2.3 Thermodynamic data tables and their use

Thermodynamic data tables are essential tools for engineers and scientists working with pure substances. They provide crucial information about properties like enthalpy, entropy, and specific volume at various temperatures and pressures.

These tables help solve real-world problems involving phase changes, heat transfer, and energy conversion. By using interpolation techniques and understanding concepts like quality, engineers can accurately analyze complex thermodynamic systems and processes.

Thermodynamic Property Tables

Saturation Tables

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• Provide thermodynamic properties of a substance at saturation conditions, where the liquid and vapor phases coexist in equilibrium
• Organized by saturation temperature or pressure, allowing users to find properties at specific saturation states
• Include properties such as specific volume, specific enthalpy, and specific entropy for both saturated liquid and saturated vapor states
• Enable users to determine the boiling point or condensation point of a substance at a given pressure or temperature
• Crucial for analyzing phase change processes, such as boiling, condensation, and evaporation (water boiling in a kettle, steam condensing in a power plant condenser)

Superheated Vapor Tables

• Contain thermodynamic properties of a substance in the superheated vapor state, where the vapor is at a temperature higher than its saturation temperature at a given pressure
• Arranged by pressure and temperature, allowing users to find properties at specific superheated vapor states
• Include properties such as specific volume, specific enthalpy, and specific entropy for the superheated vapor
• Essential for analyzing processes involving superheated vapor, such as expansion in a steam turbine or compression in a refrigeration cycle (superheated steam in a power plant, superheated refrigerant in an air conditioning system)

Compressed Liquid Tables

• Provide thermodynamic properties of a substance in the compressed liquid state, where the liquid is at a pressure higher than its saturation pressure at a given temperature
• Organized by pressure and temperature, allowing users to find properties at specific compressed liquid states
• Include properties such as specific volume, specific enthalpy, and specific entropy for the compressed liquid
• Useful for analyzing processes involving compressed liquids, such as pumping or throttling (water in a high-pressure pump, refrigerant in a throttling valve)

Property Evaluation and Interpolation

Interpolation Techniques

• Linear interpolation is a simple method for estimating properties between two known data points in a table, assuming a linear relationship between the properties and the independent variable (pressure or temperature)
• Double interpolation is required when the desired state falls between the values provided in both the pressure and temperature columns of a table, involving interpolation in one direction followed by interpolation in the other direction
• Accuracy of interpolation depends on the spacing of data points in the table and the linearity of the property relationships (closer data points and more linear relationships yield better accuracy)
• Interpolation is necessary because tables provide properties at discrete state points, while many thermodynamic problems involve states that fall between the tabulated values (estimating properties at intermediate pressures or temperatures)

Quality and Phase Equilibrium

• Quality, denoted by $x$, represents the mass fraction of vapor in a two-phase mixture of liquid and vapor in equilibrium
• Saturated liquid has a quality of 0, while saturated vapor has a quality of 1; states with 0 < x < 1 are two-phase mixtures
• Properties of a two-phase mixture can be calculated using quality and the properties of saturated liquid and saturated vapor at the given pressure or temperature: $p_{mixture} = (1 - x) \cdot p_f + x \cdot p_g$
• Quality is used to determine the state and properties of a substance during phase change processes, such as evaporation or condensation (calculating the enthalpy of a two-phase mixture in a partially filled steam boiler)

Thermodynamic Properties

Specific Enthalpy

• Specific enthalpy, denoted by $h$, is the enthalpy per unit mass of a substance, representing the total energy content (internal energy plus flow work) per unit mass
• Enthalpy is a state function, meaning its value depends only on the current state of the system and not on the path taken to reach that state
• Changes in specific enthalpy are important for analyzing heat transfer and work interactions in thermodynamic processes (calculating the energy required to heat water from room temperature to boiling point)
• Specific enthalpy values are provided in thermodynamic property tables for various states, such as saturated liquid, saturated vapor, and superheated vapor (steam tables)

Specific Entropy

• Specific entropy, denoted by $s$, is the entropy per unit mass of a substance, representing the amount of energy dispersed or unavailable for useful work per unit mass
• Entropy is a state function and a measure of the disorder or randomness of a system; it always increases in real processes due to irreversibilities
• Changes in specific entropy are used to determine the direction of heat transfer and to assess the reversibility of thermodynamic processes (comparing the entropy change of a reversible and irreversible compression)
• Specific entropy values are provided in thermodynamic property tables for various states, such as saturated liquid, saturated vapor, and superheated vapor (refrigerant tables)

Internal Energy

• Internal energy, denoted by $u$, is the energy associated with the microscopic components of a system, such as the kinetic and potential energies of molecules
• Specific internal energy is the internal energy per unit mass of a substance
• Changes in internal energy are related to heat transfer and work interactions through the first law of thermodynamics: $\Delta U = Q - W$
• Internal energy is a state function, and its value depends only on the current state of the system, not on the path taken to reach that state (comparing the internal energy change of a gas undergoing compression in a piston-cylinder device)
• Specific internal energy values can be calculated from specific enthalpy and specific volume data provided in thermodynamic property tables: $u = h - pv$