Equation of State of an Ideal Gas

PSYCHROMETRICS

Psychrometrics is the study of the thermodynamic properties of moist air. It is used extensively to illustrate and analyze the characteristics of various air conditioning processes and cycles.

Moist Air

The surface of the earth is surrounded by a layer of air called the atmosphere, or atmospheric air. From the point of view of psychrometrics, the lower atmosphere, or homosphere, is a mixture of dry air (including various contaminants) and water vapor, often known as moist air. The composition of dry air is comparatively stable. It varies slightly according to geographic location and from time to time. The approximate composition of dry air by volume percent is the following:

The amount of water vapor present in moist air at a temperature range of 0 to 100°F (17.8 to 37.8°C) varies from 0.05 to 3 percent by mass. It has a significant influence on the characteristics of moist air. Water vapor is lighter than air. A cloud in the sky is composed of microscopic beads of liquid water that are surrounded by a thin layer of water vapor. These layers give the cloud the needed buoyancy to float in the air.

Equation of State of an Ideal Gas  

The equation of state of an ideal gas indicates the relationship between its thermodynamic properties, or

                                                     

Equation of State of a Real Gas 

A modified form of the equation of state for a real gas can be expressed as

where A, B, C, ...= virial coefficients and Z =  compressibility factor. The compressibility factor Z illustrates the degree of deviation of the behavior of the real gas, moist air, from the ideal gas due to the following: 

1. Effect of air dissolved in water

2. Variation of the properties of water vapor attributable to the effect of pressure 

3. Effect of intermolecular forces on the properties of water vapor itself  

For an ideal gas, Z= 1. According to the information published by the former National Bureau of Standards of the United States, for dry air at standard atmospheric pressure (29.92 in. Hg, or 760 mm Hg) and a temperature of 32 to 100°F (0 to 37.8°C) the maximum deviation is about 0.12 percent. For water vapor in moist air under saturated conditions at a temperature of 32 to 100°F (0 to 37.8°C), the maximum deviation is about 0.5 percent. 

Calculation of the Properties of Moist Air 

The most exact calculation of the thermodynamic properties of moist air is based on the formulations developed by Hyland and Wexler of the U.S. National Bureau of Standards. The psychrometric chart and tables of ASHRAE are constructed and calculated from these formulations. Calculations based on the ideal gas equations are the simplest and can be easily formulated. According to the analysis of Nelson and Pate, at a temperature between 0 and 100°F (-17.8 and 37.8°C), calculations of enthalpy and specific volume using ideal gas equations show a maximum deviation of 0.5 percent from the exact calculations by Hyland and Wexler. Therefore, ideal gas equations will be used in this text for the formulation and calculation of the thermodynamic properties of moist air. Although air contaminants may seriously affect the health of occupants of the air conditioned space, they have little effect on the thermodynamic properties of moist air since their mass concentration is low. For simplicity, moist air is always considered as a binary mixture of dry air and water vapor during the analysis and calculation of its properties.