressed liquid, saturated liquid, liquid–vapour mixture, saturated vapour, and superheated vapour.
  • Use saturation properties to calculate quality when a state is a two-phase mixture.
  • Recognize when a table lookup requires interpolation and when quality is not defined.

1. Review the table logic

A property is a measurable state quantity, such as pressure, temperature, specific volume, or specific internal energy. For a pure substance in a single phase, two independent intensive properties generally locate the state in a property table. A saturation condition is a special boundary: liquid and vapour can coexist there, so pressure and temperature are not independent at saturation.
Saturated-water or refrigerant tables commonly list saturated-liquid values with the subscript ff, saturated-vapour values with gg, and the difference between them with fgfg. For example, vfv_f is saturated-liquid specific volume and vgv_g is saturated-vapour specific volume. The same naming pattern may be used for other properties. Confirm the fluid, units, and table headings before using an entry.
At a specified pressure, compare the state temperature with the saturation temperature at that pressure. Alternatively, at a specified temperature, compare pressure with saturation pressure at that temperature. These comparisons identify the region; they do not supply the state’s other properties unless the appropriate table provides them.
vfg=vg−vfv_{fg}=v_g-v_f
  • Use saturation values corresponding to the same pressure or temperature as the state.
  • Read the table heading and units before copying a property.
  • Do not treat pressure and temperature as independent at saturation for a pure substance.

2. Identify the phase region

At a specified pressure, a state with temperature below the saturation temperature is a compressed (or subcooled) liquid. At the saturation temperature, the state lies on the saturation boundary; additional information is needed to tell whether it is saturated liquid, saturated vapour, or a mixture. A temperature above saturation indicates superheated vapour, provided the stated conditions describe the relevant vapour region.
A second useful test applies when specific volume is known. At the same saturation pressure, compare vv with vfv_f and vgv_g. A value between the two indicates a liquid–vapour mixture. Equality with an endpoint identifies a saturated boundary state. Values outside the interval indicate a single-phase region, but use the pressure–temperature comparison or the suitable table to decide which region; do not infer a phase from an unrelated table entry.
The same interval test works with another extensive-per-unit-mass property, such as internal energy or enthalpy, when the corresponding saturated values are available. In a two-phase mixture, quality is the mass fraction that is vapour. It ranges from zero at saturated liquid to one at saturated vapour. Quality is not a measure of volume fraction and is not defined for a compressed liquid or superheated vapour.
x=mgmf+mg=y−yfyfgx=\frac{m_g}{m_f+m_g}=\frac{y-y_f}{y_{fg}}
  • Below saturation temperature at a given pressure: compressed liquid.
  • Between saturated-liquid and saturated-vapour property values: two-phase mixture.
  • Above saturation temperature at a given pressure: superheated vapour.
  • At saturation, use an additional property or a stated phase description.

3. Select and use the right table section

First identify the working fluid and the known state properties. If pressure is given and the phase is not known, consult the saturation-pressure table to obtain the saturation temperature at that pressure. Compare it with the state temperature. If temperature is given instead, use the saturation-temperature table to obtain the matching saturation pressure.
For a saturated or two-phase state, use the saturation table. For a compressed liquid, use a compressed-liquid table if one is supplied. For superheated vapour, use a superheated table and locate the entries bracketing the known state conditions. When the exact condition is not listed, interpolation may be appropriate if the table and problem permit it. Interpolate only between suitable neighboring entries; do not extrapolate beyond the table without an explicit instruction.
Once the region is known, read the requested property from that region’s table. Keep units with every value and do not mix mass-based properties with total quantities. If data are rounded, retain enough digits during intermediate calculations and report a reasonable final precision.
y=yf+xyfgy=y_f+xy_{fg}
  • Use saturation tables to locate the boundary, not as a substitute for a superheated or compressed-liquid table.
  • For a two-phase state, calculate quality from matching saturated values.
  • Interpolate only when the needed entries bracket the state and the task calls for it.

4. Check what the result means

A phase label should agree with the comparisons that produced it. A calculated mixture quality must lie from zero to one, inclusive. If it falls outside that range, the assumed two-phase region is inconsistent with the given state, or the data, units, or arithmetic need review.
At a saturation boundary, temperature and pressure alone do not specify the proportion of liquid and vapour. A problem may explicitly state saturated liquid or saturated vapour, or provide a further property from which quality can be found. Do not assign an arbitrary quality.
Property tables support later energy and performance calculations, but this topic’s task is to select the proper region and obtain valid state properties. A table lookup alone does not establish heat transfer, work, or cycle performance; those require a defined system and appropriate balances.
0≤x≤10\leq x\leq 1
  • Check quality bounds and consistency with the stated phase.
  • Do not confuse saturated liquid with a liquid–vapour mixture.
  • Do not infer heat or work from a phase classification alone.

Worked example

Classify a state using pressure and temperature

A pure working fluid is at state 1. The problem supplies pressure P1P_1 and temperature T1T_1, and the matching saturation-table entry gives Tsat(P1)T_{sat}(P_1). The supplied comparison is T1<Tsat(P1)T_1<T_{sat}(P_1). Identify the region and the table section to use for further properties.
  1. Compare with saturation
    The saturation temperature is taken from the supplied table at the same pressure as state 1. Because the state temperature is lower, the state is on the liquid side of the saturation boundary.
    T1<Tsat(P1)T_1<T_{sat}(P_1)
  2. Choose the table section
    Classify state 1 as compressed (subcooled) liquid. Use a compressed-liquid table if the problem supplies one; do not use saturated-liquid values as though they were automatically the exact state properties.
Answer: State 1 is a compressed (subcooled) liquid. Use the compressed-liquid table for its properties when available.
Check: The conclusion follows from a same-pressure comparison and does not require inventing a numerical saturation value.

Worked example

Find quality from a supplied specific volume

At state 1, a pure fluid is at a supplied saturation pressure. The supplied matching table values are vfv_f, vgv_g, and vfg=vg−vfv_{fg}=v_g-v_f. The state’s measured specific volume satisfies vf<v1<vgv_f<v_1<v_g. Determine the phase and express its quality using the supplied properties.
  1. Identify the region
    The specific volume lies strictly between the saturated-liquid and saturated-vapour values at the same pressure. Therefore state 1 is a liquid–vapour mixture.
    vf<v1<vgv_f<v_1<v_g
  2. Calculate quality
    For a two-phase mixture, specific volume is the mass-weighted average of the saturated-liquid and saturated-vapour values. Rearranging gives quality. Substitute the supplied table entries and state value, retaining consistent units; no numerical result can be reported without those values.
    x1=v1−vfvg−vfx_1=\frac{v_1-v_f}{v_g-v_f}
Answer: State 1 is a saturated liquid–vapour mixture. Its quality is x1=(v1−vf)/(vg−vf)x_1=(v_1-v_f)/(v_g-v_f), using the supplied matching table values.
Check: Because vf<v1<vgv_f<v_1<v_g, the calculated quality must satisfy 0<x1<10<x_1<1. A result outside these limits signals an inconsistency or calculation error.

Worked example

Interpret a saturation-boundary state

A pure working fluid at state 1 has supplied pressure and temperature that match the saturation-table pair. No phase description or additional property is supplied. What can be concluded, and what cannot be determined?
  1. Recognize saturation
    The matching pressure and temperature place state 1 on the saturation boundary for the specified pure fluid.
    T1=Tsat(P1)T_1=T_{sat}(P_1)
  2. Identify the missing information
    The state could be saturated liquid, saturated vapour, or a mixture. Pressure and temperature alone do not reveal the phase proportion. A stated phase or another suitable property is needed to distinguish these possibilities.
Answer: The state is on the saturation boundary, but its quality and whether it is saturated liquid, saturated vapour, or a mixture cannot be determined from the supplied pressure and temperature alone.
Check: Assigning a quality without an extra state property or phase description would add information not present in the problem.

Common mistakes and how to avoid them

Using a saturation value at a pressure different from the state pressure.
Correction: Match the saturation table entry to the state pressure, or use the saturation-pressure entry matching the state temperature.
Calling every state at saturation a two-phase mixture.
Correction: Saturation pressure and temperature identify the boundary; an additional property or phase description is needed to determine the state on that boundary.
Applying quality to compressed liquid or superheated vapour.
Correction: Quality describes the vapour mass fraction only in the liquid–vapour mixture region.
Treating a value outside the saturated-liquid-to-saturated-vapour interval as a mixture.
Correction: Use the interval test only for the corresponding property at matching saturation conditions; investigate the single-phase region using the other known properties and suitable tables.

Lesson summary

  • Identify the fluid and state information, then compare with saturation conditions from a matching table entry.
  • Use pressure–temperature comparisons or saturated-property intervals to identify the phase region.
  • Choose saturated, compressed-liquid, or superheated tables according to the identified region.
  • For a two-phase state, calculate quality from matching saturated values and verify it lies between zero and one.
  • At saturation, pressure and temperature alone do not determine quality.

Check your understanding

Question 1

At a specified pressure, a state temperature is greater than the matching saturation temperature. Which region is indicated?
  1. Compressed liquid
  2. Superheated vapour
  3. Saturated liquid only
  4. A mixture with quality zero
Show answer and explanation
Superheated vapour
At a fixed pressure, a temperature above saturation indicates superheated vapour.

Question 2

A state’s specific volume lies strictly between matching saturated-liquid and saturated-vapour values. What follows?
  1. The state is a liquid–vapour mixture
  2. The state is compressed liquid
  3. The state is superheated vapour
  4. The quality must equal one
Show answer and explanation
The state is a liquid–vapour mixture
An intermediate value of the corresponding property lies in the two-phase region; quality can then be found from the saturated endpoints.

Question 3

What information is needed to determine quality when pressure and temperature specify saturation?
  1. Only the fluid name
  2. A further property or an explicit phase description
  3. The control-volume mass balance
  4. A heat-transfer direction
Show answer and explanation
A further property or an explicit phase description
At saturation, pressure and temperature alone do not show the relative amounts of liquid and vapour.

Key terms

Saturation state
A state on the boundary where liquid and vapour phases can coexist for a pure substance.
Compressed liquid
A liquid state below its saturation temperature at the specified pressure; also called subcooled liquid.
Superheated vapour
A vapour state above its saturation temperature at the specified pressure.
Quality
The mass fraction of vapour in a liquid–vapour mixture, ranging from zero to one.
Interpolation
Estimating a property between neighboring tabulated values that bracket the specified condition.

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