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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Sprache: Englisch
The perfect primer for anyone responsible for operating or maintaining process gas compressors. Gas compressors tend to be the largest, most costly, and most critical machines employed in chemical and gas transfer processes. Since they tend to have the greatest effect on the reliability of processes they power, compressors typically receive the most scrutiny of all the machinery among the general population of processing equipment. To prevent unwanted compressor failures from occurring, operators must be taught how their equipment should operate and how each installation is different from one another. The ultimate purpose of this book is to teach those who work in process settings more about gas compressors, so they can start up and operate them correctly and monitor their condition with more confidence. Some may regard compressor technology as too broad and complex a topic for operating personnel to fully understand, but the author has distilled this vast body of knowledge into some key, easy to understand lessons for the reader to study at his or her own pace. This groundbreaking new work is a must-have for any engineer, operator, or manager working with process compressors. The main goals of this book are to: * Explain important theories and concepts about gases and compression processes with a minimum of mathematics * Identify key compressor components and explain how they affect reliability * Explain how centrifugal compressors, reciprocating compressors, and screw compressors function. * Explain key operating factors that affect reliabilityIntroduce the reader to basic troubleshooting methodologies * Introduce operators to proven field inspection techniques * Improve the confidence of personnel operating compressors by teaching them the basics of compressor theory * Improve compressor reliability plantwide by teaching operating and inspection best practices * Improve communication between operating and supporting plant personnel by providing a common vocabulary of compressor terms * Help processing plants avoid costly failures by teaching operators how to identify early compressor issues during field inspections
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Contents
Cover
Title page
Copyright page
Dedication
Acknowledgements
Preface
Chapter 1: Introduction to Gases
1.1 Ideal Gases
1.2 Properties of Gases
1.3 Temperature
1.4 Pressure
1.5 Gas Laws
1.6 Gas Mixtures
1.7 Molecular Weight of a Gas Mixture
1.8 Gas Density
1.9 Density of Mixtures
1.10 Heat of Compression
Chapter 2: Commonly Used Compressor Flow Terms
2.1 Ideal Gas Law
2.2 Visualizing Gas Flow
2.3 Compressibility Factor (Z)
2.4 Sizing Compressors
Chapter 3: Compression Processes
3.1 Adiabatic Compression
3.2 Polytropic Compression
Chapter 4: What Role the Compression Ratio Plays in Compressor Design and Selection
4.1 Compression Ratio versus Discharge Temperature
4.2 Design Temperature Margin
Chapter 5: An Introduction to Compressor Operations
5.1 Compression Basics
5.2 Defining Gas Flow
5.3 Compressor Types
5.4 Multistaging
5.5 Key Reliability Indicators
Chapter 6: Centrifugal Compressors
6.1 Centrifugal Compressor Piping Arrangements
6.2 Start-Up Configuration
6.3 Centrifugal Compressor Horsepower
6.4 Troubleshooting Tips
6.5 Centrifugal Compressor Start-Ups
6.6 Centrifugal Compressor Checklist
Chapter 7: How Process Changes Affect Centrifugal Compressor Performance
7.1 Baseball Pitcher Analogy
7.2 How Gas Density Affects Horsepower
7.3 Theory versus Practice
Chapter 8: How to Read a Centrifugal Compressor Performance Map
8.1 The Anatomy of a Compressor Map
8.2 Design Conditions
Chapter 9: Keeping Your Centrifugal Compressor Out of Harm’s Way
9.1 Compressor Operating Limits
9.2 Compressor Flow Limits
9.3 Critical Speeds
9.4 Horsepower Limits
9.5 Temperatures
Chapter 10: Troubleshooting Centrifugal Compressors in Process Services
10.1 The Field Troubleshooting Process—Step by Step
10.2 The “Hourglass” Approach to Troubleshooting
10.3 Thinking and Acting Globally
10.4 Troubleshooting Matrix and Table
10.5 Centrifugal Compressor Troubleshooting Example
Chapter 11: Reciprocating Compressors
11.1 Reciprocating Compressor Installations
11.2 Reciprocating Compressor Start-Ups
11.3 Reciprocating Compressor Checklist
11.4 Criticality
Chapter 12: Troubleshooting Reciprocating Compressors in Process Services
12.1 The Field Troubleshooting Process—Step by Step
Chapter 13: Screw Compressors
13.1 Oil Injected Screw Compressors
13.2 Screw Compressor Modulation
13.3 Pressure Pulsation Issues
13.4 Troubleshooting Screw Compressors
Chapter 14: Compressor Start-Up Procedures
14.1 Compressor Start-Up Risks
14.2 Generic Start-Up Procedure
14.3 Centrifugal Compressor Start-Ups
14.4 Reciprocating Compressor Start-Ups
14.5 Screw Compressor Start-Ups
Chapter 15: Compressor Trains: Drivers, Speed Modifiers, and Driven Machines
15.1 Driven Process Machines
15.2 Gas Turbines
15.3 Useful Gearbox Facts
15.4 Combination Machines
Chapter 16: Compressor Components
16.1 Bearing Types
16.2 Rolling Element Bearings
16.3 Plain Bearings
16.4 Compressor Bearings
16.5 Modeling Fluid Film Bearings
16.6 Thrust Loads
16.7 Kingsbury Thrust Bearing
16.8 Compressor Seals
16.9 Seal Oil System
16.10 Dry Gas Seals
16.11 Seal Gas Quality and Control
16.12 Reciprocating Compressors – Packing
Chapter 17: The Importance of Lubrication
17.1 Lubrication Regimes
17.2 Lubricating Oils
17.3 Compressor Lubricating Oil Systems
17.4 Oil Foaming
Chapter 18: Inspection Ideas for Operators and Field Personnel
18.1 Equipment Field Inspections
18.2 Tools Available to Quantify What You Have Detected
18.3 Visual Inspection Methods
18.4 IR Camera
18.5 Inspection Methods Using Vibration and Temperature Measurement Equipment
18.6 Generic Monitoring Guidelines
Chapter 19: Addressing Reciprocating Compressor Piping Vibration Problems: Design Ideas, Field Audit Tips, and Proven Solutions
19.1 Piping Restraints
19.2 Pipe Clamping Systems
19.3 Guidelines
19.4 Piping Assessment Steps
19.5 Attaching Pipe Clamps to Structural Members
Chapter 20: Collecting and Assessing Piping Vibration
20.1 Piping Analysis Steps
20.2 Piping Vibration Examples
Appendix A: Practice Problems Related to Chapters 1 Through 4 Topics
Appendix B: Glossary of Compressor Technology Terms
Index
End User License Agreement
Guide
Cover
Copyright
Table of Contents
Begin Reading
List of Illustrations
Chapter 1
Figure 1.1
Gas atoms or molecules are constantly moving and colliding with one another.
Figure 1.2
As gas is compressed, the gas molecules get closer together.
Figure 1.3
Oxygen, nitrogen, and carbon monoxide are examples of diatomic molecules. Carbon...
Figure 1.4
Starting with a piston having a given pressure and volume (far right piston)...
Figure 1.5
Dalton’s law of partial pressures.
Figure 1.6
Molecular structure of methane, ethane, and propane.
Figure 1.7
Air fin cooler, which is located on the far right of the skid, provides interstage...
Figure 1.8
Schematic of a two-stage reciprocating compressor with an intercooler between...
Chapter 2
Figure 2.1
Centrifugal Compressor in a Petrochemical Facility.
Figure 2.2
Hypothetical compressor piping system.
Figure 2.3
The three main categories of gas compressors: Screw, Reciprocating, and Centrifugal...
Chapter 3
Figure 3.1
The ideal gas laws cannot be used to predict compressor performance.
Figure 3.2
Reciprocating compressors’ performance can be approximated using the...
Figure 3.3
Pressure versus stroke diagram for a reciprocating compressor.
Figure 3.4
Centrifugal compressor performance can be approximated using polytropic formula.
Chapter 4
Figure 4.1
Skid mounted reciprocating compressor.
Figure 4.2
How the theoretical discharge temperature is affected by the compressor discharge...
Chapter 5
Figure 5.1
During the gas compression process, a volume of gas is decreased in order to...
Figure 5.2
Compressor schematic.
Figure 5.3
Basic compressor designs.
Figure 5.4
Cross section of a reciprocating compressor.
Figure 5.5
Rotary screw compressor.
Figure 5.6
Multistage centrifugal compressor.
Chapter 6
Figure 6.1
Centrifugal compressor cutaway.
Figure 6.2
Compressor rotor inside of a split casing. Notice that every impeller exit...
Figure 6.3
Labyrinth seals are used to minimize gas leakage between stages.
Figure 6.4
Cross section of centrifugal compressor.
Figure 6.5
Centrifugal Compressor Performance Curve. There is a performance curve for...
Figure 6.6
Typical single-stage compressor piping arrangement.
Chapter 7
Figure 7.1
Pitcher throws a baseball towards the batter’s box.
Figure 7.2
Cross section of a centrifugal compressor showing the impeller and diffusers.
Figure 7.3
Technically, the creation of gas pressure inside a compressor is best explained...
Chapter 8
Figure 8.1
A cutaway of a centrifugal compressor showing the rotor and diffusers.
Figure 8.2
Generalized high-pressure compressor map.
Figure 8.3
Typical high-pressure compressor map.
Figure 8.4
Typical centrifugal compressor surge control system.
Chapter 9
Figure 9.1
Multistage centrifugal compressor rotor.
Figure 9.2
Centrifugal compressor operating limits. This compressor curve represents...
Figure 9.3
Typical Centrifugal Compressor Surge Control System.
Figure 9.4
Here is a typical predicted forced response plot. The upper plot is the 1x...
Chapter 10
Figure 10.1
Hourglass approach. Funnel—pertinent data collection. Focus—analysis...
Chapter 11
Figure 11.1
Reciprocating compressor cylinder cross section.
Figure 11.2
A crankshaft is a subcomponent of a reciprocating compressor that converts...
Figure 11.3
The upper plot, comprised of points A, B, C, D, shows how the pressure changes...
Figure 11.4
There are many different types of reciprocating compressor valves. The one shown...
Figure 11.5
Valve unloaders can be used to partially unload or fully unload a reciprocating...
Figure 11.6
A volume unloader can either increase the volumetric efficiency (VE) of a...
Figure 11.7
Finger type unloaders hold a valve open to prevent the valve from working normally.
Figure 11.8
Multistage reciprocating compressor piping arrangement.
Chapter 13
Figure 13.1
Typical screw compressor rotors.
Figure 13.2
Flow and pressure range comparison of screw, reciprocating, and centrifugal...
Figure 13.3
Screw compressor compression process.
Figure 13.4
Types of screw compressors.
Figure 13.5
Oil-flooded screw compressor.
Figure 13.6
Oil-flooded screw compressor package.
Figure 13.7
An internal slide valve is used to modulate screw compressor flow.
Figure 13.8
Combination silencer.
Chapter 15
Figure 15.1
An electric motor directly coupled to a reciprocating compressor.
Figure 15.2
AC induction motor.
Figure 15.3
Cross-section of single-stage turbine and governor system.
Figure 15.4
Industrial gas turbine: The air compressor is on the right and the combustion...
Figure 15.5
Reciprocating compressor driven by a natural gas engine.
Figure 15.6
Gearbox.
Figure 15.7
Turboexpander unit removed from service. The compressor end is on the left side...
Chapter 16
Figure 16.1
Types of bearings.
Figure 16.2
Different types of rolling element bearings.
Figure 16.3
Cutaway of a plain (journal) bearing and shaft.
Figure 16.4
Tilting pad bearing.
Figure 16.5
Here are some of the many fluid film bearings available to turbomachinery...
Figure 16.6
Balance piston or drum.
Figure 16.7
Kingsbury thrust bearing.
Figure 16.8
Labyrinth seal.
Figure 16.9
Oil bushing seal.
Figure 16.10
To prevent process gas from leaking, the seal oil pressure must always be maintained...
Figure 16.11
Compressor face seal.
Figure 16.12
Dry gas compressor seal.
Figure 16.13
Typical reciprocating compressor packing box.
Chapter 17
Figure 17.1
Boundary lubrication.
Figure 17.2
Full fluid lubrication.
Figure 17.3
The rotation of a journal within a journal bearing creates a wedge-shaped oil...
Figure 17.4
Typical compressor lube oil system.
Figure 17.5
How oil appearance can change as it becomes contaminated. Remember to look for...
Figure 17.6
Oil Foaming.
Chapter 18
Figure 18.1
Operators inspecting an electric motor in the field.
Figure 18.2
Over-lubricated bearing.
Figure 18.3
Infrared temperature gun.
Figure 18.4
IR camera picture.
Figure 18.5
Pocket strobe light.
Figure 18.6
Technician using vibration meter with an accelerometer.
Figure 18.7
Vibration trend example.
Figure 18.8
Temperature trend.
Chapter 19
Figure 19.1
Operators must remain vigilant around reciprocating compressors and their associated...
Figure 19.2
If fundamental (1x) or harmonics (2x, 3x, etc.) pulsation frequencies acting on...
Figure 19.3
(a) Pipe clamp with liner material on the clamp ID and on pipe wedges. (b) Properly...
Figure 19.4
Some typical small-bore piping designs that can result in excessive vibration...
Figure 19.5
PSV support off a main piping.
Figure 19.6
Pipe clamp with integral spacers using cap screws.
Figure 19.7
A properly installed pipe clamp bolted to a concrete pier. Notice that there is...
Figure 19.8
Correctly installed pipe clamps on concrete footing.
Figure 19.9
An incorrectly installed pipe clamp. Notice that with the clamp bottomed out...
Figure 19.10
There is insufficient clamping force on this clamp due to the loss of wedge...
Chapter 20
Figure 20.1
Piping assessment chart (Based on Engineering Dynamics Inc. (EDI) guidelines).
Figure 20.2
Mag-mounted tri-axial accelerometer on a pipe.
Figure 20.3
Mag-mounted tri-axial accelerometer on a valve.
Figure 20.4
Waterfall Display of Piping Vibration.
Appendix A
Figure A.1
Gas compressed with a piston.
Figure A.2
How gas volume varies with pressure.
Figure A.3
The molecular structure of propane.
Figure A.4
Reciprocating compressor spillback line and cooler schematic.
Figure A.5
Two stage reciprocating compressor installation.
Figure A.6
Electric motor driven reciprocating compressor.
Figure A.7
Centrifugal barrel compressor.
List of Tables
Chapter 1
Table 1.1
Composition of methane.
Table 1.2
Molecular weights of some common hydrocarbons. Compare the chemical formulas in...
Table 1.3
Calculating the molecular weight of a gas mixture.
Chapter 2
Table 2.1
Below Summarizes the Change in Volumetric Flow Rates at These Conditions.
Table 2.2
Compressor Coverage Table (English Units)
(1)
.
Table 2.3
Compressor Coverage Table (Metric Units).
Chapter 3
Table 3.1
Below contains K values for some common gases.
Chapter 4
Table 4.1
Below contains K values for some common gases.
Table 4.2
The Effect of discharge pressure on the theoretical discharge temperature.
Chapter 5
Table 5.1
Compression ratio ranges.
Chapter 7
Table 7.1
The Weights and weight ratios (ball weight/foam ball weight) of various types...
Table 7.2
How deviations from design conditions affect centrifugal compressor performance.
Chapter 10
Table 10.1
Key troubleshooting questions.
Table 10.1a
Centrifugal compressor troubleshooting matrix example.
Table 10.1b
Centrifugal compressor troubleshooting matrix.
Table 10.1c
Centrifugal compressor troubleshooting tips.
Chapter 11
Table 11.1
How process conditions affect reciprocating compressor performance. Note: The...
Chapter 12
Table 12.1
Basic troubleshooting questions.
Table 12.2a
Reciprocating compressor troubleshooting matrix.
Table 12.2b
Reciprocating compressor troubleshooting matrix.
Table 12.2c
Reciprocating compressor troubleshooting tips.
Chapter 13
Table 13.1
How process conditions affect screw compressor performance. Note: The results...
Chapter 14
Table 14.1
Recommended Compressor Inspection.
Chapter 15
Table 15.1
Common Types of Process Machinery Elements.
Appendix A
Table A.1
Composition of methane.
Table A.2
Table A.3
Compressor Coverage Table (English Units)
(1)
.
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Scrivener Publishing100 Cummings Center, Suite 541JBeverly, MA 01915-6106
Publishers at ScrivenerMartin Scrivener ([email protected])Phillip Carmical ([email protected])
Operator’s Guide to Process Compressors
Robert X. Perez
This edition first published 2019 by John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA and Scrivener Publishing LLC, 100 Cummings Center, Suite 541J, Beverly, MA 01915, USA© 2019 Scrivener Publishing LLCFor more information about Scrivener publications please visit www.scrivenerpublishing.com.
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Library of Congress Cataloging-in-Publication Data
ISBN 978-1-119-58061-4
Dedication
I would like to dedicate this book to process operators around the world. In my view, they never get the recognition they deserve for their long hours and dedication to their critical machinery. Without them, safe and profitable unit operations would not be possible.
Acknowledgements
I would like to thank my wife Elaine for carefully reading and editing the various versions of my manuscript. I also want to acknowledge David Lawhon for performing a thorough technical review of my manuscript and providing valuable feedback that enabled me to improve the book’s overall content and readability. Special thanks go out to Julien LeBleu for providing content for “The Importance of Lubrication” and “Inspection Technique Available to Operators and Field Personnel” book chapters.
Preface
Gas compressors are installed in most large processing facilities. They are designed to transport gases between different locations in processing units by compressing them from a lower pressure to a higher one using some type of driver, such as an electric motor, a steam turbine, a gas turbine, etc. The process of gas compression requires that compressors be designed to handle high gas pressures, high operating temperatures, high rotational speeds, and the high component stress levels. Through their gradual technological evolution, compressors have become highly reliable and safe machines, when properly maintained and operated as intended by their designers.
Gas compressors tend to be the largest, most costly, and most critical machines employed in chemical and gas transfer processes. The most common types of compressors are centrifugal compressors, reciprocating compressors, and screw compressors. Since they tend to have the greatest effect on the reliability of processes they power, compressors typically receive the most scrutiny of all the machinery among the general population of processing equipment.
Today, there appears to be a need in industry for a review of the best in class operating methods and procedures for compressors. As the previous generation of operators retire or move on, much of the knowledge that was gained over the past years has been forgotten or lost. The attrition of experience we have all experienced in recent years has resulted in the recurrence of reliability problems that have already been solved. To prevent unwanted compressor failures from occurring, operators must be taught how the equipment should operate and how each is different from one another.
The ultimate purpose of this book is to teach those who work in process settings more about gas compressors, so they can start them up and operate them correctly and monitor them with more confidence. Some may regard compressor technology as too broad and complex a topic for operating personnel to fully understand, but I have tried to address this concern by distilling this vast body of knowledge into some key, easy to understand lessons for the reader to study at his or her own pace. My hope is that learning more about how compressors work and the factors that are key to their reliability, compressor operators can keep them running longer and more reliably.
The main goals of this book are to:
Explain important theories and concepts about gases and compression processes with a minimum of mathematics
Identify key compressor components and explain how they affect reliability
Explain how the different types of compressors function
Explain key operating factors that affect reliability
Introduce the reader to basic troubleshooting methodologies
Introduce operators to proven field inspection techniques
I hope that readers find this book useful as they progress through their careers. I recommend that occasionally readers review the book’s content to refresh their knowledge of compressors.
Always keep learning and questioning your assumptions and paradigms. I think the following quotation explains why it’s important to change your point of view from time to time:
“Your assumptions are your windows on the world. Scrub them off every once in a while, or the light won’t come in.”
— Isaac Asimov
Robert X. PerezSpring, 2019
Chapter 1Introduction to Gases
Gases represent a state of matter that has no fixed shape or fixed volume, which consist of tiny, energetic particles, i.e., atoms or molecules, that are widely spaced (Figure 1.1). Compared to the other states of matter, solids and liquids, gases have a much lower density, i.e., they have a small mass per unit volume, because there is a great deal of empty space between gas particles. At room temperature and pressure, the gas inside a container occupies only 0.1% of the total container volume. The other 99.9% of the total volume is empty space (whereas in liquids and solids, about 70% of the volume is occupied by particles). Gas particles move very fast and collide with one another, causing them to diffuse, or spread out, until they are evenly distributed throughout the volume of their container. You will never see only half of a balloon filled with air.
Figure 1.1 Gas atoms or molecules are constantly moving and colliding with one another.
Although both liquids and gases take the shape of their containers, gases differ from liquids in that there is so much space between gas molecules that they offer little resistance to motion and can be compressed to smaller and smaller volumes. As seen in Figure 1.2, as a gas is compressed, the molecules making up the gas get closer together and create a higher internal pressure.
Figure 1.2 As gas is compressed, the gas molecules get closer together.
Hydrogen is the lightest known gas. Any balloon filled with hydrogen gas will float in air if the total mass of its container is not too great. Helium gas is also lighter than air and has 92% of the lifting power of hydrogen. Today all airships, i.e., blimps, use helium instead of hydrogen because it offers almost the same lifting power and is not flammable.
Gases can be monatomic, diatomic, and polyatomic. Monatomic gases are gases composed of single atoms, diatomic gases are those composed of two atom molecules, and polyatomic gases are those made up of molecules with more than two atoms. Noble gases such as helium, neon, argon, etc., are normally found as single atoms, since they are chemically inert. Gases such as nitrogen (N2), oxygen (O2), and carbon monoxide (CO) tend to be found as diatomic molecules (Figure 1.3). Carbon dioxide (CO2), and methane (CH4) are examples of polyatomic gas molecules (Figure 1.3).
Figure 1.3 Oxygen, nitrogen, and carbon monoxide are examples of diatomic molecules. Carbon dioxide, water, nitrogen monoxide, methane, sulfur dioxide, and ozone are examples of polyatomic molecules.
Gases can be found all around us. In fact, the earth’s atmosphere is a blanket of gases composed of nitrogen (78%), oxygen (21%), argon (1%), and then trace amounts of carbon dioxide, neon, helium, methane, krypton, hydrogen, nitrous oxide, xenon, ozone, iodine, carbon monoxide, and ammonia.
Because of the large distances between gas particles, the attractions or repulsions among them are weak. The particles in a gas are in rapid and continuous motion. For example, the average velocity of nitrogen molecules, N2, at 68 °F is about 1640 ft/s. As the temperature of a gas increases, the particles’ velocity increases. The average velocity of nitrogen molecules at 212 °F is about 1886 ft/s. The particles in a gas are constantly colliding with the walls of the container and with each other. Because of these collisions, the gas particles are constantly changing their direction of motion and their velocity. In a typical situation, a gas particle moves a very short distance between collisions. For example, oxygen, O2, molecules at normal temperatures and pressures move an average of 0.000003937 inches between collisions.
1.1 Ideal Gases
Scientists often simplify the model of gases by imagining the behavior of an ideal gas. An ideal gas differs from a real gas in that the particles are assumed to be point masses, that is, particles that have a mass but occupy no volume. It is also assumed that there are no attractive or repulsive forces at all between the particles. When all these assumptions are incorporated into a gas model, the “ideal gas model” is obtained. As the name implies, the ideal gas model describes an “ideal” of gas behavior that is only approximated by reality. Nevertheless, the model has been proven to reasonably explain and predict the behavior of typical gases under typical conditions.
Note: Under ordinary conditions, the properties of gases predicted by the ideal gas law are within 5% of their actual values.
1.2 Properties of Gases
The ideal gas model is used to predict changes in four related gas properties: volume, number of particles, temperature, and pressure. Volumes of gases are usually described in cubic feet, ft3, or cubic meters, m3, and numbers of particles are usually described in moles.
1.3 Temperature
Temperature is a physical quantity expressing how hot or cold a system of atoms or physical object is. Technically, temperature is the proportional measure of the average kinetic energy related to the random motions of the constituent particles of matter in a system. Temperature is an important property of a system because it is an indication of the direction in which heat energy will spontaneously flow. Remember that heat energy always flows from a hotter body (one at a higher temperature) to a colder body (one at a lower temperature).
Temperature is a measure of the total heat energy in a system.
Gas temperatures can be measured with thermometers, infrared guns, and thermocouples. Readings can be reported in degrees Fahrenheit, °F, or Celsius, °C. However, engineers generally use Rankine, or Kelvin temperatures for calculations.
1.4 Pressure
Remember that gases have no definite shape or volume; they tend to fill whatever container they are in. They can compress and expand and have extremely low densities when compared to a liquid or solid. Combinations of gases tend to mix together spontaneously; that is, they form gas mixtures. Air, for example, is a solution of mostly nitrogen and oxygen. Any understanding of the properties of gases must be able to explain the properties of gas mixture.
The kinetic theory of gases indicates that gas particles are always in motion and are colliding with other particles and the walls of the container holding them. Although collisions with container walls are elastic (i.e., there is no net energy gain or loss because of the collision), a gas particle does exert a force on the wall during the collision. Each time a gas particle collides with and ricochets off one of the walls of its container, it exerts a tiny force against the wall. The accumulation of all these forces distributed over the area of the walls of the container causes something we call pressure. Pressure (P) is defined as the force of all the gas particle-wall collisions divided by the area of the wall:
In English units, pressure is measured in psi, or pounds per square in. The formal, SI-approved unit of pressure is the pascal (Pa), which is defined as 1 N/m2 (one newton of force over an area of one square meter). However, this is usually too small in magnitude to be useful. A common unit of pressure is the atmosphere (atm), which was originally defined as the average atmospheric pressure at sea level.
1.5 Gas Laws
When seventeenth-century scientists began studying the physical properties of gases, they noticed simple relationships between some of the measurable properties of gases. For example, scientists noted that for a given quantity of gas, usually expressed in units of moles, i.e., number of molecules [n] in a system, if the temperature (T) of the gas is kept constant, pressure and volume are related: as one variable increases, the other variable decreases. Conversely, as one variable decreases, the other variable increases. Therefore, we say that pressure and volume are inversely related.
take pressure (P) and volume (V), for example:
There is more to it, however: pressure and volume of a given amount of gas at a constant temperature are numerically related. If you take the pressure value and multiply it by the volume value, the product is a constant for a given amount of gas at a constant temperature:
(1.1)
If either volume or pressure changes while the amount and temperature stays the same, then the other property must change so that the product of the two properties still equals that same constant. That is, if the original conditions are labelled P1 and V1 and the new conditions are labelled P2 and V2, we have
(1.2)
where the properties are assumed to be multiplied together. Leaving out the middle part, we have simply:
(1.3)
This equation is an example of a gas law. A gas law is a simple mathematical formula that allows you to model, or predict, the behavior of a gas. This particular gas law is called Boyle’s Law, after the English scientist Robert Boyle, who first announced it in 1662. Figure 1.4 shows two representations of what Boyle’s Law describes.
Figure 1.4 Starting with a piston having a given pressure and volume (far right piston), the volume continuously decreases as the applied pressure increases. If you plot pressure (P) as a function of the volume (V) for a given amount of gas at a certain temperature, you will get a plot that looks like the one shown here.
Boyle’s law example:
A tire with a volume of 11.41 L (0.4029 ft3) reads 44 psia (pounds per square inch absolute) on the tire gauge. What is the new tire pressure if you compress the tire to a new volume of 10.6 L (0.3743 ft3)?
Answer:
First, we write out Boyle’s Law:
(1.4)
Solving for P2 we get:
