♨️Thermodynamics of Fluids Unit 7 – Fluid Thermodynamic Properties

Key Concepts and Definitions

• Thermodynamic system refers to a specific quantity of matter or region in space chosen for analysis
• Surroundings include everything external to the system that can interact with it
• Thermodynamic properties describe the state of a system (temperature, pressure, volume, internal energy, enthalpy, entropy)
• Intensive properties are independent of the amount of mass (temperature, pressure, density)
  • Remain constant when a system is divided into smaller subsystems
• Extensive properties depend on the size or extent of a system (volume, internal energy, enthalpy, entropy)
  • Change proportionally when a system is divided into smaller subsystems
• Thermodynamic equilibrium occurs when a system's properties remain constant over time without external influences
• Quasi-equilibrium process involves infinitesimal changes in state variables, allowing the system to remain infinitesimally close to equilibrium

Fundamental Laws and Principles

• Zeroth Law of Thermodynamics states that if two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other
  • Establishes the concept of temperature and the basis for temperature measurement
• First Law of Thermodynamics expresses the conservation of energy principle
  • Energy cannot be created or destroyed, only converted from one form to another
  • Change in internal energy $(\Delta U) = Q - W$, where $Q$ is heat added to the system and $W$ is work done by the system
• Second Law of Thermodynamics introduces the concept of entropy and the irreversibility of natural processes
  • Entropy of an isolated system always increases or remains constant
  • Heat flows spontaneously from a hot body to a cold body, never the reverse
• Third Law of Thermodynamics states that the entropy of a perfect crystal approaches zero as its temperature approaches absolute zero
  • Provides a reference point for determining absolute entropy values

Properties of Pure Substances

• Pure substance consists of a single chemical species with a unique chemical composition
• Phase refers to a particular state of matter (solid, liquid, or gas) with distinct physical properties
• Saturation condition occurs when a pure substance exists as a mixture of two phases in equilibrium (saturated liquid and saturated vapor)
• Critical point represents the highest temperature and pressure at which liquid and vapor phases can coexist in equilibrium
  • Beyond the critical point, distinct liquid and vapor phases do not exist
• Triple point is the unique temperature and pressure at which all three phases (solid, liquid, and gas) coexist in equilibrium
• Compressed liquid refers to a liquid at a pressure higher than its saturation pressure at a given temperature
• Superheated vapor is a vapor at a temperature higher than its saturation temperature at a given pressure

Phase Diagrams and State Changes

• Phase diagram graphically represents the equilibrium states of a pure substance as a function of pressure and temperature
  • Shows regions of solid, liquid, and vapor phases, as well as phase transition lines
• Sublimation is the phase transition directly from solid to vapor without passing through the liquid phase
• Vaporization (boiling) occurs when a liquid is heated and converted into its vapor phase
  • Saturation temperature (boiling point) depends on the pressure
• Condensation is the phase transition from vapor to liquid when a vapor is cooled below its saturation temperature
• Melting is the phase transition from solid to liquid at the melting point temperature
  • Melting point depends on pressure, but the dependence is usually negligible
• Freezing (solidification) occurs when a liquid is cooled below its freezing point and transforms into a solid
• Supercritical fluid exists at temperatures and pressures above the critical point, exhibiting properties of both liquid and gas

Equations of State

• Equation of state is a mathematical relationship between state variables (pressure, volume, temperature) that describes the behavior of a substance
• Ideal gas law, $PV = nRT$, relates pressure, volume, temperature, and amount of an ideal gas
  • $P$ is pressure, $V$ is volume, $n$ is number of moles, $R$ is the universal gas constant, and $T$ is absolute temperature
• Van der Waals equation is a modification of the ideal gas law that accounts for the finite size of molecules and intermolecular attractions
  • $\left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT$, where $a$ and $b$ are substance-specific constants
• Virial equation of state is a power series expansion in terms of molar density, used for more accurate descriptions of real gases
  • $\frac{PV}{RT} = 1 + \frac{B(T)}{V} + \frac{C(T)}{V^2} + \cdots$, where $B(T)$, $C(T)$, etc., are temperature-dependent virial coefficients
• Cubic equations of state, such as the Redlich-Kwong and Peng-Robinson equations, are widely used in the oil and gas industry for their simplicity and accuracy

Thermodynamic Tables and Charts

• Thermodynamic tables provide tabulated data for properties of pure substances at various state points
  • Commonly used tables include saturated liquid and vapor tables, superheated vapor tables, and compressed liquid tables
• Saturated tables list properties at saturation conditions for different temperatures or pressures
  • Include specific volume, internal energy, enthalpy, and entropy for both saturated liquid and saturated vapor
• Superheated vapor tables provide properties of vapors at temperatures above their saturation temperatures for various pressures
• Compressed liquid tables give properties of liquids at pressures above their saturation pressures for different temperatures
• Enthalpy-entropy (Mollier) diagram is a graphical representation of the relationship between enthalpy and entropy for a pure substance
  • Useful for analyzing thermodynamic processes and cycles
• Temperature-entropy (T-s) diagram plots temperature against entropy, showing regions of different phases and constant pressure lines
  • Helps visualize heat transfer and work in thermodynamic processes

Real-World Applications

• Power generation cycles, such as the Rankine cycle and Brayton cycle, rely on thermodynamic principles to convert heat into mechanical work
  • Efficiency of these cycles depends on the properties of the working fluid and operating conditions
• Refrigeration and heat pump systems exploit the thermodynamic behavior of refrigerants to transfer heat from low-temperature sources to high-temperature sinks
  • Coefficient of Performance (COP) is a key metric for evaluating the efficiency of these systems
• Combustion processes in internal combustion engines and gas turbines involve the release of chemical energy and its conversion into mechanical work
  • Thermodynamic analysis helps optimize fuel efficiency and minimize emissions
• Phase change materials (PCMs) utilize latent heat during phase transitions for thermal energy storage and temperature regulation
  • Applications include solar energy storage, building insulation, and thermal management of electronic devices
• Desalination processes, such as multi-stage flash distillation and reverse osmosis, use thermodynamic principles to separate fresh water from saline water
  • Energy efficiency and minimizing environmental impact are crucial considerations in desalination plant design

Problem-Solving Techniques

• Identify the system and surroundings, specifying the system boundaries and interactions with the environment
• Determine the process type (isothermal, isobaric, isochoric, adiabatic) based on the given information and assumptions
• Apply the appropriate thermodynamic laws and principles to the problem, such as the First Law of Thermodynamics for energy conservation
• Use equations of state, such as the ideal gas law or real gas equations, to relate state variables and calculate unknown properties
• Consult thermodynamic tables and charts to obtain property values at specific state points
  • Interpolate between tabulated values when necessary
• Apply the conservation of mass principle for closed systems (no mass transfer) or open systems (mass transfer across boundaries)
• Utilize the concept of specific heats (constant pressure and constant volume) to determine heat transfer and temperature changes
• Employ the definition of work as the product of pressure and volume change ($W = \int P dV$) for boundary work calculations
• Solve for unknown variables using algebraic manipulation, substitution, and iteration techniques
  • Use software tools like Excel, MATLAB, or EES for complex calculations and property lookups