Properties of Pure Substances Study Notes

PROPERTIES OF PURE SUBSTANCES

First Law of Thermodynamics

• Definition: Energy is conserved.

  • The total energy of an isolated system is constant; energy can be transformed from one form to another but cannot be created or destroyed.

First Law of Thermodynamics for a Closed System

• Energy Change of a System, \Delta E{system} = E2 - E_1 = Q - W

  • Where:

  • \Delta E = change in energy

  • Q = heat added to the system

  • W = work done by the system

  • Energy Components:

  • \Delta KE + \Delta PE + \Delta U = Q - W

    • \Delta KE = change in kinetic energy

    • \Delta PE = change in potential energy

    • \Delta U = change in internal energy

Objectives

• Introduce the concept of a pure substance.

• Discuss the physics of phase-change processes.

• Illustrate the P-v, T-v, and P-T property diagrams and P-v-T surfaces of pure substances.

• Demonstrate the procedures for determining thermodynamic properties of pure substances from tables of property data.

• Describe the hypothetical substance “ideal gas” and the ideal-gas equation of state.

• Apply the ideal-gas equation of state in the solution of typical problems.

• Introduce the compressibility factor, which accounts for the deviation of real gases from ideal-gas behavior.

• Present some of the best-known equations of state.

3-1 Pure Substance

• Definition: A substance that has a fixed chemical composition throughout.

  • Example: Air is a mixture of several gases, but it is considered to be a pure substance.

  • Figures:

  • Figure 3–1: Nitrogen and gaseous air are pure substances.

  • Figure 3–2: A mixture of liquid and gaseous water is a pure substance, but a mixture of liquid and gaseous air is not.

3-2 Phases of a Pure Substance

• Molecular Behavior in Different Phases:

  • Solid Phase (Figure 3–3): Molecules are kept at fixed positions by strong intermolecular forces.

  • Liquid Phase (Figure 3–4): Molecules move around each other but are still in contact.

  • Gas Phase (Figure 3–4): Molecules move about randomly and are far apart.

3-3 Phase-Change Processes of Pure Substances

• 1. Compressed Liquid (Subcooled Liquid): A substance that is not about to vaporize.

  • Figure 3–5: At 1 atm and 20°C, water exists in the liquid phase (subcooled liquid).

• 2. Saturated Liquid: A liquid that is about to vaporize.

  • Figure 3–6: At 1 atm pressure and 100°C, water exists as a liquid that is about to vaporize (saturated liquid).

• 3. Saturated Liquid-Vapor Mixture: The state at which the liquid and vapor phases coexist in equilibrium.

  • Figure 3–7: As more heat is transferred, part of the saturated liquid vaporizes (saturated liquid-vapor mixture).

• 4. Saturated Vapor: A vapor that is about to condense.

  • Figure 3–8: At 1 atm pressure, the temperature remains constant at 100°C until the last drop of liquid is vaporized (saturated vapor).

• 5. Superheated Vapor: A vapor that is not about to condense (i.e., not a saturated vapor).

  • Figure 3–9: As more heat is transferred, the temperature of the vapor begins to rise (superheated vapor).

• 6. Reversibility of Phase Change: If the entire process between state 1 and state 5 is reversed by cooling the water while maintaining pressure, the heat released matches the heat added during the heating process.

  • Figure 3–10: T-v diagram for the heating process of water at constant pressure.

• 7. Saturation Temperature and Saturation Pressure:

  • Saturation Temperature: The temperature at which a pure substance changes phase at a given pressure.

  • Saturation Pressure: The pressure at which a pure substance changes phase at a given temperature.

  • Figure 3–11: Liquid-vapor saturation curve of a pure substance (numerical values are for water).

• 8. Saturation (Vapor) Pressure Table (Table 3–1) for Water at Various Temperatures:

  • \text{Temperature (°C)}

    • -10: P_{sat} = 0.260 kPa

    • -5: P_{sat} = 0.403 kPa

    • 0: P_{sat} = 0.611 kPa

    • 5: P_{sat} = 0.872 kPa

    • 10: P_{sat} = 1.23 kPa

    • 15: P_{sat} = 1.71 kPa

    • 20: P_{sat} = 2.34 kPa

    • 25: P_{sat} = 3.17 kPa

    • 30: P_{sat} = 4.25 kPa

    • 40: P_{sat} = 7.38 kPa

    • 50: P_{sat} = 12.35 kPa

    • 100: P_{sat} = 101.3 kPa (1 atm)

    • 150: P_{sat} = 475.8 kPa

    • 200: P_{sat} = 1554 kPa

    • 250: P_{sat} = 3973 kPa

    • 300: P_{sat} = 8581 kPa

3-4 Property Diagrams for Phase-Change Processes

• Understanding Phase Changes: The variations of properties during phase change processes are studied with the help of property diagrams such as T-v, P-v, and P-T diagrams for pure substances.

  • Figure 3–15: T-v diagram of constant-pressure phase-change processes of a pure substance at various pressures (numerical values are for water).

• Critical Point: The point at which the saturated liquid and saturated vapor states are identical.

  • Figure 3–16: At supercritical pressures, there is no distinct phase-change (boiling) process.

• Regions on Property Diagrams:

  • Saturated Liquid Line

  • Saturated Vapor Line

  • Compressed Liquid Region

  • Saturated Liquid-Vapor Mixture Region (Wet Region)

  • Superheated Vapor Region

  • Figure 3–17: Property diagrams of a pure substance.

• Pressure in Piston-Cylinder Device: The pressure can be reduced by decreasing the weight of the piston.

  • Figure 3–18 illustrates this concept.

• Triple Point: The unique temperature and pressure at which a substance's solid, liquid, and vapor phases coexist in equilibrium.

  • Figure 3–20: At triple-point pressure and temperature, a substance exists in all three phases in equilibrium.

  • T{tp} = 0.01 °C, P{tp} = 0.6117 kPa

• Sublimation: The process of passing from the solid phase directly into the vapor phase.

  • Figure 3–21: At low pressures (below the triple-point value), solids evaporate without melting first.

3-5 Property Tables

• Purpose of Property Tables: Relationships among thermodynamic properties are complex; therefore, properties are often presented in table form.

• Measurable vs. Calculable Properties: Some thermodynamic properties can be measured easily, while others are calculated using relationships between them and measurable properties.

  • Results are presented in tables in a convenient format.

• Saturated Liquid and Saturated Vapor States:

  • Figure 3–27: Depicts a partial list from Table A–4 detailing saturation properties of water.

  • Definitions:

  • v_f = specific volume of saturated liquid

  • v_g = specific volume of saturated vapor

  • v{fg} = vg - v_f

Examples

• Example Questions:

  • If T{sat} = 30°C → Determine P? , vf?

  • If T{sat} = 100°C → Determine P? , vg?

  • If P{sat} = 1.0 kPa → Determine T? , vf?

  • If P{sat} = 10.0 kPa → Determine T? , vg?

Example Problems

• EXAMPLE 3-1: Pressure of Saturated Liquid in a Tank

  • A rigid tank contains 50 kg of saturated liquid water at 90°C.

  • Determine:

  • Saturation Pressure:

    • P_{sat} = 70.183 kPa

  • Volume of Tank:

    • V = (50 kg) imes (0.001036 m³/kg) = 0.0518 m³ → 51.8 L

• EXAMPLE 3-2: Temperature of Saturated Vapor in a Cylinder

  • A piston-cylinder device contains 2 ft³ of saturated water vapor at 50 psia pressure.

  • Determine: Temperature and mass of vapor inside the cylinder using English unit tables.