# A-level Chemistry/AQA/Module 5/Thermodynamics/Second Law of Thermodynamics

When did thermodynamics begin? Possibly with Fahrenheit (1724) and his puzzling discovery that liquids boil at constant temperatures. Or maybe with Benjamin Thompson's cannon-boring experiments (1798) and his presentation to the Royal Society in London proclaiming that heat is not a substance but produced by motion of particles. But what has become known as the Three Laws of Thermodynamics probably started with the Carnot Principle.

Sadi Carnot, French engineer interested in designing an efficient steam engine, is considered the founder of thermodynamics. In 1824 he published Reflections on the Motive Power of Fire. In the book, less than a 120 pages, he founded the Carnot Principle or what we call today the Second Law of Thermodynamics. Carnot showed that the work produced by a steam engine is proportional to the heat transferred from the boiler to the condenser, and work could only be gained from heat by a transfer from a warmer to a colder body. The principle was never applied during Carnot's lifetime; he died of cholera at the age of 36. The absolute temperature scale proposed by Lord Kelvin (1848) was based on Carnot's theory of heat. Lazare Carnot, the father of Sadi, was a noted mathematician as well as Napoleon's Minister of War.

Émile Clapeyron, another French engineer, restated Carnot's principle in mathematical form (1834). He also devised the Clapeyron equation, a formula for the heat of vaporization of a liquid based on temperature and volume change. Gustave Eiffel listed prominent French scientists, including Clapeyron, on plaques around the first stage of Eiffel Tower.

## Contents

## First Law[edit]

**In a nutshell:** *Total energy of universe constant*

### James Prescott (1818-1889) Joule Hermann von Helmholtz (1821-1894)[edit]

Joule is considered the founder of experimental thermodynamics although his lack of advanced mathematical training compelled him to leave the development of thermodynamic derivations to others like Helmholtz, Kelvin, Clausius, and Gibbs. Joule's skillful and accurate experimental work made significant contributions and he shares in discovering the law of the conservation of energy with Helmholtz. Joule established that the various types of energy—mechanical, electrical, and heat—are basically the same and can be changed from one form into another. He also formulated what has become known as Joule's Law: the heat produced in a wire by an electric current is proportional to the product of the resistance of the wire and the square of the current. On his honeymoon, Joule just had to compare temperatures of water at top and bottom of waterfall (he predicted the temperature would be greater at the bottom). The unit of work or energy, the joule, is named in his honor.

Helmholtz presented a mathematical proof for his law of conservation of force (1847). Helmholtz's use of the word "force" corresponds to what later became known as energy. This application led to his classic 1847 paper, "On the Conservation of Energy," in which he outlined the philosophical and physical basis of the law of the conservation of energy. It was von Helmholtz who first informed us in 1856 that "the universe is dying!"

## Entropy and Second Law[edit]

**In a nutshell:** *Total entropy of universe always increasing*

### Rudolf Clausius (1822-1888)[edit]

Clausius restated Carnot's principle as: Work produced by heat is not only proportional to the heat transferred from the warmer to the colder body, but is also proportional to the temperature difference of the two bodies. Clausius formulated the second law and coined the term "entropy" after the Greek word meaning transformation. According to Clausius, entropy was the amount of thermal energy not available to do work (opposite of energy). In a closed system, available energy can never increase, so its opposite, entropy, can never decrease. In an 1865 paper Clausius restated the first law as the energy of the universe is constant and the second law as the entropy of the universe tends to a maximum.

The physical meaning of entropy (disorder) was interpreted in the 1890's by Ludwig Boltzmann.

Boltzmann used molecules of gas as a model, along with the laws of probability, to show that heat, no matter how it was introduced, would soon become evenly diffused throughout the gas. He formulated the equation S = k logW, where S is entropy, k is now called the Boltzmann constant, and W represents the number of ways particles can be arranged in a given state while keeping the total energy constant. If there are only a few ways to arrange atoms or molecules, the entropy is low; the entropy is high when there are many possible arrangements. Boltzmann's proposal was met with skepticism and not accepted in his lifetime. Suffering from poor health and despondent over the rejection of his work, Boltzmann committed suicide. The famous equation is engraved at the top of his tombstone .

## Free Energy[edit]

### Josiah Willard Gibbs (1839-1903)[edit]

Gibbs, one of the founders of modern thermodynamics and statistical mechanics, wrote the first authoritative book on the subject in 1902 (Elementary Principles in Statistical Mechanics). Gibbs developed the concept of free energy (G), where DG is the compromise between enthalpy changes (DH) and entropy changes (DS): DG = DH - TDS

Although General Chemistry texts always detail the work of Gibbs, the texts rarely tell about the scientist. So who was Gibbs? At the time of his death, Europeans considered Gibbs the greatest born American scientist. Entering Yale at age 15 and receiving a Ph.D. in engineering (1863), Gibbs returned to Yale in 1869 as professor of mathematical physics. Gibbs held the position without salary (living on the inheritance left by his father) until 1880—Yale initiated a salary only when Johns Hopkins University invited Gibbs to join the faculty.

Gibbs published only reluctantly on the subjects of thermodynamics, electromagnetic theory, and statistical mechanics. In all, he published 25 papers and the book on statistical mechanics. Gibbs never made an effort to popularize his results and would not get involved in disputes. When Boltzmann's views were under attack—Gibbs had been working on the same problem and came to the same conclusions as Boltzmann—Gibbs never wrote Boltzmann to offer encouragement.

## Third Law[edit]

**In a nutshell:** *Perfect crystal has zero entropy at absolute zero*

### Walther Nernst (1864-1941)[edit]

Nernst applied the principles of thermodynamics to the electrochemistry and formulated what has become known as the Nernst equation (relates voltage of a cell to its properties). He showed that charged ions dissociate because they have difficulty attracting each other through insulating water. Nernst was awarded the 1920 Nobel Prize in chemistry for his discovery of the third law: Entropy approaches a minimum as temperature approaches absolute zero. During his visit to Yale in 1906, Nernst donated a bronze memorial to honor Gibbs.