Part II: Cycles and Fluid Properties · Topic 5 of 8 · 19 min read

Pure Substances and Phase Change

Identify thermodynamic regions and calculate two-phase mixture properties.

What you'll learn

Classify compressed liquid, saturated mixture and superheated vapour states.
Interpret a saturation dome and quality.
Use supplied saturation property data for mixture calculations.
Interpolate within tabulated property ranges without extrapolating silently.

A saturation dome separates liquid, two-phase and vapour thermodynamic regions.

Understand the concepts

Pure substance and phase

A pure substance has a fixed chemical composition even if liquid and vapour coexist. Its intensive state requires sufficient independent properties to identify the region. Phase-change data must be interpreted with the correct reference pressure or temperature.

Saturation boundary

At a specified saturation pressure, liquid and vapour can coexist at the saturation temperature. A saturated liquid is just about to vaporise; saturated vapour is just about to condense. At the critical point the two saturated states become indistinguishable.

Quality is a mass fraction

For a saturated liquid-vapour mixture, quality $x$ is the vapour mass divided by total mass. It lies between zero and one only inside the two-phase dome. Quality cannot be used to label a single-phase superheated vapour.

Mixture interpolation

A specific mixture property $y$ varies linearly with mass quality between its saturated-liquid and saturated-vapour values: $y = y_{f}$ . This is a mass-weighted relationship, not an assertion that the liquid occupies the same volume as the vapour.

Assumptions and sign conventions

Property values in questions are self-contained, illustrative data for the stated working fluid and state.
Use two-phase interpolation only when the specific volume or energy lies between saturated endpoints.
Ignore vessel deformation and changes in kinetic or potential energy unless included.

Equations that matter

x=\frac{m_g}{m_f+m_g}

Step-by-step method

Identify the working fluid and its supplied pressure-temperature region.
Compare the known property with the saturated endpoint values to establish phase.
For a mixture, calculate quality from a known specific property.
Use mass-weighted interpolation for other mixture properties.
Apply the appropriate energy balance and check $0\le x\le1$ if two-phase.

Worked example: Quality from a supplied property row

At a stated saturation pressure, a fluid has $v_f=0.0012$ and $v_g=0.220\,\mathrm{m^3/kg}$ . A sample has specific volume . Estimate its quality.

Common mistakes

Treating quality as a volume fraction.
Using mixture interpolation outside the saturation dome.
Comparing properties at different pressures.
Using vapour tables for compressed liquids without checking assumptions.

Check yourself

Why can a small vapour mass occupy most of the vessel volume?
What does $x=0$ mean?
Which properties stay constant in a sealed rigid tank?

Ready to try it yourself?

Try Practice Questions (4)

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