2.2 Property tables and their use

Property tables are essential tools in thermodynamics, providing key data for various substances. They organize information about temperature, pressure, and other properties, allowing engineers to analyze and solve real-world problems efficiently.

Understanding how to use these tables is crucial for thermodynamic calculations. By mastering table navigation, interpolation techniques, and problem-solving strategies, you'll be equipped to tackle complex scenarios involving pure substances in different phases and conditions.

Thermodynamic Property Tables

Table Organization and Structure

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• Thermodynamic property tables are organized by substance, typically with one table for each phase (solid, liquid, vapor) and one for the saturated state
• Tables are typically organized with one property (such as temperature or pressure) varying in the first column, and other properties (such as specific volume, internal energy, enthalpy, and entropy) listed in subsequent columns
• The critical point, where the distinction between liquid and vapor phases disappears, is typically noted in the tables

Saturated and Single-Phase States

• Saturated liquid and saturated vapor states coexist in the saturated tables, with the same values of saturation pressure and temperature
• Quality, often denoted as x, represents the fraction of vapor in the saturated mixture
• Compressed liquid tables cover states where the pressure exceeds the saturation pressure for a given temperature
• Superheated vapor tables cover states where the temperature exceeds the saturation temperature for a given pressure

Determining Properties from Tables

Identifying Appropriate Tables

• To find properties, first identify the appropriate table based on the known properties and the phase of the substance
• For single-phase states, locate the state by finding the row corresponding to one known property (e.g., temperature) and reading off the other properties from that row
• For saturated mixtures, use the saturated tables. If the quality is known, the properties can be calculated as a weighted average of the saturated liquid and saturated vapor values

Specific and Extensive Properties

• Specific properties (properties per unit mass) are most commonly tabulated. To find extensive properties, multiply the specific properties by the total mass of the system
• Pay close attention to units when reading properties from tables. Conversion factors may be necessary to obtain properties in desired units (e.g., converting from kJ/kg to J/kg)

Interpolation and Extrapolation of Properties

Linear Interpolation

• Linear interpolation can be used to estimate properties at conditions between two tabulated states. This assumes a linear variation of the property between the tabulated points
• To interpolate, identify the two closest tabulated states that bracket the state of interest. Then, perform a weighted average based on the proximity of the state of interest to each tabulated state
• For example, to find the enthalpy at a temperature between two tabulated temperatures, use the formula: $h = h_1 + \frac{T - T_1}{T_2 - T_1}(h_2 - h_1)$

Extrapolation and Higher-Order Methods

• Extrapolation, estimating properties outside the tabulated range, is generally less accurate than interpolation and should be used with caution
• Higher-order interpolation methods, such as quadratic or cubic interpolation, can provide better accuracy but are more complex to implement
• These methods consider the curvature of the property variation and use additional tabulated points to construct the interpolating function

Solving Problems with Tables

Problem-Solving Strategy

• Start by carefully reading the problem statement and listing the known properties and the properties to be found
• Determine which properties are necessary to find the desired solution. It may be necessary to find intermediate properties in multiple steps
• Use the known properties to locate the appropriate state(s) in the tables, interpolating if necessary

Calculations and Unit Conversions

• Once all necessary properties are found, use them to calculate the desired quantities, paying attention to units and converting if necessary
• For example, if the table provides specific enthalpy in kJ/kg, but the problem requires enthalpy in J, multiply the specific enthalpy by the mass and convert from kJ to J: $H = m \cdot h \cdot 1000 \frac{J}{kJ}$

Checking Solutions

• Check the solution for reasonableness. Consider the magnitude and sign of the result, and compare to any available estimates or approximations
• Verify that the units of the final answer are consistent with the problem statement and cancel out correctly in any calculations performed