Thermodynamics I Unit 2 Review: Properties of Pure Substances

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 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: $(P + a/V_m^2)(V_m - b) = RT$
  • $V_m$ 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 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 = 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