1.2 Properties of Pure Substances

Pure substances are the building blocks of thermodynamics. They have unique properties that change with temperature and pressure. Understanding these properties is crucial for analyzing energy systems and processes in engineering applications.

Phase diagrams and property tables are essential tools for thermodynamicists. They help visualize and quantify how substances behave under different conditions. Mastering these tools allows engineers to predict and optimize the performance of various thermal systems.

Phase diagrams and property tables

Phase diagram features

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• A phase diagram is a graphical representation of the equilibrium states of a pure substance, showing pressure on the vertical axis and temperature on the horizontal axis
• Key features of a phase diagram include:
  • Triple point: The point where all three phases (solid, liquid, and gas) coexist in equilibrium (water triple point: 0.01°C and 0.6 kPa)
  • Critical point: The point where the distinction between liquid and gas phases disappears (water critical point: 374°C and 22.1 MPa)
  • Sublimation curve: Represents the equilibrium between solid and gas phases (dry ice sublimation at atmospheric pressure)
  • Fusion curve: Represents the equilibrium between solid and liquid phases (water freezing at 0°C and 1 atm)
  • Vaporization curve: Represents the equilibrium between liquid and gas phases (water boiling at 100°C and 1 atm)

Property tables and interpolation

• Property tables provide thermodynamic data for pure substances at various temperatures and pressures
• Properties listed in the tables include specific volume, internal energy, enthalpy, and entropy
• Saturated liquid and saturated vapor states are represented in property tables (water at 100°C and 1 atm)
• Superheated vapor and compressed liquid regions are also included in the tables (steam at 200°C and 1 atm)
• Interpolation may be necessary to determine properties at conditions not explicitly listed in the tables
  • Linear interpolation is used for most properties (specific volume, internal energy, enthalpy)
  • Logarithmic interpolation is used for entropy due to its logarithmic nature

Using phase diagrams and property tables together

• Phase diagrams and property tables can be used together to determine the state and properties of a pure substance at a given temperature and pressure
• Locate the given temperature and pressure on the phase diagram to identify the state (solid, liquid, gas, or two-phase mixture)
• Use the property tables to find the corresponding thermodynamic properties for the identified state
• If the state is a two-phase mixture, use quality and the properties of the saturated liquid and saturated vapor to calculate the mixture properties (water at 50°C and 1 atm)

Thermodynamic property calculations

Steam tables

• Steam tables provide thermodynamic properties of water and steam at various temperatures and pressures
• Properties listed in steam tables include specific volume, internal energy, enthalpy, and entropy
• Saturated water and saturated steam properties are listed (water at 100°C and 1 atm)
• Superheated steam and compressed water regions are also included in the tables (steam at 200°C and 1 atm)
• Interpolation may be necessary to determine properties at conditions not explicitly listed in the tables
  • Linear interpolation is used for most properties (specific volume, internal energy, enthalpy)
  • Logarithmic interpolation is used for entropy due to its logarithmic nature

Refrigerant charts

• Refrigerant charts provide thermodynamic properties for common refrigerants at various temperatures and pressures
• Properties listed in refrigerant charts are similar to those in steam tables (specific volume, internal energy, enthalpy, and entropy)
• Refrigerant charts are used to determine properties of refrigerants in vapor compression refrigeration cycles (R-134a in a household refrigerator)

Calculating properties using tables and charts

• To calculate thermodynamic properties using steam tables or refrigerant charts, locate the appropriate table or chart based on the given temperature and pressure conditions
• If the given conditions match a table entry exactly, the properties can be read directly from the table
• If the given conditions fall between table entries, interpolation is required to estimate the properties
  • Use linear interpolation for most properties (specific volume, internal energy, enthalpy)
  • Use logarithmic interpolation for entropy due to its logarithmic nature

Pure substance phase changes

Types of phase changes

• Phase changes occur when a pure substance transitions between solid, liquid, and gas phases due to changes in temperature or pressure
• Melting (solid to liquid) and freezing (liquid to solid) occur at the fusion curve on a phase diagram (ice melting at 0°C and 1 atm)
• Vaporization (liquid to gas) and condensation (gas to liquid) occur at the vaporization curve on a phase diagram (water boiling at 100°C and 1 atm)
  • Boiling is a specific type of vaporization that occurs at the saturation temperature corresponding to the given pressure
• Sublimation (solid to gas) and deposition (gas to solid) occur at the sublimation curve on a phase diagram (dry ice sublimating at -78°C and 1 atm)

Behavior during phase changes

• During a phase change, the temperature of a pure substance remains constant as heat is added or removed
• The specific volume and other properties may change significantly during a phase change
  • Specific volume increases during melting and vaporization (water expanding when frozen)
  • Specific volume decreases during freezing and condensation (steam condensing to a smaller volume)
• The latent heat of fusion, vaporization, or sublimation is the amount of energy required to change the phase of a unit mass of a pure substance at a constant temperature and pressure
  • Latent heat of fusion for water: 333.55 kJ/kg at 0°C and 1 atm
  • Latent heat of vaporization for water: 2257 kJ/kg at 100°C and 1 atm

Two-phase mixture properties

Quality and the lever rule

• A two-phase mixture is a system in which two phases of a pure substance coexist in equilibrium (liquid-vapor mixture in a steam power plant)
• Quality (x) is the mass fraction of vapor in a two-phase mixture, ranging from 0 (saturated liquid) to 1 (saturated vapor)
• Quality can be calculated using the lever rule:
  • $x = (v - v_f) / (v_g - v_f)$
  • where $v$ is the specific volume of the mixture, $v_f$ is the specific volume of saturated liquid, and $v_g$ is the specific volume of saturated vapor

Calculating mixture properties

• The specific volume of a two-phase mixture can be determined using the quality and the specific volumes of the saturated liquid and saturated vapor
  • $v = (1 - x) \cdot v_f + x \cdot v_g$
  • where $v$ is the specific volume of the mixture, $x$ is the quality, $v_f$ is the specific volume of saturated liquid, and $v_g$ is the specific volume of saturated vapor
• Other thermodynamic properties of a two-phase mixture, such as internal energy, enthalpy, and entropy, can be calculated using quality and the respective properties of the saturated liquid and saturated vapor
  • $u = (1 - x) \cdot u_f + x \cdot u_g$ (internal energy)
  • $h = (1 - x) \cdot h_f + x \cdot h_g$ (enthalpy)
  • $s = (1 - x) \cdot s_f + x \cdot s_g$ (entropy)
• Example: A two-phase mixture of water at 100°C and 1 atm with a quality of 0.5 has a specific volume of 0.8263 m³/kg, internal energy of 1443.5 kJ/kg, enthalpy of 1675.4 kJ/kg, and entropy of 4.1758 kJ/(kg·K)