Thermodynamics I Unit 2 ReviewProperties of Pure Substances

Properties of pure substances form the foundation of thermodynamics. This unit covers key concepts like phases, equilibrium, and state changes. Understanding these basics is crucial for analyzing thermodynamic systems and processes in engineering applications. The unit delves into phase diagrams, equations of state, and ideal vs. real gas behavior. These tools help predict substance properties under various conditions, essential for designing and optimizing thermal systems in industries like power generation and HVAC.

2.1

Phase changes and phase diagrams

2.2

Property tables and their use

2.3

Ideal gas equation and other equations of state

unit 2 review

Key Concepts and Definitions

Thermodynamic system consists of a fixed quantity of matter and its boundaries
Surroundings include everything external to the system
Boundary separates the system from its surroundings and can be fixed or movable, real or imaginary
Pure substance has a homogeneous and invariable chemical composition
Phase refers to a quantity of matter that is homogeneous throughout in chemical composition and physical structure
Thermodynamic equilibrium occurs when there is no tendency for a system's properties to change over time
- Characterized by thermal, mechanical, and chemical equilibrium
Thermodynamic process represents a change in the state of a system described by thermodynamic properties (pressure, temperature, volume)

Phase Changes and Diagrams

Phase change occurs when a substance transitions from one phase to another (solid, liquid, gas)
- Melting/freezing between solid and liquid phases
- Vaporization/condensation between liquid and gas phases
- Sublimation/deposition between solid and gas phases
Saturation temperature ( $T_{sat}$ ) is the temperature at which a pure substance changes phase at a given pressure
Saturation pressure ( $P_{sat}$ ) is the pressure at which a pure substance changes phase at a given temperature
Phase diagram graphically represents the various phases of a substance and the conditions at which phase changes occur
- Pressure-temperature (P-T) diagram most commonly used
Triple point is the unique point on a phase diagram where all three phases (solid, liquid, gas) coexist in equilibrium
Critical point represents the highest temperature and pressure at which liquid and vapor phases can coexist in equilibrium

Thermodynamic Properties

Thermodynamic properties describe the state of a system and include pressure (P), temperature (T), volume (V), internal energy (U), enthalpy (H), and entropy (S)
Intensive properties are independent of the system size (pressure, temperature)
Extensive properties depend on the size or extent of the system (volume, mass)
Specific properties are extensive properties per unit mass (specific volume, specific enthalpy)
State postulate asserts that the state of a simple compressible system is completely specified by two independent, intensive properties
Pressure is the force per unit area exerted by a fluid
- Absolute pressure is measured relative to a perfect vacuum
- Gauge pressure is measured relative to the local atmospheric pressure
Temperature is a measure of the average kinetic energy of the particles in a substance
- Kelvin (K) and Rankine (°R) are absolute temperature scales
- Celsius (°C) and Fahrenheit (°F) are relative temperature scales

Equations of State

Equation of state is a mathematical relationship between the thermodynamic properties of a substance
Ideal gas equation of state: $PV = nRT$ $P V = n RT$
- P is the absolute pressure
- V is the volume
- n is the number of moles
- R is the universal gas constant
- T is the absolute temperature
van der Waals equation of state accounts for the non-ideal behavior of gases: $(P + a/V_m^2)(V_m - b) = RT$ $(P + a / V_{m}^{2}) (V_{m} - b) = RT$
- $V_m$ is the molar volume
- a and b are van der Waals constants specific to the gas
Virial equation of state is a power series expansion in terms of molar density: $Z = 1 + B\rho_m + C\rho_m^2 + D\rho_m^3 + ...$ $Z = 1 + B ρ_{m} + C ρ_{m}^{2} + D ρ_{m}^{3} + ...$
- Z is the compressibility factor
- $\rho_m$ is the molar density
- B, C, D, ... are virial coefficients that depend on temperature and the specific gas

Ideal Gas Behavior

Ideal gas is a hypothetical gas that perfectly follows the ideal gas equation of state
Ideal gas assumptions:
- Particles are point masses with no volume
- No attractive or repulsive forces between particles
- Collisions between particles are perfectly elastic
Ideal gas law relates pressure, volume, temperature, and amount of substance: $PV = nRT$
Dalton's law of partial pressures states that the total pressure of a mixture of ideal gases is equal to the sum of the partial pressures of the individual gases
Amagat's law of partial volumes states that the total volume of a mixture of ideal gases is equal to the sum of the partial volumes of the individual gases
Kinetic theory of gases relates the macroscopic properties of an ideal gas to the microscopic behavior of its particles
- Average kinetic energy of gas particles is directly proportional to the absolute temperature

Real Gas Behavior

Real gases deviate from ideal gas behavior due to intermolecular forces and the finite volume of gas particles
Compressibility factor (Z) quantifies the deviation of a real gas from ideal gas behavior: $Z = \frac{PV}{nRT}$ $Z = \frac{P V}{n RT}$
- Z = 1 for an ideal gas
- Z < 1 for a gas with attractive intermolecular forces
- Z > 1 for a gas with repulsive intermolecular forces
Critical properties (critical temperature, pressure, and volume) define the point beyond which distinct liquid and gas phases do not exist
Reduced properties (reduced temperature, pressure, and volume) are the ratio of a property to its critical value
Principle of corresponding states suggests that gases with similar reduced properties exhibit similar deviations from ideal gas behavior
Pseudocritical properties are used to estimate the behavior of gas mixtures using the principle of corresponding states

Applications in Engineering

Psychrometric charts are used to analyze the thermodynamic properties of moist air (HVAC systems)
Compressibility factor charts and tables are used to estimate the properties of real gases in various engineering applications (natural gas pipelines, refrigeration systems)
Equations of state are used to predict the behavior of fluids in chemical processes and equipment design (distillation columns, heat exchangers)
Phase diagrams are used to understand the behavior of substances under different conditions (materials science, geothermal systems)
Thermodynamic property tables provide accurate data for pure substances and are used in energy analysis and design calculations (power plants, engines)
Ideal gas law is used in the analysis of combustion processes, gas turbines, and internal combustion engines
Real gas behavior is considered in the design and operation of high-pressure systems (compressed natural gas vehicles, gas storage tanks)

Problem-Solving Techniques

Identify the system and its boundaries
Determine the relevant thermodynamic properties and processes
Select the appropriate equation of state or property tables based on the substance and conditions
Apply the conservation laws (mass, energy) and thermodynamic principles to set up the problem
Use the given information to solve for the unknown properties or quantities
Verify the results using alternative methods or by checking the units and orders of magnitude
Interpret the results in the context of the problem and consider the limitations of the assumptions made
Perform sensitivity analysis to understand the impact of uncertainties or changes in input parameters on the solution

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