target="_blank" rel="nofollow" href="#ulink_b1f785b3-ff1f-5f30-954d-e6acdb05fe49">* Frenchman Joseph Gay-Lussac (1778–1850) established this law based on the earlier work of Englishman Robert Boyle and Frenchman Edme Mariotte.2 † We will generally refer to it merely as the gas constant.
3 ‡ Named for Lord Kelvin. Born William Thomson in Scotland in 1824, he was appointed professor at Glasgow University at the age of 22. Among his many contributions to physics and thermodynamics was the concept of absolute temperature. He died in 1907.
4 § This may seem intuitively obvious to us, but it was not to James Joule (1818–1889), English brewer and physicist, who postulated it on the basis of experimental results. It was not obvious to his contemporaries either. His presentation of the idea of equivalence of heat and work to the British Association in 1843 was received with “entire incredulity” and “general silence”. The Royal Society rejected his paper on the subject a year later. If you think about it a bit, it is not so obvious – in fact, there is no good reason why heat and work should be equivalent. This law is simply an empirical observation. The proof is a negative one: experience has found no contradiction of it. German physician Julius Mayer (1814–1878) formulated the idea of conservation of energy in 1842, but his writing attracted little attention. It was Joule's experiments with heat and work that conclusively established the principle of conservation of energy. By 1850, the idea of conservation of energy began to take hold among physicists, thanks to Joule's persistence and the support of a brilliant young physicist named William Thomson (later Lord Kelvin), who also had been initially skeptical.
5 * The pascal, the SI unit of pressure, is equal to 1 kg/m-s2. Thus if pressure is measured in MPa (megapascals, 1 atm ≈ 1 bar ≈ 0.1 MPa) and volume in cc (= 10−6 m−3), the product of pressure times volume will be in Joules. This is rather convenient. It is named for French mathematician and physicist Blaise Pascal (1623–1662). Among his many contributions was the demonstration that atmospheric pressure was lower atop the Puy de Dome volcano than in the town of Clermont-Ferrand below it.
6 † Rudolf Clausius (1822–1888), a physicist at the Prussian military engineering academy in Berlin, formulated what we now refer to as the second law and the concept of entropy in a paper published in 1850. Similar ideas were published a year later by William Thomson (Lord Kelvin), who is responsible for the word entropy. Clausius was a theorist who deserves much of the credit for founding what we now call thermodynamics (he was responsible for, among many other things, the virial equation for gases). However, a case can be made that Sadi Carnot (1796–1832) should be given the credit. Carnot was a Parisian military officer (the son of a general in the French revolutionary army) interested in the efficiency of steam engines. The question of credit hinges on whether he was referring to what we now call entropy when he used the word calorique.
7 ‡ This is the equation when there are two possible outcomes. A more general form for a situation where there are m possible outcomes (e.g., copper blocks) would be:(2.36a) where there are n1 outcomes of the first kind (i.e., objects assigned to the first block), n2 outcomes of the second, etc. and N = ∑ni (i.e., N objects to be distributed).
8 † In Microsoft Excel™, you can use the BINOMDIST function to compute the outcome of this equation, which makes computing graphs such as Figure 2.8 much easier. In MATLAB™, you can compute the distribution using the probability distribution command: pd=makedist (‘Binomial’,N,p), where N is the number of trials (e) and p is the probability of success (p). A plot similar to Figure 2.8a can be created using the Probability Distribution Function App with the distool command.
9 * Either a maximum or minimum can occur where the derivative is 0, and a function may have several of both; so some foreknowledge of the properties of the function of interest is useful in using this property.
10 † This equation, which relates microscopic and macroscopic variables, is inscribed on the tombstone of Ludwig Boltzmann (1844–1906), the Austrian physicist responsible for it.
11 † R. Clausius recognized the possibility that molecules might have these three kinds of motion in 1855.
12 * We now understand and interpret this law in terms of quantum physics, but Boltzmann formulated it 30 years before Planck and Einstein laid the foundations of quantum theory. Ludwig Boltzmann's work in the second half of the nineteenth century laid the foundations of statistical mechanics and paved the way for quantum theory in the next century. His work was heavily attacked by other physicists of the time, who felt physics should deal only with macroscopic observable quantities and not with atoms, which were then purely hypothetical constructs. These attacks contributed to increasingly frequent bouts of depression, which ultimately led to Boltzmann's suicide in 1906. Ironically and sadly, this was about the time that Perrin's experiments with Brownian motion, Millikan's oil drop experiment, and Einstein's work on the photoelectric effect confirmed the discrete nature of mass, charge, and energy, and thereby the enduring value of Boltzmann's work.
13 * Albert Einstein (1879–1955), though best known for his relativity theories, was also the founder, along with Max Planck, of quantum physics. His work on the quantum basis of heat capacity of solids was published in 1907. Einstein was born in Ulm, Germany, and published some of his most significant papers while working as a patent clerk in Bern, Switzerland. He later joined the Prussian Academy of Sciences in Berlin. A dedicated and active pacifist, Einstein left Germany when Hitler came to power in 1933. He later joined the Center for Advanced Studies in Princeton, New Jersey.
14 † Peter Debye (1884–1966) was born in Maastricht, Netherlands (as Petrus Debije), but spent much of his early career in Germany, eventually becoming director of the Kaiser-Wilhelm-Institut in Berlin. While he was visiting Cornell University in 1940, Germany invaded Holland and Debye simply remained at Cornell, eventually becoming chairman of the Chemistry Department. Debye made numerous contributions to physics and physical chemistry; we shall encounter his work again in the next chapter.
15 * The Maxwell relations are named for Scottish physicist James Clerk Maxwell (1831–1879), perhaps the most important figure in nineteenth-century physics. He is best known for his work on electromagnetic radiation, but he also made very important contributions to statistical mechanics and thermodynamics.
Chapter 3 Solutions and thermodynamics of multicomponent systems
3.1 INTRODUCTION
In the previous chapter, we introduced thermodynamic tools that allow us to predict the equilibrium mineral assemblage under a given set of conditions. For example, having specified temperature, we were able to determine the pressure at which the assemblage anorthite + forsterite is in equilibrium
