Properties of Pure Substance

Introduction

A pure substance is a material that has a homogeneous chemical composition throughout its mass and consists of a single component system. A pure substance may exist in one or more phases (solid, liquid, vapour). The thermodynamic behaviour of a pure substance is described by its pressure (P), temperature (T), specific volume (v) and other properties such as enthalpy (h), internal energy (u) and entropy (s).

Saturation and Phase Change

• Saturation state: A saturation state is a state at which a change of phase can occur without a change in pressure or temperature (for example, liquid ↔ vapour at the saturation temperature for a given pressure).
• Degree of superheat: The difference between the temperature of a superheated vapour and the temperature of the saturated vapour at the same pressure.
• Sublimation: Direct transformation of a solid to vapour (solid → vapour).
• Deposition (ablimation): Direct transformation of vapour to solid (vapour → solid). Some texts use the term ablimation for this process.

Critical Point

• Critical temperature (T_c): At the critical temperature a liquid and its vapour become identical in properties and the distinct liquid-vapour boundary disappears. Above this temperature a vapour cannot be liquefied by any increase of pressure.
• Critical pressure (P_c): The minimum pressure required to liquefy a vapour at the critical temperature.
• The line that joins the critical points at varying conditions is often called the critical line on two- and three-dimensional phase diagrams.

Triple Point

• Triple point: The unique temperature and pressure at which solid, liquid and vapour phases of a substance coexist in equilibrium.
• At the triple point for a pure substance the number of degrees of freedom is zero (see Gibbs phase rule later).
• Common reference convention: at the triple point many property tables choose the triple point as a convenient reference. For such references it is sometimes stated that internal energy = 0 and entropy = 0 while enthalpy > 0 (these are reference choices, not absolute physical requirements).

Phase Diagrams and Curves

• Phase diagrams (P-T, P-v, T-v, h-s and Mollier (h-s) diagrams) show regions of solid, liquid and vapour and the lines of equilibrium between phases (fusion, vaporization, sublimation).
• The slope of the fusion (solid-liquid) curve is positive for most substances; however, for water it is negative because water expands on freezing (ice is less dense than liquid water).
• The slopes of the vaporization and sublimation curves are positive for all substances.
• The Clapeyron equation gives the slope of the coexistence (phase-change) curve on a P-T diagram:

Clapeyron equation: dp/dT = L / (T · Δv)

where L is the latent heat (per unit mass) for the phase change and Δv is the change in specific volume between the two phases (for example v_g - v_f for vaporization).

Examples - Properties of Water (values given in input)

• Critical pressure, P_c: 221.2 bar
• Critical temperature, T_c: 374.15 °C
• Critical specific volume, v_c: 0.00317 m³/kg
• Triple point pressure: 4.58 mm Hg
• Triple point temperature: 273.16 K

Mollier Diagram (h-s) and Dryness Lines

• The Mollier diagram (h-s diagram) is frequently used for moist vapour/steam calculations and shows constant-pressure lines, constant-temperature lines, and lines of constant dryness fraction (quality).
• Dryness fraction (x): The mass fraction of vapour in a two-phase (mixture) system. If m_v is mass of vapour and m_l is mass of liquid then

x = m_v / (m_v + m_l)

• For saturated liquid, x = 0.
• For saturated vapour, x = 1.
• Dryness-quality lines (constant x) in P-V, h-s and other diagrams typically originate from the critical line and span the two-phase dome.

Properties of Two-Phase Mixture (Mixture Relations)

• For a two-phase mixture at given pressure or temperature the specific properties can be expressed in terms of the saturated liquid and saturated vapour properties and the dryness fraction x.
• Notation:

v = specific volume of the mixture

v_f = specific volume of saturated liquid

v_g = specific volume of saturated vapour

v_fg = v_g - v_f

h = specific enthalpy of the mixture

h_f = specific enthalpy of saturated liquid

h_g = specific enthalpy of saturated vapour

h_fg = h_g - h_f

s = specific entropy of the mixture

s_f = specific entropy of saturated liquid

s_g = specific entropy of saturated vapour

s_fg = s_g - s_f

• Mixture relations (linear mixing using dry mass fraction x):

v = (1 - x)·v_f + x·v_g = v_f + x·v_fg

h = (1 - x)·h_f + x·h_g = h_f + x·h_fg

s = (1 - x)·s_f + x·s_g = s_f + x·s_fg

Degrees of Freedom and Gibbs Phase Rule

• The Gibbs phase rule for a system with C components and P phases is: F = C - P + 2, where F is the number of degrees of freedom (intensive properties that can be changed independently, e.g., P and T).
• For a pure substance (C = 1): F = 3 - P.
• Consequences for a one-component system:
• If P = 1 (single-phase, e.g. a gas), F = 2: two independent intensive properties (such as P and T) must be specified to fix the state.
• If P = 2 (two phases in equilibrium, e.g. saturated liquid + vapour), F = 1: only one intensive property (either P or T) is independent along the saturation line.
• If P = 3 (triple point: solid + liquid + vapour in equilibrium), F = 0: the temperature and pressure are fixed (unique) for the triple point.

Measurement of Dryness Fraction - Throttling Calorimeter

• Throttling calorimeter: An apparatus used to determine the dryness fraction (quality) of a wet steam (two-phase) sample by throttling (an irreversible adiabatic expansion through a valve or porous plug) the mixture to a lower pressure where the outlet is single-phase vapour.
• Throttling process is adiabatic and irreversible, and under typical assumptions it is approximately isenthalpic (h_in = h_out), i.e., enthalpy remains constant across the throttle if no heat transfer and no work interaction other than flow work occur.
• Because direct measurement of quality in a two-phase mixture is difficult, the mixture is throttled to a condition where all liquid flashes to vapour (or where the downstream condition is a known saturated vapour); the downstream temperature and pressure are measured and used, together with energy relations, to determine the upstream dryness fraction.

Useful Remarks and Practical Points

• Dryness fraction may be determined from enthalpy measurements using: x = (h - h_f) / h_fg.
• Similarly, x = (v - v_f) / v_fg or x = (s - s_f) / s_fg when the corresponding properties are used.
• Dryness quality lines on diagrams such as h-s or P-v help visualise two-phase mixture behaviour and are useful for steam-engine, turbine and boiler calculations.

Summary

The properties of a pure substance and its phase behaviour are essential for thermodynamic analysis. Key concepts include saturation, critical point, triple point, phase diagrams (including the Mollier h-s diagram), dryness fraction and the mixture relations that allow calculation of specific volume, enthalpy and entropy for two-phase mixtures. The Gibbs phase rule gives the degrees of freedom for a given number of phases. Practical measurement techniques such as the throttling calorimeter make it possible to determine the quality of wet steam for engineering applications.