Week 4: Pure Substances, Ideal Gas Equation Introduction

• Energy interactions across the boundary cause energy changes within the system.

• Energy and mass interactions cause other properties of the substance or material in the system to change.

• Consider the concept of a pure substance and the physics of phase change processes.

• Consider the ideal gas equation which relates temperature, pressure, and volume for ideal gases.

Week 4 Objectives (Learning Outcomes)

• Discuss the concept of a pure substance.

• Discuss the physics of phase change processes.

• Determine energy changes during typical phase change processes (temperature change and phase change).

• Describe and sketch 𝑃−𝑣 and 𝑇−𝑣 property diagrams and identify phases of a substance on those diagrams.

• Discuss the meaning of an ideal gas.

• Discuss and apply the ideal gas equation of state to determine property changes for ideal gases.

Pure Substance

• Definition: A substance with a fixed chemical composition throughout.

• Examples:

  • Single chemical element: Nitrogen, copper

  • Compound: Water, carbon dioxide

  • Mixture of elements and compounds: Air

  • Mixture of phases: Ice and liquid water (if chemical composition is identical)

• Notes:

  • Nitrogen and gaseous air are pure substances.

  • A mixture of liquid and gaseous water is a pure substance, but a mixture of liquid and gaseous air is not.

Phases of a Pure Substance

• Definition: A phase is identified by a distinct molecular arrangement that is homogeneous throughout.

• Principal Phases:

  • Solid

  • Liquid

  • Gas

• Examples:

  • Iron has three solid phases (bcc, fcc, hcp).

  • Carbon has two solid phases.

• Molecular Arrangements:

  • Solid: Molecules are at relatively fixed positions.

  • Liquid: Groups of molecules move about each other.

  • Gas: Molecules move about at random.

Phase-Change Processes of Pure Substances

1. Solid to Liquid:

   • Process 1 → 2: Solid increases in temperature (sensible energy increases).

   • Process 2 → 3: Solid melts (latent energy increases, temperature remains constant).

2. Liquid to Gas:

   • Process 3 → 4: Liquid increases in temperature (sensible energy increases).

   • Process 4 → 5: Liquid vaporizes (latent energy increases, temperature remains constant).

   • Process 5 → 6: Gas increases in temperature (sensible energy increases).

Energy Changes During Phase Change Processes

• Heating a Solid, Liquid, or Gas:

  • Increases sensible internal energy (U).

  • Specific heat capacity (c) relates internal energy change with temperature change.

  • Equation: 𝑄 = Δ𝑈 = 𝑚𝑐𝑝(𝑇2 − 𝑇1)

• Melting or Vaporizing:

  • Increases latent internal energy (U).

  • Latent heat of vaporization (ℎv) and fusion (ℎf) are defined.

  • Equations:

    • Vaporization: 𝑄 = 𝑚ℎv

    • Fusion: 𝑄 = 𝑚ℎf

Specific Heat Capacities and Latent Heats

• Specific Heat Capacities (𝑐𝑝):

  • Liquids:

    • Water (25°C): 4.18 kJ/kg°C

    • Ethanol (25°C): 2.46 kJ/kg°C

  • Solids:

    • Aluminium (17°C): 0.902 kJ/kg°C

    • Copper (27°C): 0.386 kJ/kg°C

  • Gases:

    • Air (27°C): 1.005 kJ/kg°C

    • Hydrogen (27°C): 14.307 kJ/kg°C

• Latent Heats:

  • Fusion:

    • Water/Ice (0°C): 333.7 kJ/kg

    • Aluminium (650°C): 390 kJ/kg

  • Vaporization:

    • Water (100°C): 2257 kJ/kg

    • Ethanol (78.2°C): 838.3 kJ/kg

Property Diagrams for Phase Change Processes

• 𝑇−𝑣 Diagram:

  • Critical point

  • Saturation lines (liquid and vapor)

  • Regions: Saturated liquid-vapor, compressed liquid, superheated vapor

  • Constant pressure lines (isobars)

• 𝑃−𝑣 Diagram:

  • Similar to 𝑇−𝑣 diagram

  • Constant temperature lines (isotherms) have a downward trend

  • Example: Constant temperature boiling process

Ideal Gas Equation of State

• Equation: 𝑃𝑉 = 𝑚𝑅𝑇

  • 𝑅 = specific gas constant (kJ/kg.K)

  • 𝑇 = absolute temperature (K)

  • 𝑃 = absolute pressure (Pa)

  • 𝑉 = volume (m³)

  • 𝑚 = mass of the gas (kg)

• Specific Volume: 𝑣 = 𝑉/𝑚, so 𝑃𝑣 = 𝑅𝑇

• Ideal Gas Assumptions:

  • Intermolecular forces are small.

  • Volume occupied by particles is small.

  • Applies to gases with low density (high temperatures, low pressures).

• Applicability:

  • Air, hydrogen, helium, carbon dioxide can be treated as ideal gases.

  • Steam and refrigerant vapors near the phase change region cannot be treated as ideal gases.

Is Water Vapor an Ideal Gas?

• Normally treated as non-ideal.

• Can be treated as an ideal gas under certain conditions (low density).

• Errors are large near the phase change region.

• In air-conditioning applications, water vapor can be treated as an ideal gas.