Property Tables

Property tables also known as thermodynamic tables, are tables that will provide information for temperature, pressure, specific volume, internal energy, enthalpy, and entropy at a certain value of temperature or pressure. There are two different types of tables that you could come across. The first type of table considers that property when it is in saturated state between a liquid or a gas. To use this table you need to know the saturation temperature or saturation pressure that you are interested in looking up. Below there are two saturation tables for water. One table considers the saturation temperature, and the other considers the saturation pressure.

Saturated Temprature Water Table
Source: Thermodynamics an Engineering Approach ISBN 978-0-07-352921-9

 

Saturated Pressure Water Table
Source: Thermodynamics an Engineering Approach ISBN 978-0-07-352921-9

 

Another property that you should know when using a saturation table is the quality of the mixture (x). By knowing what the quality of the mixture is you can determine how much of the saturated mixture is liquid and how much is gas. Knowing this will allow you to calculate the correct specific volume, internal energy, enthalpy, and entropy. For example, to calculate the internal energy of a saturated mixture when you know the quality the following equation would be used.

(Eq 1) $x=\frac{u_{avg}-u_f}{u_{fg}}$

The same type of equation would be used to calculate the values for specific volume, enthalpy, and entropy. If the mixture was 100% liquid x would equal 0 and if it was 100% gas x would equal 1.

The second table that you could come across is a table that represents a superheated substance. Below you can see the table for superheated water at a constant pressure of 100kPa.

Superheated Water Table at 100KPa

The tables above represent only a portion of the data for water. However, any thermodynamics book will provide a more complete set of data in addition to other substances.

Interpolation

Interpolation is a mathematical method used to predict a value when it is not provided on a table. Knowing how to interpolate is very useful when using thermodynamic tables because it is very rare that you would be looking up a temperature or pressure that is on the tables. Instead what you want to know could be in between a value that is higher and a value that is lower. The equation below shows how to linear interpolate to find a value that is not provided on the tables.

(Eq 2)  $Y=\frac{(X-X_1)(Y_2-Y_1)}{(X_2-X_1)+Y_1}$

For the equation above Y represents the value you are trying to find, X represents the value you know but is not on the table, X₁ and Y₁ represent the two lower values on the table, and X₂ and Y₂ represent the two higher values on the table.

Enthalpy and Entropy

Enthalpy and entropy are two new properties that you may or may not be familiar with. Enthalpy, or sometimes referred to as the heat content or total heat of a substance, is typically used to analyze steam engines. Enthalpy is the combination of internal energy and the product of pressure and specific volume; refer to equation 3.

(Eq 3) $h=u+Pν$

Entropy on the other hand is the measurement of thermal energy per unit mass that is not available to perform work.