how to use Steam tables (saturated and superheated tables)

 How to Use Steam Tables: Saturated and Superheated Tables

In thermodynamics, vapor tables are essential tools for analyzing properties of substances in various states, particularly when dealing with water or steam. These tables provide critical thermodynamic data that aid in the understanding and calculation of processes involving energy transfer. Vapor tables are divided into two main types: saturated tables and superheated tables, each serving a distinct purpose in determining state properties.

properties of saturated steam:

Saturated tables are used when a substance exists as a mixture of liquid and vapor at equilibrium. These tables are divided into two sections: saturated liquid and saturated vapor. They provide key state properties, such as temperature, pressure, specific volume, enthalpy, and entropy at the phase-change boundary. To use saturated tables, one must know either the pressure or temperature of the system. For instance, if the pressure is known, one can locate the corresponding temperature, and then reference the enthalpy (hf, hfg, or hg) or specific volume values depending on the desired phase (liquid, vapor, or a mixture).

In thermodynamic analysis, particularly concerning phase change processes in fluids, the concepts of specific enthalpy, internal energy, and entropy play crucial roles. When dealing with saturated mixtures of liquid and vapor, the dryness fraction (x), which represents the mass ratio of vapor to the total mass of the mixture, is pivotal in deriving these thermodynamic properties. The following discourse outlines the relevant formulas necessary for calculating specific enthalpy, internal energy, and entropy from the dryness fraction in a saturated state.

Specific Enthalpy (h)

The specific enthalpy of a saturated mixture can be expressed as a function of the dryness fraction. The formula is formulated as follows:

$$h=h_f+x\cdot (h_g-h_f)$$

In this equation, $h_f$ denotes the specific enthalpy of the saturated liquid, and $h_g$ signifies the specific enthalpy of the saturated vapor. Here, $x$ varies between 0 (saturated liquid) and 1 (saturated vapor), enabling the representation of any mixture state.

Internal Energy (u)

Analogously, the specific internal energy of a saturated mixture is defined by the equation:

$$u=u_f+x\cdot (u_g-u_f)$$

In this formulation, $u_f$ refers to the specific internal energy of the saturated liquid, while $u_g$ is the specific internal energy of the saturated vapor. This formula similarly allows for the comprehensive characterization of the mixture state based upon the dryness fraction.

Entropy (s)

The calculation of specific entropy for a saturated mixture is similarly structured and can be articulated as follows:

$$s=s_f+x\cdot (s_g-s_f)$$

In this context, $s_f$ represents the specific entropy of the saturated liquid, and $s_g$ is the specific entropy of the saturated vapor. This relationship, like the previous formulas, facilitates the determination of entropy for any state of the saturated mixture, contingent upon the value of the dryness fraction $x$.

properties of superheated vapor:

Superheated tables, on the other hand, apply to a substance in the vapor state beyond the saturation point. These tables are organized by pressure levels and include properties such as temperature, specific volume, enthalpy, and entropy. When using superheated tables, it is necessary to identify both the pressure and temperature of the superheated vapor to interpolate the desired values. This is commonly encountered in processes like steam turbines, where steam often operates above its saturation point.

The study of thermodynamics entails various parameters that characterize the energetic state of substances. Among these parameters, specific enthalpy (h), internal energy (u), and entropy (s) play crucial roles, particularly in the analysis of superheated states. A superheated vapor is a phase in which a substance exists above its boiling point at a given pressure, and its associated thermodynamic properties can be derived from established formulations.

1. Specific Enthalpy (h)

The specific enthalpy of a superheated vapor can be calculated using the formula:

$$h=h_g+c_p\cdot (T-T_g)$$

Where $h_g$ represents the specific enthalpy of the saturated vapor at the same pressure, $c_p$ denotes the specific heat capacity at constant pressure, $T$ is the superheated temperature, and $T_g$ is the saturation temperature corresponding to the same pressure. This formula underlines that the specific enthalpy increases with temperature in the superheated domain.

2. Internal Energy (u)

The internal energy for a superheated vapor can be calculated with a similar approach, depicted by the equation:

$$u=u_g+c_v\cdot (T-T_g)$$

In this context, $u_g$ is the specific internal energy of the saturated vapor at the pressure in question, while $c_v$ signifies the specific heat capacity at constant volume. This expression highlights that, like enthalpy, the internal energy is also a function of temperature changes relative to the saturation state.

3. Entropy (s)

Entropy, an essential thermodynamic property, can also be derived for superheated vapors as follows:

$$s=s_g+\frac{c_p}{T}\cdot (T-T_g)$$

Here, $s_g$ is the specific entropy of the saturated vapor, and the term $c_p\mathrm{/}T$ reflects the change in entropy per unit temperature variation. The equation illustrates that the entropy increases with the addition of heat to the superheated vapor, which is consistent with the second law of thermodynamics.

To effectively use vapor tables, it is critical to first determine whether the substance is in a saturated, superheated, or compressed state. Accurate input parameters, such as pressure and temperature, ensure appropriate selection of the table. For intermediate values, interpolation is frequently required to achieve precise thermodynamic calculations.

In conclusion, saturated and superheated tables are indispensable resources for analyzing and solving thermodynamic problems. A methodical approach to identifying the state of the substance and referencing the correct table allows engineers and scientists to extract valuable information for system analysis and design. Understanding these tools is fundamental in advancing efficiency and precision in thermodynamic applications.