Over the Christmas break I was browsing through the Guidebook for the Scientific Traveler: Visiting Physics and Chemistry Sites Across America, and it got me to wondering what sites a reader of the 4th edition of Intermediate Physics for Medicine and Biology might want to visit. Apparently having too much time on my hands, I devised a trip through the United States for our readers. (Perhaps I’ll prepare an international edition later.) The trip starts and ends in Rochester, Michigan, where I work, but the path consists of a large circle and you can begin anywhere. I have not visited all these places, but I know enough about them to suspect you would enjoy them all. Tell me if I have forgotten any important sites. Happy travels!
Oakland University in Rochester, Michigan. OU is home to Intermediate Physics for Medicine and Biology (IPMB) coauthor Brad Roth, in the Department of Physics. Here Roth collaborated with Russ Hobbie to prepare the 4th edition of IPMB.
Morrison, Illinois. Robert Millikan was born in Morrison, and a downtown park in this small town about 120 miles west of Chicago bears his name (although there is no sign or marker to indicate it). IPMB coauthor Brad Roth grew up in Morrison.
University of Minnesota, in Minneapolis, Minnesota. IPMB’s author Russ Hobbie worked at the University of Minnesota for years, and remains an emeritus faculty member in the Department of Physics and Astronomy. Stop by a visit him in nearby Saint Paul. While in Minneapolis, be sure to visit the Bakken Museum, perhaps the only museum in the country dedicated entirely to electricity and magnetism, and especially bioelectricity and biomagnetism, as discussed in Chapters 6–9 of IPMB. Earl Bakken was one of the founders of the medical device company Medtronic. Stop by at Medtronic's nearby Mounds View Bakken Education Center.
Vanderbilt University, in Nashville, Tennessee. IPMB coauthor Brad Roth attended graduate school at Vanderbilt, working with John Wikswo in the Department of Physics and Astronomy. There, they measured the magnetic field of a single nerve axon, as described in Chapter 8 of IPMB. IPMB author Russ Hobbie was a Visiting Professor at Vanderbilt in 1999. Max Delbruck, an early biological physicist who contributed to our understanding of genetics, performed many of his Nobel Prize winning experiments at Vanderbilt.
Framingham, Massachusetts. Visit the town that contributed more to uncovering the diseases of the heart than any other, through the Framingham Heart Study. Framingham is one of the few locations mentioned explicitly in IPMB, in Chapter 2.
Oakland University, in Rochester Michigan. Back to the starting point. Be sure to stop by Brad Roth’s office (166 Hannah Hall) and see his collection of all four editions of IPMB sitting on his bookshelf.
The American Association of Physicists in Medicine (AAPM) acknowledges that medical imaging procedures should be appropriate and conducted at the lowest radiation dose consistent with acquisition of the desired information. Discussion of risks related to radiation dose from medical imaging procedures should be accompanied by acknowledgement of the benefits of the procedures. Risks of medical imaging at effective doses below 50 mSv for single procedures or 100 mSv for multiple procedures over short time periods are too low to be detectable and may be nonexistent. Predictions of hypothetical cancer incidence and deaths in patient populations exposed to such low doses are highly speculative and should be discouraged. These predictions are harmful because they lead to sensationalistic articles in the public media that cause some patients and parents to refuse medical imaging procedures, placing them at substantial risk by not receiving the clinical benefits of the prescribed procedures.
AAPM members continually strive to improve medical imaging by lowering radiation levels and maximizing benefits of imaging procedures involving ionizing radiation.
The 4th edition of Intermediate Physics for Medicine and Biology discusses the risk of radiation in Section 16.13. Dose is the energy deposited by radiation in tissue per unit mass, and its unit of a gray is equal to one joule per kilogram. A sievert is also a J/kg, but it differs from a gray in that it includes a weighting factor that measures the relative biological effectiveness of the radiation, and is used to measure the equivalent dose (although often, including in the remainder of this blog entry, people get a little sloppy and just say “dose” when they really mean “equivalent dose”). A sievert is a rather large dose of radiation, and when discussing medical imaging or background radiation exposure, scientists often use the millisievert (mSv).
Table 16.7 of Intermediate Physics for Medicine and Biology lists typical radiation doses for many medical imaging procedures. For example, a simple chest X ray has a dose of about 0.06 mSv, and a CT scan is 1–10 mSv. The average radiation dose from all natural (background) sources is given in Table 16.6 as 3 mSv per year (primarily from exposure to radon gas). A pilot logging 1000 hours in the air per year receives on the order of 7 mSv annually.
Perhaps the most interesting sentence in the AAPM position statement is “Risks of medical imaging at effective doses below 50 mSv for single procedures or 100 mSv for multiple procedures over short time periods are too low to be detectable and may be nonexistent.” To me, the phrase “may be nonexistent” seems to cast doubt on the linear nonthreshold model often used when discussing the risk of low-dose radiation. Russ Hobbie and I discuss this model in Intermediate Physics for Medicine and Biology.
In dealing with radiation to the population at large, or to populations of radiation workers, the policy of the various regulatory agencies has been to adopt the linear-nonthreshold (LNT) model to extrapolate from what is known about the excess risk of cancer at moderately high doses and high dose rates, to low doses, including those below natural background.
We also consider other ideas, such as a threshold model for radiation effects and even hormesis, the idea that very low doses of radiation may be beneficial. The controversy over the biological effects of low-dose radiation is fascinating, but as best I can tell the validity of each of these models remains uncertain; getting accurate data when measuring tiny effects is difficult. I assume this is what motivates the word “may” in the phrase “may be nonexistent” from the position statement (although, I hasten to add, I have no inside information about the intent of the authors of the position statement—I’m just guessing). In our book, Russ and I come to a conclusion that is fairly consistent with the AAPM position statement.
Some investigators feel that there is evidence for a threshold dose, and that the LNT model overestimates the risk [Kathren (1996); Kondo (1993); Cohen (2002)]. Mossman (2001) argues against hormesis but agrees that the LNT model has led to ‘enormous problems in radiation protection practice’ and unwarranted fears about radiation.
Although I find the AAPM position statement to have a slightly condescending tone, I applaud it primarily as an antidote for those “unwarranted fears about radiation.” My impression is that many in the general public have a fear of the word radiation that borders on the irrational, stemming from a lack of knowledge about the basic physics governing how radiation interacts with tissue, and a poor understanding of risk analysis. I hope the AAPM position statement (and, immodestly, our textbook) helps change those concerns from irrational fears to reasoned and fact-based assessment. I would not discourage analysis of public safety, but I definitely encourage an intelligent and scientific analysis.
The journal Medical Physics is one of the leading publications in the field of physics applied to medicine. Recently, many articles in Medical Physics have become free to everyone (open access) (see the editorial here). This is great news to those readers of the 4th edition of Intermediate Physics for Medicine and Biology who do not have a personal or institutional subscription to Medical Physics. Some of the articles that can now be downloaded for free are the ever-popular point/counterpoint debates, review papers, award papers, and something called the “editor’s picks.” Also available free are the special 50th anniversary articles published as part of the celebration of half a century of contributions by the American Association of Physicists in Medicine in 2008. Several of these were cited by Russ Hobbie and me in our American Journal of Physics “Resource Letter MP-2: Medical Physics” (Volume 77, Pages 967–978, 2009). To access this wealth of free material, just go to the home page of the Medical Physicswebsite and click on the Open Access Tab.
Open Access to journal articles should benefit readers of Intermediate Physics for Medicine and Biology, because it will allow those readers immediate access to cutting-edge papers that otherwise would require a journal subscription. Another source of open access papers is BioMed Central:
BioMed Central is an independent publishing house committed to providing immediate open access to peer-reviewed biomedical research. All original research articles published by BioMed Central are made freely and permanently accessible online immediately upon publication. BioMed Central views open access to research as essential in order to ensure the rapid and efficient communication of research findings.
The Open Access movement continues, slowly but steadily, to remake scientific publication. There are now hundreds of Open Access journals. Even some of the most prestigious leading publishers are getting into the act: the American Physical Society recently initiated the open access, all on-line journal Physical Review X to go along with its other Physical Review journals.
In the spirit of Open Access, I’m pleased to announce that the 4th edition of Intermediate Physics for Medicine and Biology will now be given away, free of cha... just kidding. Maybe someday the Open Access movement will reach to textbooks, but not yet. At least this blog is free. ;)
The book tells the fascinating story of Garfield’s nomination at the Republican National Convention in 1880, back in a time when conventions were less choreographed and predictable than they are today. Garfield nominated his fellow Ohioan John Sherman (General William Tecumseh Sherman’s brother), who was running against Senator James Blaine and former president Grant. After many ballots in which no nominee obtained a majority, the delegates turned to Garfield as their compromise choice. After being chosen the Republican nominee, he defeated Democrat and former Civil War general Winfield Scott Hancock in the general election.
A few months after being sworn in, Garfield was shot by Guiteau, who had applied for a job in the new administration but had been turned down. The bullet did not kill Garfield immediately, and he lingered on for weeks. At this point, medical physics enters the story through one of the book’s subplots about the career of Alexander Graham Bell, inventor of the telephone. Millard tells the tale of how Bell set up one of his early telephones for demonstration at the 1876 Centennial Exposition, but was ignored until a chance meeting with his acquaintance, Emperor Pedro II of Brazil, who drew attention to Bell’s display. Upon hearing that the President had been shot, Bell quickly invented a metal detector with the goal of locating the bullet still lodged in Garfield’s abdomen. The detector is based on the principle of electromagnetic induction, discussed in Section 8.6 of the 4th edition of Intermediate Physics for Medicine and Biology. A changing magnetic field induces eddy currents in a nearby conductor. These eddy currents produce their own magnetic field, which is then detected. Essentially, the device monitored changes in the inductance of the metal detector caused by the bullet. Such metal detectors are now common, particularly for nonmedical uses such as searching for metal objects buried shallowly in the ground. At the time, the device was rather novel. Michael Faraday (and, independently, Joseph Henry) had discovered electromagnetic induction in 1831, and Maxwell’s equations summarizing electromagnetic theory were formulated by James Maxwell in 1861, only twenty years before Garfield’s assassination. Being a champion of medical and biological physics, I wish I could say that Bell’s invention saved the president’s life, or at least had a positive effect during his treatment. Unfortunately, it did not, in part because of interference from metal springs in the mattress Garfield laid on, but mainly because the primary physician caring for Garfield, Dr. Willard Bliss, insisted that Bell only search the right side of the body where he believed the bullet was located, when in fact it was on the unexplored left side.
Another issue discussed in the book is the development of antiseptic methods in medicine, pioneered by Joseph Lister in the 1860s. Apparently the direct damage caused by the bullet was not life-threatening, and Millard suggests that if Garfield had received no treatment whatsoever for his wounds, he would have likely survived. Unfortunately, the doctors of that era, being skeptical or hostile to Lister’s new ideas, probed Garfield’s wound with various non-sterile instruments, including their fingers. Garfield died of an infection, possibly caused by these actions.
I enjoyed Millard’s book, and came away with a greater respect for President Garfield. Bell’s metal detector was used to locate bullets in injured soldiers throughout the rest of the 19th century, until X rays became the dominant method for finding foreign objects. It is an early example of the application of electricity and magnetism to medicine.
Problem 8 The obsolete unit, the roentgen (R), is defined as 2.08 x 109 ion pairs produced in 0.001 293 g of dry air. (This is 1 cm3 of dry air at standard temperature and pressure.) Show that if the average energy required to produce an ion pair in air is 33.7 eV (an old value), then 1 R corresponds to an absorbed does of 8.69 x 10-3Gy and that 1 R is equivalent to 2.58 x 10-4C kg-1.
Asimov's Biographical Encyclopedia of Science and Technology,
by Isaac Asimov.
…The great moment that lifted Roentgen out of mere competence and made him immortal came in the autumn of 1895 when he was head of the department of physics at the University of Wurzburg in Bavaria. He was working on cathode rays and repeating some of the experiments of Lenard and Crookes. He was particularly interested in the luminescence these rays set up in certain chemicals.
In order to observe the faint luminescence, he darkened the room and enclosed the cathode ray tube in thin black cardboard. On November 5, 1895, he set the enclosed cathode ray tube into action and a flash of light that did not come from the tube caught his eye. He looked up and quite a distance from the tube he noted that a sheet of paper coated with bariumplatinocyanide was glowing. It was one of the luminescent substances, but it was luminescing now even though the cathode rays, blocked off by the cardboard, could not possibly be reaching it.
He turned off the tube; the coated paper darkened. He turned it on again; it glowed. He walked into the next room with the coated paper, closed the door, and pulled down the blinds. The paper continued to glow while the tube was in operation…
For seven weeks he experimented furiously and then, finally, on December 28, 1895 [116 years ago this week], submitted his first paper, in which he not only announced the discovery but reported all the fundamental properties of X rays...
The first public lecture on the new phenomenon was given by Roentgen on January 23, 1896. When he had finished talking, he called for a volunteer, and Kolliker, almost eighty years old at the time, stepped up. An X-ray photograph was taken of this hand—which shows the bones in beautiful shape for an octogenarian. There was wild applause, and interest in X rays swept over Europe and America.
You can learn more about X rays in Chapter 15 (Interaction of Photons and Charged Particles with Matter) and Chapter 16 (Medical Use of X Rays) in Intermediate Physics for Medicine and Biology.
Problem 25Figure 1.20, showing a rod subject to a force along its length, is a simplification. Actually, the cross-sectional area of the rod shrinks as the rod lengthens. Let the axial strain and stress be along the z axis. They are related to Eq. 1.25, sz = E εz. The lateral strains εx and εy are related to sz by sz = - (E/ν) εx = -(E/ν) εy, where ν is called the “Poisson’s ratio” of the material. (a) Use the result of Problem 13 to relate E and ν to the fractional change in volume ΔV/V. (b) The change in volume caused by hydrostatic pressure is the sum of the volume changes caused by axial stresses in all three directions. Relate Poisson’s ratio to the compressibility. (c) What value of ν corresponds to an incompressible material? (d) For an isotropic material, -1 ≤ ν ≤ 0.5. How would a material with negative ν behave? Elliott et al. (2002) measured Poisson’s ratio for articular (joint) cartilage under tension and found 1 ≤ ν ≤ 2. This large value is possible because cartilage is anisotropic: Its properties depend on direction.
As hinted at in our homework problem, a particularly fascinating type of material has negative Poisson’s ratio. Some foams expand laterally, rather than contract, when you stretch them; see Roderic Lakes, “Foam Structures with a Negative Poisson’s Ratio,” Science, Volume 235, Pages 1038–1040, 1987. A model for such a material is shown in this video. Lakes’ website contains much interesting information about Poisson’s ratio. For instance, cork has a Poisson’s ratio of nearly zero, making it ideal for stopping wine bottles.
Simeon Denis Poisson (1781–1840) was a French mathematician and physicist whose name appears several times in Intermediate Physics for Medicine and Biology. Besides Poisson’s ratio, in Chapter 9 Russ and I present the Poisson equation in electrostatics, and its extension the Poisson-Boltzmann equation governing the electric field in salt water. Appendix J reviews the Poisson probability distribution. Finally, Poisson appeared in this blog before, albeit as something of a scientific villain, in the story of Poisson’s spot. Poisson is one of the 72 names appearing on the Eiffel Tower.
Differences in relaxation time are easily detected in an image. Different tissues have different relaxation times. A contrast agent containing gadolinium (Gd3+), which is strongly paramagnetic, is often used in magnetic resonance imaging. It is combined with many of the same pharmaceuticals used with 99mTc, and it reduces the relaxation time of nearby nuclei.
Gadolinium, an obscure lanthanide element buried in the middle of the periodic table, has in the course of a decade become commonplace in medical diagnostics.
Like platinum in cancer therapeutics and technetium in cardiac scanning, the unique magnetic properties of the gadolinium(III) ion placed it right in the middle of a revolutionary development in medicine: magnetic resonance imaging (MRI). While
it is odd enough to place patients in large superconducting magnets and noisily pulse water protons in their tissues with radio waves, it is odder still to inject into their veins a gram of this potentially toxic metal ion which swiftly floats among the water molecules, tickling them magnetically.
The successful penetration of gadolinium(III) chelates into radiologic practice and medicine as a whole can be measured in many ways. Since the approval of [Gd(DTPA)(H2O)]2- in 1988, it can be estimated that over 30 metric tons of gadolinium have been administered to millions of patients worldwide. Currently, approximately 30% of MRI exams include the use of contrast agents, and this is projected to increase as new agents and applications arise; Table 1 lists agents currently approved or in clinical trials. In the rushed world of modern medicine, radiologists, technicians, and nurses often refrain from calling the agents by their brand names, preferring instead the affectionate “gado.” They trust this clear, odorless 'magnetic light', one of the safest class of drugs ever developed. Aside from the cost ($50–80/bottle), asking the nurse to “Give him some gado” is as easy as starting a saline drip or obtaining a blood sample.
Gadolinium is also finding a place in medical research. When one of us reviewed the field in its infancy, in 1987, only 39 papers could be found for that year in a Medline search for “gado-” and MRI. Ten years later over 600 references appear each year. And as MRI becomes relied upon by different specialties, “gado” is becoming known by neurologists, cardiologists, urologists, opthamologists, and others in search of new ways to visualize functional changes in the body.
While other types of MRI contrast agents have been approved, namely an iron particle-based agent and a manganese(II) chelate, gadolinium(III) remains the dominant starting material. The reasons for this include the direction of MRI development and the nature of Gd chelates.
In Section 18.12 about Functional MRI, Russ and I again mention gadolinium.
Magnetic resonance imaging provides excellent structural information. Various contrast agents can provide information about physiologic function. For example, various contrast agents containing gadolinium are injected intravenously. They leak through a damaged blood-tissue barrier and accumulate in the damaged region. At small concentrations T1 is shortened.
The 4th edition of Intermediate Physics for Medicine and Biology has its own Facebook group, and any readers of this blog who use Facebook are welcome to join. One nice feature of Facebook is that is encourages comments, such as the recent one that asked “Why isn’t there a chapter or a subchapter in the textbook ‘Intermediate physics for medicine and biology’ that refers to the fundamental concepts of the cyclotron and the betatron and how are they used in medicine?” This is a good question, because undoubtedly cyclotrons are important in nuclear medicine. I can’t do anything to change the 4th edition of our book, but this blog provides an opportunity to address such comments, and to try out possible text for a 5th edition.
Although the term does not appear in the index (oops…), the cyclotron is mentioned in Intermediate Physics for Medicine and Biology at the end of Section 17.9 (Radiopharmaceuticals and Tracers).
Positron emitters are short-lived, and it is necessary to have a cyclotron for producing them in or near the hospital. This is proving to be less of a problem than initially imagined. Commercial cyclotron facilities deliver isotopes to a number of nearby hospitals. Patterson and Mosley (2005) found that 97% of the people in the United States live within 75 miles of a clinical PET facility.
(Note: on page 513 of our book, we omitted the word “emission” from the phrase “positron emission tomography” in the title of the Patterson and Mosley paper; again, oops…)
Perhaps the best place in Intermediate Physics for Medicine and Biology to discuss cyclotrons would be after Section 8.1 (The Magnetic Force on a Moving Charge). Below is some sample text that serves as a brief introduction to cyclotrons.
8.1 ½ The Cyclotron
One important application of magnetic forces in medicine is the cyclotron. Many hospitals have a cyclotron for the production of radiopharmaceuticals, or for the generation of positron emitting nuclei for use in Positron Emission Tomography (PET) imaging (see Chapter 17).
Consider a particle of charge q and mass m, moving with speed v in a direction perpendicular to a magnetic field B. The magnetic force will bend the path of the particle into a circle. Newton’s second law states that the mass times the centripetal acceleration, v2/r, is equal to the magnetic force
m v2/r = q v B . (8.4a)
The speed is equal to circumference of the circle, 2 π r, divided by the period of the orbit, T. Substituting this expression for v into Eq. 8.4a and simplifying, we find
T = 2 π m/(q B) . (8.4b)
In a cyclotron particles orbit at the cyclotron frequency, f = 1/T. Because the magnetic force is perpendicular to the motion, it does not increase the particles’ speed or energy. To do that, the particles are subjected periodically to an electric field that must change direction with the cyclotron frequency so that it is always accelerating, and not decelerating, the particles. This would be difficult if not for the fortuitous disappearance of both v and r from Eq. 8.4b, so that the cyclotron frequency only depends on the charge-to-mass ratio of the particles and the magnetic field, but not on their energy.
Typically, protons are accelerated in a magnetic field of about 1 T, resulting in a cyclotron frequency of approximately 15 MHz. Each orbit raises the potential of the proton by about 100 kV, and it must circulate enough times to raise its total energy to at least 10 MeV so that it can overcome the electrostatic repulsion of the target nucleus and cause nuclear reactions. For example, the high-energy protons may be incident on a target of 18O (a rare but stable isotope of oxygen), initiating a nuclear reaction that results in the production of 18F, an important positron emitter used in PET studies.
Finally, I think it’s appropriate that Intermediate Physics for Medicine and Biology should have a section about the cyclotron, because my coauthor Russ Hobbie (who was the sole author of the first three editions of the textbook) obtained his PhD while working at the Harvard cyclotron. Thus, an unbroken path leads from Ernest Lawrence and the cyclotron to the publication of our book and the writing of this blog.
Negative feedback is an important concept in physiology. Russ Hobbie and I discuss feedback loops in Chapter 10 of the 4th edition of Intermediate Physics for Medicine and Biology. In the text and homework problems, we discuss several examples of negative feedback, including the regulation of breathing rate by the concentration of carbon dioxide in the alveoli, the prevention of overheating of the body by sweating, and the control of blood glucose levels by insulin. You can never have enough of these examples. Therefore, here is another homework problem related to negative feedback: regulation of blood osmolarity by antidiuretic hormone. Warning: the model is greatly simplified. It should be correct qualitatively, but not accurate quantitatively.
Section 10.3
Problem 15 ½ The osmolarity of plasma (C, in mosmole) is regulated by the concentration of antidiuretic hormone (ADH, in pg/ml, also known as vasopressin). As antidiuretic hormone increases, the kidney reabsorbs more water and the plasma osmolarity decreases, C=700/ADH. When osmoreceptors in the hypothalamus detect an increase of plasma osmolarity, they stimulate the pituitary gland to produce more antidiuretic hormone, ADH = C-280 for C greater than 280, and zero otherwise. (a) Draw a block diagram of the feedback loop, including accurate plots of the two relationships. (b) Calculate the operating point and the open loop gain (you may need to use four to six significant figures to determine the operating point accurately). (c) Suppose the behavior of the kidney changed so now C=750/ADH. First determine the new value of C if the regulation of ADH is not functioning (ADH is equal to that found in part b), and then determine the value of C taking regulation of ADH by the hypothalamus into account.
You should find that this feedback loop is very effective at holding the blood osmolarity constant. For more about osmotic effects, see Chapter 5 of Intermediate Physics for Medicine and Biology.
Textbook of Medical Physiology,
by Guyton and Hall.
When osmolarity (plasma sodium concentration) increases above normal because of water deficit, for example, this feedback system operates as follows:
1. An increase in extracellular fluid osmolarity (which in practical terms means an increase in plasma sodium concentration) causes the special nerve cells called osmoreceptor cells, located in the anterior hypothalamus near the supraoptic nuclei, to shrink.
2. Shrinkage of the osmoreceptor cells casuse them to fire, sending nerve signals to additional nerve cells in the supraoptic nuclei, which then relay these signals down the stalk of the pituitary gland to the posterior pituitary.
3. These action potentials conducted to the posterior pituitary stimulate the release of ADH, which is stored in secretory granules (or vesicles) in the nerve endings.
4. ADH enters the blood stream and is transported to the kidneys, where it increases the water permeability of the late distal tubules, cortical collecting tubules, and the medullary collecting ducts.
5. The increased water permeability in the distal nephron segments causes increased water reabsorption and excretion of a small volume of concentrated urine.
Thus, water is conserved in the body while sodium and other solutes continue to be excreted in the urine. This causes dilution of the solutes in the extracellular fluid, thereby correcting the initial excessively concentrated extracellular fluid.
Feedback loops are central to physiology. Guyton and Hall write in their first introductory chapter
Thus, one can see how complex the feedback control systems of the body can be. A person’s life depends on all of them. Therefore, a major share of this text is devoted to discussing these life-giving mechanisms.
In some cases, thermal energy can be converted into work. When gas in a cylinder is heated, it expands against a piston that does work. Energy can be supplied to an organism and it lives. To what extent can these processes, which apparently contradict the normal increase of entropy, be made to take place? The questions can be stated in a more basic form.
1. To what extent is it possible to convert internal energy distributed randomly over many molecules into energy that involves a change of a macroscopic parameter of the system? (How much work can be captured from the gas as it expands the piston?)
2. To what extent is it possible to convert a random mixture of simple molecules into complex and highly organized macromolecules?
Both these questions can be reformulated: under what conditions can the entropy of a system be made to decrease?
The answer is that the entropy of a system can be made to decrease if, and only if, it is in contact with one or more auxiliary systems that experience at least a compensating increase in entropy. Then the total entropy remains the same or increases. This is one form of the second law of thermodynamics. For a fascinating discussion of the second law, see Atkins (1994).
The Second Law: Energy, Chaos, and Form,
by Peter Atkins.
The book by Peter Atkins, The Second Law, is published by the Scientific American Library, and is aimed at a general audience. It’s a wonderful book, and provides the best non-mathematical description of thermodynamics I know of. Atkins’ preface begins
No other part of science has contributed as much to the liberation of the human spirit as the Second Law of thermodynamics. Yet, at the same time, few other parts of science are held to be so recondite. Mention of the Second Law raises visions of lumbering steam engines, intricate mathematics, and infinitely incomprehensible entropy. Not many would pass C. P. Snow’s test of general literacy, in which not knowing the Second Law is equivalent to not having read a work of Shakespeare.
In this book I hope to go some way toward revealing the workings of the Law, and showing its span of application. I start with the steam engine, and the acute observations of the early scientists, and I end with a consideration of the processes of life. By looking under the classical formulation of the Law we see its mechanism. As soon as we do so, we realize how simple it is to comprehend, and how wide is its application. Indeed, the interpretation of the Second Law in terms of the behavior of molecules is not only straightforward (and in my opinion much easier to understand that the First Law, that of the conservation of energy), but also much more powerful. We shall see that the insight it provides lets us go well beyond the domain of classical thermodynamics, to understand all the processes that underlie the richness of the world.
Atkins’s book is at the level of a Scientific American article, with many useful (and colorful) pictures and historical anecdotes. The writing is excellent. For instance, consider this excerpt:
The Second Law recognizes that there is a fundamental dissymmetry in Nature…hot objects cool, but cool objects do not spontaneously become hot; a bouncing ball comes to rest, but a stationary ball does not spontaneously begin to bounce. Here is the feature of Nature that both Kelvin and Clausius disentangled from the conservation of energy: although the total quantity of energy must be conserved in any process…, the distribution of that energy changes in an irreversible manner…
I particularly like Atkins’ analysis of the equivalence of two statements of the second law: No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work (Kelvin statement); and no process is possible in which the sole result is the transfer of energy from a cooler to a hotter body (Clausius statement). Atkins writes
The Clausius statement, like the Kelvin statement, identifies a fundamental dissymmetry in Nature, but ostensibly a different dissymmetry. In the Kelvin statement the dissymmetry is that between work and heat; in the Clausius statement there is no overt mention of work. The Clausius statement implies a dissymmetry in the direction of natural change: energy may flow spontaneously down the slope of temperature, not up. The twin dissymmetries are the anvils on which we shall forge the description of all natural change.
Peter Atkins has written several books, including another of my favorites: Peter Atkins’ Molecules. Here is a video of Atkins discussing his book the Four Laws that Drive the Universe. Not surprisingly, the four laws are the laws of thermodynamics.
Peter Atkins discussing the Four Laws that Drive the Universe.
I am an emeritus professor of physics at Oakland University, and coauthor of the textbook Intermediate Physics for Medicine and Biology. The purpose of this blog is specifically to support and promote my textbook, and in general to illustrate applications of physics to medicine and biology.
