Equation of State of an Ideal Gas
The equation of state of an ideal gas is a mathematical relationship that describes the behavior of an ideal gas under different conditions of pressure, volume, and temperature. It is typically represented by the equation PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. This equation helps to predict and understand the properties of ideal gases.
7 Key excerpts on "Equation of State of an Ideal Gas"
eBook - ePub- A. D. Johnson(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
...Properties of fluids 12 12.1 Aims To define the equation of state for an ideal gas. To define the specific heats for an ideal gas and the relationship between them. To define the basic relationships for an ideal gas undergoing an adiabatic process. To explain the changes that take place during a two-phase process. To introduce the saturated conditions, dryness fraction and superheated conditions for a two-phase fluid. 12.2 Properties to be Considered Fluids and their properties have already been introduced in section 11.3. Fluids are defined by their physical state as: gases, liquids or vapours, and these defined states form the basis for the present chapter. Although the title of this chapter implies a study of all the properties necessary to define the state of a fluid, in reality it is proposed to concentrate on those properties necessary to analyse processes within a closed thermofluid system. These properties are: temperature, T (K) pressure, P (Pa) density, ρ (kg/m 3) internal energy, u (J/kg) enthalpy, h (J/kg). Viscosity is defined later in Chapter 14 in connection with flow of fluids through pipes and systems having friction. Since the study of these properties depends on the fluids being studied, it is proposed to consider the properties of gases separately from the properties of liquids and vapours. 12.3 Ideal Gases In order to simplify the analysis of. gases, it is necessary to introduce the concept of an ‘ideal gas’. Just as real situations have to be modelled in order for them to be analysed, so real gases are assumed to behave as ideal gases. Within reasonable limits this assumption is realistic and most gases behave close to the ideal within the range of temperatures and pressures found in most thermofluid situations. The concept of an ideal gas is one in which the physical matter within the gas is assumed to be in the form of spheres of negligible volume...
eBook - ePub- Gavin Whittaker, Andy Mount, Matthew Heal(Authors)
- 2000(Publication Date)
- Taylor & Francis(Publisher)
...The molecules or atoms which make up a gas interact only weakly with one another. They move rapidly, and collide randomly and chaotically with one another. The physical properties of an ideal gas are completely described by four parameters which, with their respective SI units are: • the amount of substance of which it is comprised, n, in moles; • the temperature of the gas, T, in Kelvin; • the pressure of the gas, p, in Pascal; • the volume occupied by the gas, V, in m 3. The four parameters are not independent, and the relations between them are expressed in the gas laws. The gas laws are unified into a single equation of state for a gas which fully expresses the relationships between all four properties. These relationships, however, are based on approximations to experimental observations, and only apply to a perfect gas. In what might be deemed a circular argument, a perfect gas is defined as one which obeys the perfect gas equation of state. In practical terms, however, adherence to the perfect gas equation of state requires that the particles which make up the gas are infinitesimally small, and that they interact only as if they were hard spheres, and so perfect gases do not exist. Fortunately, it is found that the behavior of most gases approximates to that of a perfect gas at sufficiently low pressure, with the lighter noble gases (He, Ne) showing the most ideal behavior. The greatest deviations are observed where strong intermolecular interactions exist, such as water and ammonia...
- Ali Danesh(Author)
- 1998(Publication Date)
- Elsevier Science(Publisher)
...Developments in Petroleum Science, Vol. 47, Suppl. (C), 1998 ISSN: 0376-7361 doi: 10.1016/S0376-7361(98)80026-5 4 Equations of State The equality of fugacity of each component throughout all phases was proved, in Chapter 3, to be the requirement for chemical equilibrium in multicomponent systems. The fugacity coefficient, φ i, defined as the ratio of fugacity to pressure, of each component in any phase is related to pressure, temperature and volume by Eq.(3.31), (3.31) The fugacity coefficient can, therefore, be determined from the above with the aid of an equation relating pressure, temperature, volume and compositions, that is, an equation of state (EOS). In general, any equation of state which provides reliable volumetric data over the full range of the integral in Eq.(3.31) can be used to describe the fluid phase behaviour. Several types of EOS have been successfully applied to hydrocarbon reservoir fluids. The simplest, and highly successful equation, is the semi-empirical van der Waals type EOS with two or three parameters. Since 1873, when van der Waals improved the ideal gas equation by including parameters that represented the attractive and repulsive intermolecular forces, the equation has been revised and modified by numerous investigators. Other equations with many parameters have also been used to describe the phase behaviour, some with reasonable success. Amongst these equations, the Benedict-Webb-Rubin (BWR) type[l], which is an empirical extension to the virial EOS, can be applied to both liquid and vapour phases of reservoir fluids. These equations provide no additional reliability in phase behaviour studies, in spite of their complexity, in comparison with the van der Waals type EOS...
eBook - ePubCompressors
Selection and Sizing
- Royce N. Brown(Author)
- 2011(Publication Date)
- Gulf Professional Publishing(Publisher)
...In the past, these equations required the use of a mainframe computer not only to solve the equations themselves, but to store the great number of constants required. This has been true particularly if the gas mixture contains numerous components. With the power and storage capacity of personal computers available, the equations have the potential of becoming more readily available for general use. The equations of state calculations are covered in more detail later in Chapter 2 in the section entitled “Real Gas Tools.” Mollier Charts Another form in which gas properties are presented is found in plots of pressure, specific volume, temperature, entropy, and enthalpy. The most common form, the Mollier chart, plots enthalpy against entropy. A good example of this is the Mollier chart for steam. Gases are generally plotted as pressure against enthalpy (P-h charts). These are also sometimes referred to as Mollier charts. The charts are readily available for a wide range of pure gases, particularly hydrocarbons and refrigerants. Some of the more common charts are included in Appendix B. First Law of Thermodynamics The first law of thermodynamics states that energy cannot be created or destroyed, although it may be changed from one form to another...
eBook - ePub- Kevin R. Reel(Author)
- 2013(Publication Date)
- Research & Education Association(Publisher)
...CHAPTER 3 The States of Matter CHAPTER 3 THE STATES OF MATTER GASES Ideal Gas Laws • Ideal gases are gases that behave according to an approximation that includes the following assumptions: 1. The volume of the gas molecule is negligible compared to the space between the molecules. 2. There is negligible intermolecular attraction between gas molecules. • The ideal gas approximation is most accurate for gases at low pressure and high temperature. • Under ideal conditions, the following laws hold true: Boyle’s Law • Boyle’s law states that the volume of a gas is inversely proportional to pressure, when temperature is constant. • This can be summarized by the following expression: Example: A 4.0-liter elastic weather balloon travels from sea level, at 1.0 atm pressure, to a higher altitude, where the pressure is 0.20 atm. What is the new volume of the balloon? Solution: Charles’s Law • Charles’s law states that the volume of a given amount of gas is directly proportional to temperature, when pressure is constant. • This can be summarized by the following expression: Example: A gas occupies 2.0 L at 300 K. What is the volume of the gas at 200 K, assuming that the pressure is constant? Solution: Laws of Gay-Lussac • The law of Gay-Lussac states that at constant volume, the pressure exerted by a given mass of gas varies directly with the absolute temperature. • This can be summarized by the following expression: Example: A gas in a rigid container exerts 6.0 atm at 300 K...
eBook - ePub- John Bird(Author)
- 2019(Publication Date)
- Routledge(Publisher)
...Chapter 32 Ideal gas laws Why it is important to understand: Ideal gas laws The relationships that exist between pressure, volume and temperature in a gas are given in a set of laws called the gas laws, the most fundamental being those of Boyle, Charles, and the pressure or Gay-Lussac’s law, together with Dalton’s law of partial pressures and the characteristic gas equation. These laws are used for all sorts of practical applications, including for designing pressure vessels, in the form of circular cylinders and spheres, which are used for storing and transporting gases. Another example of this is the pressure in car tyres, which can increase due to a temperature increase, and can decrease due to a temperature decrease. Other examples are large and medium size gas storage cylinders and domestic spray cans, which can explode if they are heated. In the case of domestic spray cans, these can explode dangerously in a domestic situation if they are left on a window sill where the sunshine acting on them causes them to heat up or, if they are thrown on to a fire. In these cases, the consequence can be disastrous, so don’t throw your ‘full’ spray can on to a fire; you may very sadly and deeply regret it! Another example of a gas storage vessel is that used by your ‘local’ gas companies, which supply natural gas (methane) to domestic properties, businesses, etc. At the end of this chapter, you should be able to: state and perform calculations involving Boyle’s law understand the term isothermal state and perform calculations involving Charles’ law understand the term isobaric state and perform calculations involving the pressure or Gay-Lussac law state and perform calculations on Dalton’s law of partial pressures state and perform calculations on the characteristic gas equation understand the term STP Science and Mathematics for Engineering. 978-0-367-2O475-4, © John Bird. Published by Taylor & Francis...
eBook - ePub- Nayef Ghasem(Author)
- 2021(Publication Date)
- CRC Press(Publisher)
...1 Thermodynamics and Fluid-Phase Equilibria DOI: 10.1201/9781003167365-1 At the end of this chapter, students should be able to: Estimate the vapor pressure of pure components. Determine the boiling point and dew point of a mixture. Estimate the molar volume using the equation of state (EOS). Plot the effect of temperature versus density. Use UniSim/Hysys, Aspen Plus, PRO/II, SuperPro, and Aveva Process Simulation software packages to estimate physical properties. 1.1 INTRODUCTION Phase-equilibrium thermodynamics deals with the relationships that govern the distribution of a substance between gas and liquid phases. When a species is transferred from one phase to another, the transfer rate decreases with time until the second phase is saturated with the species, holding as much as it can hold at the prevailing process conditions. When concentrations of all species in each phase cease to change, the phases are at phase equilibrium. When two phases are in contact, a redistribution of the components of each phase occurs through evaporation, condensation, dissolution, and precipitation until a state of equilibrium is reached in which the temperatures and pressures of both phases are the same, and the compositions of each phase no longer change with time. A species’ volatility is the degree to which the species tends to be transferred from the liquid phase to the vapor phase. The vapor pressure of a species is a measure of its volatility. Estimation of vapor pressure can be carried out by empirical correlation. When a liquid is heated slowly at constant pressure, the temperature at which the first vapor bubble forms is called bubble point temperature. When the vapor is cooled slowly at constant pressure, the temperature at which the first liquid droplet forms is known as dew point temperature. 1.2 BOILING POINT CALCULATIONS When heating a liquid consisting of two or more components, the bubble point is where the first formed bubble of vapor...
