Thermodynamics

• 1. Introduction

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  In 1650, Otto von Guericke wanted to prove a Greek philosopher wrong. Aristotle had insisted that nature abhors a vacuum, that emptiness could not exist. So Guericke built the world's first vacuum pump and staged a demonstration with his Magdeburg hemispheres. From that act of stubborn curiosity grew an entire branch of physics. Thermodynamics deals with heat, work, and temperature, and how they relate to energy, entropy, and the physical properties of matter and radiation. It began with a very practical hunger, the desire to make early steam engines burn less and do more. Yet it now reaches into black holes, tropical cyclones, cell biology, and economics. How did a science born from leaky pistons and exploding vessels come to describe the event horizon of a black hole? Who decided that heat could only flow one way? And why does one of its four governing laws carry the strange number zero?

• 2. From Steam To Science

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  Robert Boyle learned of Guericke's designs and, in 1656, worked with the English scientist Robert Hooke to build an air pump. The two noticed a correlation between pressure, temperature, and volume. From this came Boyle's Law, the statement that pressure and volume are inversely proportional. In 1679, an associate of Boyle named Denis Papin took the next step. He built a steam digester, a closed vessel with a tightly fitting lid that trapped steam until a high pressure built inside.

  Later designs added a steam release valve so the machine would not explode. Watching that valve rise and fall in a steady rhythm, Papin imagined a piston moving inside a cylinder. He never pursued the idea himself. Others did. In 1697, Thomas Savery built the first engine on Papin's foundation, and Thomas Newcomen followed in 1712. These machines were crude and inefficient, yet they pulled the attention of the leading scientists of the age.

  At the University of Glasgow, Professor Joseph Black worked out the ideas of heat capacity and latent heat, concepts thermodynamics could not do without. James Watt was employed there as an instrument maker. Black and Watt ran experiments together, but it was Watt who conceived the external condenser, a change that sharply raised steam engine efficiency. All of this led to Sadi Carnot, the French physicist remembered as the father of thermodynamics, who published Reflections on the Motive Power of Fire in 1824.

• 3. Naming The Discipline

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  Lord Kelvin, the Scots-Irish physicist, gave thermodynamics its first concise definition in 1854. He called it "the subject of the relation of heat to forces acting between contiguous parts of bodies, and the relation of heat to electrical agency." Before that, in 1849, he had already used the adjective thermo-dynamic. In 1854 he and William Rankine used the noun thermo-dynamics to mean the science of generalized heat engines.

  The word itself reaches back to Ancient Greek. The first part traces to the root therme, meaning heat, the same root behind thermometer. The second part traces to dynamis, meaning power. Pierre Perrot claims the term thermodynamics was coined by James Joule in 1858. Joule, however, never used that exact word. He instead spoke of a perfect thermo-dynamic engine, borrowing from Kelvin's 1849 phrasing.

  William Rankine wrote the first thermodynamic textbook in 1859. Trained as a physicist, he taught civil and mechanical engineering at the University of Glasgow. The first and second laws emerged together in the 1850s, drawn chiefly from the work of Rankine, Rudolf Clausius, and William Thomson.

• 4. Entropy And Its Founders

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  Rudolf Clausius published his most important paper, "On the Moving Force of Heat," in 1850, and within it he first stated the second law of thermodynamics. The German physicist and mathematician had restated Carnot's principle, the Carnot cycle, giving the theory of heat a sounder basis. In 1865 he named the concept of entropy. In 1870 he introduced the virial theorem and applied it to heat. He is remembered as one of the founding fathers of thermodynamics.

  Josiah Willard Gibbs, the American mathematical physicist, published a series of three papers during the years 1873-76. The most famous bears the title On the Equilibrium of Heterogeneous Substances. In it Gibbs showed how thermodynamic processes, including chemical reactions, could be graphically analyzed. By studying energy, entropy, volume, temperature, and pressure together, one could determine whether a process would occur spontaneously.

  Pierre Duhem wrote on chemical thermodynamics in the 19th century. Early in the 20th century, chemists such as Gilbert N. Lewis, Merle Randall, and E. A. Guggenheim applied the mathematical methods of Gibbs to chemical processes. The foundations of statistical thermodynamics were laid by James Clerk Maxwell, Ludwig Boltzmann, Max Planck, Clausius, and Gibbs.

• 5. The Four Laws

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  The zeroth law of thermodynamics earned its odd number by arriving late. It states that if two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other. The first, second, and third laws had already been stated and accepted before physicists realized this rule was needed to define temperature. Renumbering the others was impractical, so it became the zeroth. James Maxwell noted in 1872 that this principle is what makes measuring temperature possible.

  The first law says that in a process without transfer of matter, the change in a system's internal energy equals the heat gained minus the work the system does on its surroundings. Put another way, perpetual motion machines of the first kind are impossible. The law is an expression of the conservation of energy, which can be transformed but never created or destroyed.

  The second law, in a traditional version, states that heat does not spontaneously flow from a colder body to a hotter body. When an isolated system starts with inhomogeneities in temperature and pressure, its entropy increases as internal constraints are removed, reaching a maximum at equilibrium. Every version of the law expresses the irreversibility of these transitions.

  The third law states that as temperature approaches absolute zero, all processes cease and entropy approaches a minimum. It is impossible to reach absolute zero by any finite number of processes. That point sits at minus 273.15 degrees Celsius, or minus 459.67 degrees Fahrenheit, or 0 kelvin, or 0 degrees Rankine.

• 6. Many Thermodynamics

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  Classical thermodynamics, the first level of understanding to develop in the 19th century, describes systems near equilibrium using macroscopic, measurable properties. It models exchanges of energy, work, and heat through the laws, and treats a system in terms of large-scale parameters one can actually measure. A microscopic interpretation came later.

  Statistical mechanics, also called statistical thermodynamics, emerged with atomic and molecular theory in the late 19th and early 20th centuries. It links the microscopic behavior of individual atoms and molecules to the bulk properties of materials we observe on a human scale. In doing so it explains classical thermodynamics as a natural result of statistics, classical mechanics, and quantum theory.

  Chemical thermodynamics studies how energy interrelates with chemical reactions and changes of state. Its primary objective is to determine the spontaneity of a given transformation. Equilibrium thermodynamics deals with systems driven from one balanced state to another, where all macroscopic flows are zero and no unbalanced driving forces remain.

  Non-equilibrium thermodynamics handles systems that are not in balance, which describes most systems found in nature. These are continuously subject to flux of matter and energy from other systems. Many natural systems still lie beyond the reach of currently known macroscopic thermodynamic methods. In 1909, Constantin Carathéodory offered a purely mathematical, axiomatic formulation in his work Investigations on the Foundations of Thermodynamics, using Pfaffian systems and his own concept of adiabatic accessibility.

• 7. Systems And Their Walls

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  Max Planck in 1900 defined a system as small as the region surrounding a single atom resonating energy. The thermodynamic system is a precisely defined region of the universe under study, and everything else is the surroundings. A boundary separates the two, confining the system to a finite volume. Segments of that boundary are often called walls, each with its own permeability that decides what may cross as work, heat, or matter.

  Boundaries come in four types: fixed, movable, real, and imaginary. In an engine, a locked piston gives a fixed boundary and a constant volume. Let the piston move and that boundary becomes movable, while the cylinder and cylinder head stay fixed. For a jet engine, an imaginary boundary might sit at the intake, fixed surfaces run along the case, and another imaginary boundary crosses the exhaust nozzle.

  The scale of a system can stretch far beyond a piston. Sadi Carnot in 1824 took his system to be a body of steam or air in a steam engine. Kerry Emanuel theorized in 1986 that the body of a tropical cyclone could serve as a thermodynamic system in atmospheric thermodynamics. Quantum thermodynamics has even hypothesized a single nuclide, a system of quarks, as a system in its own right.

• 8. Tools Of Measurement

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  An idealized thermometer is simply a sample of an ideal gas held at constant pressure. From the ideal gas law, written pV equals nRT, the volume of that sample serves as an indicator of temperature, and in this way it defines temperature. A barometer can likewise be built from a sample of ideal gas held at constant temperature. A calorimeter measures and defines the internal energy of a system.

  The second class of instrument is the thermodynamic reservoir, a system so large that contact with a smaller system barely changes its state. The Earth's atmosphere is often used as a pressure reservoir. The ocean can act as a temperature reservoir when it cools power plants.

  Thermodynamic processes are sorted by what is held constant. An adiabatic process occurs without loss or gain of heat. An isentropic process is a reversible adiabatic one at constant entropy, an isobaric process holds pressure constant, an isochoric process holds volume constant, and an isothermal process holds temperature constant. Energy ties these together through conjugate variables, paired like a force and its displacement: pressure with volume, temperature with entropy, and chemical potential with particle number. From these pairings come the thermodynamic potentials, among them the Helmholtz and Gibbs energies, which measure the useful work available when temperature and volume, or pressure and temperature, are fixed.