Thermodynamics – One of the main pillar of engineering science

Thermodynamics is the oldest branch of engineering science and specifically of physics. It deals with the relationships between heat and other forms of energy. In another terms we can say that it deals with the transfer of energy from one form to another form and one place to another place.

Thermodynamic focuses on concepts surrounding energy, and in the various states that systems possess, as defined by their state variables such as pressure, temperature, volume, entropy, concentration and so on.

In thermodynamics various fundamentals and various laws are applicable which we studied in our upcoming topics.


1. Historical Development of Thermodynamics

2. Branches of Thermodynamics

3. Some of the useful Fundamentals of Thermodynamics

4. Four laws of Thermodynamics

5. System models

6. States and processes

7. Potential

1. Historical Development of Thermodynamics [1]

Thermodynamics had a long historical development from the ancient times to the 20th century. The invention of the thermometer was the first important step that made possible to formulate the first precise speculations on heat.

There were no exact theories about the nature of heat for a long time and even the majority of the scientific world in the 18th and the early 19th century viewed heat as a substance and the representatives of the Kinetic Theory were rejected and stayed in the background. The Caloric Theory successfully explained plenty of natural phenomena like gas laws and heat transfer and it was impossible to refute it until the 1850 when the Principle of Conservation of Energy was introduced (Mayer, Joule, Helmholtz).

The Second Law of Thermodynamics was discovered soon after that explanation of the tendency of thermodynamic processes and the heat loss of useful heat. The Kinetic Theory of Gases motivated the scientists to introduce the concept of entropy that was a basis to formulate the laws of thermodynamics in a perfect mathematical form and founded a new branch of physics called statistical thermodynamics.

The Third Law of Thermodynamics was discovered in the beginning of the 20th century after introducing the concept of thermodynamic potentials and the absolute temperature scale. At the same period of time the scientific issue of thermal radiation was also solved.

The invention of the thermometer

The first important step to discover the principle of thermodynamics was the invention of the thermometer because precise and reliable survey results were needed. In the Ancient Times scientists wanted to measure the attributes of substances including their temperature. Philo of Byzantium (280 BC – 220 BC) reported in his manuscript about a heat-sensing instrument. He constructed tube with a hollow sphere that was extended over a jug of water. When the sphere was placed in the sun the water began to bubble as the air expanded out of the sphere. If he put it in the shade the water rose in the tube as the air contracted in the sphere. Hero of Alexandria (10 AD – 70 AD) also inspected that the water level in a container rises and sinks due to the change in temperature. In the Middle Ages scientists and physicians raised the necessity of measuring temperature. They knew that the flame has higher intensity of heat than a hot piece of iron while the quantity of heat is much lower in it but they could not clearly define the difference between temperature and quantity of heat The Persian polymath Avicenna (980-1037) also recorded that he knew a mechanism to show the hotness and coldness of the air and developed an instrument in which the water level was controlled by the contraction and expansion of air but the really improvement came in Europe in the 16th century. The Italian Galileo Galilei (1564-1642) created the first thermometer in 1597 which was really a thermoscope because it did not have numerical scale so Galilei could find out only the relative differences between air temperature. Scientists in the 17th century constructed lots of thermometers (Sagredo, Santorio, Fludd, Drebbel) but they all suffered from the disadvantage that they were also barometers. In 1654 Ferdinando II de’ Medici (1610-1670), Grand Duke of Tuscany made a thermometer of sealed tube filled with alcohol that was only sensible to temperature and it was independent of air pressure. The Englishman, Robert Boyle (1627-1691) was the first who realized the necessity of standard scales in 1662 during his experiments with that he discovered his law (Boyle’s Law) that describes the relationship between the absolute pressure and volume of gas if the temperature is kept constant within a closed system. In 1665 Christiaan Huygens (1629-1695) suggested to use the melting and boiling point of water as a standard scale and in 1694 Carlo Renaldini (1615-1698) proposed to use them as fix points with twelve equal parts between them but it was not accepted immediately because scholars were unsure that the freezing and boiling points of water are constant. In 1724 the German physicist and glassblower Daniel Gabriel Fahrenheit (1686-1736) proposed a thermometer with reliable universal scale using mercury instead alcohol as the fluid within and it had three fix points. Zero was the coldest day of the winter in Danzig, the freezing point of the water was 32 degrees and the healthy human body temperature was 96 degrees that resulted 212 degrees for the boiling point of the water. Fahrenheit’s thermometer was the first standardised instrument that was suitable for scientific measurements. It was cleared that all substances have defined freezing and boiling points. Starting from this fact in 1742 the Swedish astronomer Anders Celsius (1701-1744) produced a thermometer with a standard scale using the melting point of water as zero and boiling point of water as 100 degrees. This scale bears his name and it is under use with Fahrenheit scale world-wide nowadays. Because of its simplicity the Celsius scale is more popular.

The first scientific issue:

Is heat a substance or a motion? Ancient people related heat with flame and fire. The ancient Egyptians viewed it as a formation with mysterious origins. The Chinese Taoists believed that fire is one of the five principle elements like air, wood, metal and water. Ancient Greeks generally viewed fire and heat as a substance and often connected it with life and motion. Heraclitus (535 BC – 475 BC) was the first who framed a theory on heat. He argued that there are three principle elements in nature – fire, water, earth – from which the fire is the central element controlling and modifying the other two. Heraclitus claimed that heat is connected with the motion because he observed that living creatures are warm and died bodies are cold. The later ancient scholars (Empedocles, Aristotle) believed in four principle elements (water, earth, air, fire) and they also connected the heat with life and coldness with death. In the Middle Ages some Islamic scientists examined heat and fire and all of them connected it clearly with motion. Abū Rayhān Bīrūnī (973-1038) stated that the causes of heat are movement and friction. Avicenna and Abd Allah Baydawi (?-1286) also made similar discoveries that heat is generated from motion of external things and it may occur through motion-change. Even all the scientists of the 17th century believed in the essential connection between heat and motion. The English philosopher, Francis Bacon (1561-1626) in his work called Novum Organum demonstrated that heat is a kind of motion. Robert Boyle and his colleague Robert Hooke (1635-1703) had comparable opinion that heat is nothing else but vehement motion of the elementary particles.

Roundabout ways:

The Phlogiston and the Caloric Theory [5][9][11][12] Now we would think that it led directly to the Kinetic Theory, but the level of the mathematical knowledge was not enough high to create satisfying answers to a lot of questions. This is why the theories on the material nature of heat became conspicuous because they were much more suitable for explaining the phenomena like melting heat, boiling heat, thermal radiation, heat transfer etc. In 1669 Joachim Johann Becher (1635- 1682) established the Phlogiston Theory that was later developed by Georg Ernst Stahl (1659-1735). In his work entitled Experimenta chymicae et physicae (1731) proposed that heat was associated with an undetectable substance called phlogiston that was driven out of the material when it was burnt. The theory was finally refuted in 1783 by Antoine-Laurent de Lavoisier (1743-1794) proving the participation of oxygen in burning. He framed instead the Caloric Theory that saw heat as a weightless and invisible fluid that moves to hot bodies from the cold ones. Herman Boerhaave (1668-1738) was the first who went to the very limits of the Caloric Theory. He pronounced that we can not make equal sign between heat, fire and light because they can manifest separately. Boerhaave supposed connection between heat and motion because rubbing together two parts of flint-stones fire came into being no matter how hot or cold they were. He tried to determine the weight of Caloricum and examined the phenomena of thermal expansion. The concept of fire and heat became clear only in the middle of the 18th century as the Scottish physicist, Joseph Black (1728-1799), started his experiments at the Glasgow University in the 1750s. He defined the difference between temperature and the quantity of heat and founded the concept of specific heat that is the measure of heat (or thermal energy) required to increase the temperature of a unit quantity of a substance by one unit. Black’s most important discovery was the observation that melting ice absorbs heat without changing temperature. From this recognition he came to a conclusion that ice needs latent heat for this modification of physical condition. It was the main substantial proof of the material nature of heat for him and in 1779 one of his students, William Cleghorn (1754-1783), formulated the precise definition of the Caloricum.

The first attempts of the Kinetic Theory

In spite of the rapid successes and propagation of the Caloric Theory there were a few scientists who took a stand for the Kinetic Theory of heat. In 1716 Jakob Hermann (1678-1733) pointed out that the atmospheric pressure is proportional to the air density and to the square of the average velocity of moving particles in atmosphere. Leonhard Paul Euler (1707-1783) even computed the value of this average velocity as 477 m/s. In 1738 Daniel Bernoulli (1700-1782) published his most important work called Hydrodynamique (Hydrodynamics). Based on the relation of Boyle’s Law showed that as temperature changes the pressure will change proportionally to the square of the particle velocities. In 1745 the Russian chemist Mikhail Vasilyevich Lomonosov (1711-1765) also wrote a relevant work against Caloric Theory under the title of Размышления о причине теплоты и холода (Reflections on the Reason of Heat and Cold). He reported that heat is generated by motion because when we rub our hands together or strike the iron intensively they become warmer. He explained that heat is nothing else but the highspeed velocity of motion of invisible material particles. In his later works he tried to put into words the Principle of Conservation of Energy and diagnosed that however much matter is added to any body, as much is taken away from another. In the 18th century works of these scientists about the Kinetic Theory created little stir throughout the world because of the huge popularity of the Caloric Theory. In addition there were lingual difficulties too, because Lomonosov published his works in Russian and they were not attractive in Western Europe. Caloric Theory had only two weak points – the friction heat and the weight of the Caloricum – and a few practical researchers tried to take advantage of this situation. The cannon manufacturer Benjamin Thomson, Count Rumford (1753-1814) realized that the most suitable moments to take the weight of Caloricum when the ice is melting because at this moment ice absorbs a lot of heat without changing temperature. He took absolutely accurate and precise measurements with his apparatus and finally declared that even if Caloricum had weight it is immensely small. In 1798 Rumford made a study about the frictional heat that was generated through boring the cannons. He immersed a cannon barrel in water and showed that the water could be boiled by the frictional heat generated by the boring tool. Rumford demonstrated through the use of friction that it was possible to convert work to heat and this heat seemed to be inexhaustible. As a result of these experiments Rumford suggested that heat is a form of motion. The connection between heat and friction was also analysed in 1799 by Humphrey Davy (1778-1829). In his experiment he rubbed two pieces of insulated ice together and showed that melting heat could be originated only from mechanical work. Rumford and Davy were very close to refute the Caloric Theory but the advocates of it could easily explain the results of their experiments supposing the weightlessness of Caloricum.

The First Law of Thermodynamics

The Principle of Conservation of Energy The German surgeon Julius Robert von Mayer (1814-1878) started a study on the physical side of the symptoms of life during his journey in Dutch East India in 1840 and noticed that the venous blood of the sailors in the tropics is much darker than in cold climates. He concluded that the chemical processes of the body get their sources of energy for oxidation from the nature. Arriving home he wrote a scientific paper in 1841 under the name of Über die quantitative und qualitative Bestimmung der Kräfte (On the Quantitative and Qualitative Determination of Forces). It was ignored by the physicists because of its strange argumentation that were based on the principle of causa aequat effectum so he could publish it next year in a chemical journal under the title of Bemerkungen über die Kräfte der unbelebten Natur (Remarks on the Forces of Inorganic Nature). This fundamental paper contained the first adequate formulation about the Law of Conservation of Energy that although work and heat are different forms of energy, they can be transformed into one another. He also specified theoretically the numerical value of the mechanical equivalent of heat as 365mkp (3580J) which is a little bit far from the real value but the order of size and the deduction was correct. Mayer also gave suggestions how to transform experimentally kinetic energy into heat. Contemporaneously James Prescott Joule (1818-1889) made experiments and measurements to estimate the mechanical equivalent of heat and in 1843 he announced his results in a scientific meeting in Cork but there was only meagre attendance. In 1845 Joule wrote a paper On the Existence of an Equivalment Relation Between Heat and the Ordinary Forms of Mechanical Power and sent it to the British Association meeting in Cambridge. He reported about his best-known experiment using a falling weight to spin a paddle-wheel in an insulated barrel of water that increased the water temperature. Firstly he estimated the mechanical equivalent of heat as 424mkp (4158J) that was later refined by him as 427mkp (4187J). The Law of Conservation of Energy was outlined in the works of Mayer and Joule but the modern form of it was formulated by the German physician Ludwig Ferdinand von Helmholtz (1821-1894). Studying the muscle metabolism he observed that no energy is lost in the muscle movement. In 1847 he based his book Über die Erhaltung der Kraft (On the Conservation of Energy) on a rule that all form of energy (mechanic, heat, light, magnetism) are equivalent. His theorem was hardly disputed and the Law of Conservation of Energy could be gone out of mind if did not raise up the interest of William Thomson, Lord Kelvin (1824-1907) who recognized the significance of Helmholtz’s paper. He experimented in order to bloster Joule’s results and in 1848 he published his article On the Absolute Thermometric Scale. He suggested the introduction of an absolute temperature scale about which Amontons had speculated in 1695. Based on the Celsius scale Kelvin determined the absolute zero temperature in – 273°C under which the kinetic energy of material particles is as low as possible.

The Second Law of Thermodynamics and the Kinetic Theory of Gases

In the middle of the 19th century it was trivial that the Law of Conservation of Energy in not enough to explain the natural phenomenon because – as Carnot stated formerly – there is a determined tendency of the thermodynamic processes and the heat can spontaneously flow only from hot to cold materials. This is why the Second Law of Thermodynamics was needed and this necessity was recognized by Rudolf Julius Emanuel Clausius (1822-1888). In 1850 he wrote his famous paper Über die bewegende Kraft der Wärme (On the Moving Force of Heat and the Laws of Heat) in which he stated the basic idea of the second law that heat generally cannot flow spontaneously from cold to hot bodies. If it could happen it would be possible to transform the 100% of heat into mechanical energy. Another formulation of the second law was written down in 1851 by Lord Kelvin in his work entitled On the Dynamical Theory of Heat that it is impossible to convert heat completely into work in a cyclic process. These negative sentences as the law of thermodynamics sounded very strange for the physicists so a new idea was needed to formulate a more adequate definition. It is going to be the idea of entropy a decade later. At the same time the work of Bernoulli was rediscovered by John Herapath (1790- 1868) in 1816 and submitted a paper to the Royal Society but it was rejected because its conclusions were seemed to be erroneous. After the studying of Bernoulli’s and Herapath’s work John James Waterston (1811- 1883) wrote a publication in 1843 under the title of Thoughts on the Mental Functions. He correctly derived the consequence that the gas pressure is generated by the highspeed motion of the material particles and countable with multiplying the number of molecules per unit volume, the molecular mass, and the molecular mean-squared velocity. However it contained the elementary form of the Kinetic Theory of Gases this paper was rejected by the Royal Society because of its modern intonation and he could publish a short abstract of it. In 1848 Joule made calculations in order to compute the speed of the hydrogen molecule but his article in 1851 did not arouse the interest so together with Waterston’s work it had only a little influence on the next generation. The real breakthrough came after the article of August Karl Krönig (1822-1879) in 1856. It was based on Waterston’s work and its simple gas-kinetic model gave plenty of motivations and ideas for the other researchers. In 1857 Clausius wrote a paper under the title of Über die Art der Bewegung, welche wir Wärme nennen (On the Kind of Motion which we call Heat) in which he stated that the internal energy of gases equals with the kinetic energy of the atoms or molecules of gases He developed a much more complex but sophisticated theory than Kröning that included not only the translational but also the rotational and vibrational molecular motions. This article motivated the Scottish physicist, James Clerk Maxwell (1831-1879) to give up the theorem that in a given amount of gas the molecules have the same speed and formulated the Maxwell Distribution of Molecular Velocities with which he founded a new branch of physics called statistical thermodynamics. He published his formula in 1860 in his work called Illustrations of the Dynamical Theory of Gases that described the particle speeds of gases at a determinate temperature and showed the statistical distribution of it. Maxwell worked out the equipartition theorem which means that in thermal equilibrium the total kinetic energy of a system is shared equally (in average) among all of its various forms, so the average kinetic energy in the translational motion of a molecule should equal the average kinetic energy in its rotational motion. After universalizing this law he also stated that the internal energy is equally shared between the degrees of freedom and it depends only on the temperature of the system.

Entropy, Statistical Thermodynamics and the Third Law of Thermodynamics

Joule and Kelvin also speculated that there was an inevitable loss of useful heat in all thermodynamic processes and observed that natural processes are tended from an organized to a disorganized state. In addition in the 1850s it was necessary to find a correct mathematical description for the Second Law of Thermodynamics because the former definitions were not as accurate as needed. This is why coined Clausius the concept of entropy in 1865 which means how organized or disorganized a system is. With the help of entropy we can explain the tendency of processes because the most likely event happens in the nature. It was also possible to formulate mathematically why flows spontaneously heat from hot into cold bodies. Because decreasing of temperature results the increasing of entropy. The young Austrian physicist Ludwig Eduard Boltzmann (1844-1906) started to deal with the Kinetic Theory of gases in 1866. His work was promoted by Maxwell’s book called Theory of Heat in 1871 and confirmed that the thermodynamic systems is tended towards the thermal equilibrium because this is the most likely state. Developing Maxwell’s equipartition theory and the distribution of molecular velocities he calculated the value of kinetic energy to each degree of freedom with the formula of: 1/2 * K*T where T is the absolute temperature and k is the Boltzmann’s constant and equals to 1,38065×10–23 J/K. With the help of entropy Boltzmann redefined the Second Law of Thermodynamics in 1877. He introduced the concept of thermodynamics probability as the number of micro-states corresponding to the current macro-state and formulated the connection between entropy and molecular motion showing that the logarithm of thermodynamic probability (W) is directly proportional with the entropy (S). S = k ∗ lnW

Before the Third Law of Thermodynamics the last important step was taken by the American physicist and chemist Josiah Willard Gibbs (1839-1903) by introducing the concept of the thermodynamic potentials and free energy in 1876 in his monograph called On the Equilibrium of Heterogeneous Substances. Thermodynamic potentials could be formulated with the help of the state parameters like volume (V), pressure (p), temperature (T) and internal energy (U) and they make easier to calculate some characteristics of the system (heat capacity, reaction heat). These potentials are free energy (F), enthalpy (H) and free enthalpy (Gibbs energy, G) and they measure the useful work of a closed thermodynamic system at constant temperature and volume (free energy), or at constant pressure (enthalpy) or at constant pressure and temperature (Gibbs energy). Studying the high-temperature reaction of gases Walther Hermann Nernst (1864-1941) analyzed these kinds of thermodynamic potentials in 1889. He was deeply influenced by the thermodynamic researches of Max Karl Ernst Ludwig Planck (1858-1947) and the birth of quantum mechanics in 1900 and started to examine the change in specific heat of different materials. In 1906 he published his theorem with which he established the Third Law of Thermodynamics. This law describes the behaviour of a thermodynamic system as the temperature decreases to the absolute zero. Nernst stated that the entropy of a system at a temperature of absolute zero becomes zero in the case of perfect crystalline substances. He also laid down that it is impossible to reduce the temperature of any system to the absolute zero in the finite number of steps. lim (T → 0)  ∆S = 0  In this formula T is the absolute temperature and S is the entropy of the system.

2. Branches of thermodynamics [2]

The study of thermodynamical systems has developed into several related branches, each using a different fundamental model as a theoretical or experimental basis, or applying the principles to varying types of systems.

Classical thermodynamics

Classical thermodynamics is the description of the states of thermodynamic systems at near-equilibrium, that uses macroscopic, measurable properties. It is used to model exchanges of energy, work and heat based on the laws of thermodynamics. The qualifier classical reflects the fact that it represents the first level of understanding of the subject as it developed in the 19th century and describes the changes of a system in terms of macroscopic empirical (large scale, and measurable) parameters. A microscopic interpretation of these concepts was later provided by the development of statistical mechanics.

Statistical mechanics

Statistical mechanics, also called statistical thermodynamics, emerged with the development of atomic and molecular theories in the late 19th century and early 20th century, and supplemented classical thermodynamics with an interpretation of the microscopic interactions between individual particles or quantum-mechanical states. This field relates the microscopic properties of individual atoms and molecules to the macroscopic, bulk properties of materials that can be observed on the human scale, thereby explaining classical thermodynamics as a natural result of statistics, classical mechanics, and quantum theory at the microscopic level.

Chemical thermodynamics

Chemical thermodynamics is the study of the interrelation of energy with chemical reactions or with a physical change of state within the confines of the laws of thermodynamics.

Equilibrium thermodynamics

Equilibrium thermodynamics is the systematic study of transfers of matter and energy in systems as they pass from one state of thermodynamic equilibrium to another. The term ‘thermodynamic equilibrium’ indicates a state of balance. In an equilibrium state there are no unbalanced potentials, or driving forces, between macroscopically distinct parts of the system. A central aim in equilibrium thermodynamics is: given a system in a well-defined initial equilibrium state, and given its surroundings, and given its constitutive walls, to calculate what will be the final equilibrium state of the system after a specified thermodynamic operation has changed its walls or surroundings.

Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are not in stationary states, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.

3. Some of the Useful Fundamentals of Thermodynamics [3]

Thermodynamics, then, is concerned with several properties of matter; foremost among these is heat. Heat is energy transferred between substances or systems due to a temperature difference between them, according to Energy Education. As a form of energy, heat is conserved, i.e., it cannot be created or destroyed. It can, however, be transferred from one place to another. Heat can also be converted to and from other forms of energy. For example, a steam turbine can convert heat to kinetic energy to run a generator that converts kinetic energy to electrical energy. A light bulb can convert this electrical energy to electromagnetic radiation (light), which, when absorbed by a surface, is converted back into heat.

The amount of heat transferred by a substance depends on the speed and number of atoms or molecules in motion, according to Energy Education. The faster the atoms or molecules move, the higher the temperature, and the more atoms or molecules that are in motion, the greater the quantity of heat they transfer.

Temperature is “a measure of the average kinetic energy of the particles in a sample of matter, expressed in terms of units or degrees designated on a standard scale,” according to the American Heritage Dictionary. The most commonly used temperature scale is Celsius, which is based on the freezing and boiling points of water, assigning respective values of 0 degrees C and 100 degrees C. The Fahrenheit scale is also based on the freezing and boiling points of water which have assigned values of 32 F and 212 F, respectively.

Scientists worldwide, however, use the Kelvin (K with no degree sign) scale, named after William Thomson, 1st Baron Kelvin, because it works in calculations. This scale uses the same increment as the Celsius scale, i.e., a temperature change of 1 C is equal to 1 K. However, the Kelvin scale starts at absolute zero, the temperature at which there is a total absence of heat energy and all molecular motion stops. A temperature of 0 K is equal to minus 459.67 F or minus 273.15 C.

The amount of heat required to increase the temperature of a certain mass of a substance by a certain amount is called specific heat, or specific heat capacity, according to Wolfram Research. The conventional unit for this is calories per gram per kelvin. The calorie is defined as the amount of heat energy required to raise the temperature of 1 gram of water at 4 C by 1 degree.

The specific heat of a metal depends almost entirely on the number of atoms in the sample, not its mass.  For instance, a kilogram of aluminum can absorb about seven times more heat than a kilogram of lead. However, lead atoms can absorb only about 8 percent more heat than an equal number of aluminum atoms. A given mass of water, however, can absorb nearly five times as much heat as an equal mass of aluminum. The specific heat of a gas is more complex and depends on whether it is measured at constant pressure or constant volume.

Thermal conductivity (k) is “the rate at which heat passes through a specified material, expressed as the amount of heat that flows per unit time through a unit area with a temperature gradient of one degree per unit distance,” according to the Oxford Dictionary. The unit for k is watts (W) per meter (m) per kelvin (K). Values of k for metals such as copper and silver are relatively high at 401 and 428 W/m·K, respectively. This property makes these materials useful for automobile radiators and cooling fins for computer chips because they can carry away heat quickly and exchange it with the environment. The highest value of k for any natural substance is diamond at 2,200 W/m·K.

Other materials are useful because they are extremely poor conductors of heat; this property is referred to as thermal resistance, or R-value, which describes the rate at which heat is transmitted through the material. These materials, such as rock wool, goose down and Styrofoam, are used for insulation in exterior building walls, winter coats and thermal coffee mugs. R-value is given in units of square feet times degrees Fahrenheit times hours per British thermal unit  (ft2·°F·h/Btu) for a 1-inch-thick slab.

In 1701, Sir Isaac Newton first stated his Law of Cooling in a short article titled “Scala graduum Caloris” (“A Scale of the Degrees of Heat”) in the Philosophical Transactions of the Royal Society. Newton’s statement of the law translates from the original Latin as, “the excess of the degrees of the heat … were in geometrical progression when the times are in an arithmetical progression.” Worcester Polytechnic Institute gives a more modern version of the law as “the rate of change of temperature is proportional to the difference between the temperature of the object and that of the surrounding environment.”

This results in an exponential decay in the temperature difference. For example, if a warm object is placed in a cold bath, within a certain length of time, the difference in their temperatures will decrease by half. Then in that same length of time, the remaining difference will again decrease by half. This repeated halving of the temperature difference will continue at equal time intervals until it becomes too small to measure.

Heat can be transferred from one body to another or between a body and the environment by three different means: conduction, convection and radiation. Conduction is the transfer of energy through a solid material. Conduction between bodies occurs when they are in direct contact, and molecules transfer their energy across the interface.

Convection is the transfer of heat to or from a fluid medium. Molecules in a gas or liquid in contact with a solid body transmit or absorb heat to or from that body and then move away, allowing other molecules to move into place and repeat the process. Efficiency can be improved by increasing the surface area to be heated or cooled, as with a radiator, and by forcing the fluid to move over the surface, as with a fan.

Radiation is the emission of electromagnetic (EM) energy, particularly infrared photons that carry heat energy. All matter emits and absorbs some EM radiation, the net amount of which determines whether this causes a loss or gain in heat.

In 1824, Nicolas Léonard Sadi Carnot proposed a model for a heat engine based on what has come to be known as the Carnot cycle. The cycle exploits the relationships among pressure, volume and temperature of gasses and how an input of energy can change form and do work outside the system.

Compressing a gas increases its temperature so it becomes hotter than its environment. Heat can then be removed from the hot gas using a heat exchanger. Then, allowing it to expand causes it to cool. This is the basic principle behind heat pumps used for heating, air conditioning and refrigeration.

Conversely, heating a gas increases its pressure, causing it to expand. The expansive pressure can then be used to drive a piston, thus converting heat energy into kinetic energy. This is the basic principle behind heat engines.

All thermodynamic systems generate waste heat. This waste results in an increase in entropy, which for a closed system is “a quantitative measure of the amount of thermal energy not available to do work,” according to the American Heritage Dictionary. Entropy in any closed system always increases; it never decreases. Additionally, moving parts produce waste heat due to friction, and radiative heat inevitably leaks from the system.

This makes so-called perpetual motion machines impossible. Siabal Mitra, a professor of physics at Missouri State University, explains, “You cannot build an engine that is 100 percent efficient, which means you cannot build a perpetual motion machine. However, there are a lot of folks out there who still don’t believe it, and there are people who are still trying to build perpetual motion machines.”

Entropy is also defined as “a measure of the disorder or randomness in a closed system,” which also inexorably increases. You can mix hot and cold water, but because a large cup of warm water is more disordered than two smaller cups containing hot and cold water, you can never separate it back into hot and cold without adding energy to the system. Put another way, you can’t unscramble an egg or remove cream from your coffee. While some processes appear to be completely reversible, in practice, none actually are. Entropy, therefore, provides us with an arrow of time: forward is the direction of increasing entropy.

The fundamental principles of thermodynamics were originally expressed in three laws. Later, it was determined that a more fundamental law had been neglected, apparently because it had seemed so obvious that it did not need to be stated explicitly. To form a complete set of rules, scientists decided this most fundamental law needed to be included. The problem, though, was that the first three laws had already been established and were well known by their assigned numbers. When faced with the prospect of renumbering the existing laws, which would cause considerable confusion, or placing the pre-eminent law at the end of the list, which would make no logical sense, a British physicist, Ralph H. Fowler, came up with an alternative that solved the dilemma: he called the new law the “Zeroth Law.” In brief, these laws are:

The Zeroth Law states that if two bodies are in thermal equilibrium with some third body, then they are also in equilibrium with each other. This establishes temperature as a fundamental and measurable property of matter.

The First Law states that the total increase in the energy of a system is equal to the increase in thermal energy plus the work done on the system. This states that heat is a form of energy and is therefore subject to the principle of conservation.

The Second Law states that heat energy cannot be transferred from a body at a lower temperature to a body at a higher temperature without the addition of energy. This is why it costs money to run an air conditioner.

The Third Law states that the entropy of a pure crystal at absolute zero is zero. As explained above, entropy is sometimes called “waste energy,” i.e., energy that is unable to do work, and since there is no heat energy whatsoever at absolute zero, there can be no waste energy. Entropy is also a measure of the disorder in a system, and while a perfect crystal is by definition perfectly ordered, any positive value of temperature means there is motion within the crystal, which causes disorder. For these reasons, there can be no physical system with lower entropy, so entropy always has a positive value.

The science of thermodynamics has been developed over centuries, and its principles apply to nearly every device ever invented. Its importance in modern technology cannot be overstated.

5. System models [2] 

A diagram of a generic thermodynamic system

An important concept in thermodynamics is the thermodynamic system, which is a precisely defined region of the universe under study. Everything in the universe except the system is called the surroundings. A system is separated from the remainder of the universe by a boundary which may be a physical boundary or notional, but which by convention defines a finite volume. Exchanges of work, heat, or matter between the system and the surroundings take place across this boundary.

In practice, the boundary of a system is simply an imaginary dotted line drawn around a volume within which is going to be a change in the internal energy of that volume. Anything that passes across the boundary that effects a change in the internal energy of the system needs to be accounted for in the energy balance equation. The volume can be the region surrounding a single atom resonating energy, such as Max Planck defined in 1900; it can be a body of steam or air in a steam engine, such as Sadi Carnot defined in 1824; it can be the body of a tropical cyclone, such as Kerry Emanuel theorized in 1986 in the field of atmospheric thermodynamics; it could also be just one nuclide (i.e. a system of quarks) as hypothesized in quantum thermodynamics, or the event horizon of a black hole.

Boundaries are of four types: fixed, movable, real, and imaginary. For example, in an engine, a fixed boundary means the piston is locked at its position, within which a constant volume process might occur. If the piston is allowed to move that boundary is movable while the cylinder and cylinder head boundaries are fixed. For closed systems, boundaries are real while for open systems boundaries are often imaginary. In the case of a jet engine, a fixed imaginary boundary might be assumed at the intake of the engine, fixed boundaries along the surface of the case and a second fixed imaginary boundary across the exhaust nozzle.

Generally, thermodynamics distinguishes three classes of systems, defined in terms of what is allowed to cross their boundaries:

Interactions of thermodynamic systems
Type of system Mass flow Work Heat
Open Green tick Green tick Green tick
Closed Red X Green tick Green tick
Thermally isolated Red X Green tick Red X
Mechanically isolated Red X Red X Green tick
Isolated Red X Red X Red X

As time passes in an isolated system, internal differences of pressures, densities, and temperatures tend to even out. A system in which all equalizing processes have gone to completion is said to be in a state of thermodynamic equilibrium.

Once in thermodynamic equilibrium, a system’s properties are, by definition, unchanging in time. Systems in equilibrium are much simpler and easier to understand than are systems which are not in equilibrium. Often, when analysing a dynamic thermodynamic process, the simplifying assumption is made that each intermediate state in the process is at equilibrium, producing thermodynamic processes which develop so slowly as to allow each intermediate step to be an equilibrium state and are said to be reversible processes.

6. States and processes [2]

When a system is at equilibrium under a given set of conditions, it is said to be in a definite thermodynamic state. The state of the system can be described by a number of state quantities that do not depend on the process by which the system arrived at its state. They are called intensive variables or extensive variables according to how they change when the size of the system changes. The properties of the system can be described by an equation of state which specifies the relationship between these variables. State may be thought of as the instantaneous quantitative description of a system with a set number of variables held constant.

A thermodynamic process may be defined as the energetic evolution of a thermodynamic system proceeding from an initial state to a final state. It can be described by process quantities. Typically, each thermodynamic process is distinguished from other processes in energetic character according to what parameters, such as temperature, pressure, or volume, etc., are held fixed; Furthermore, it is useful to group these processes into pairs, in which each variable held constant is one member of a conjugate pair.

Several commonly studied thermodynamic processes are:

  • Adiabatic process: occurs without loss or gain of energy by heat
  • Isenthalpic process: occurs at a constant enthalpy
  • Isentropic process: a reversible adiabatic process, occurs at a constant entropy
  • Isobaric process: occurs at constant pressure
  • Isochoric process: occurs at constant volume (also called isometric/isovolumetric)
  • Isothermal process: occurs at a constant temperature
  • Steady state process: occurs without a change in the internal energy
7. Potentials [2]

Thermodynamic potentials are different quantitative measures of the stored energy in a system. Potentials are used to measure the energy changes in systems as they evolve from an initial state to a final state. The potential used depends on the constraints of the system, such as constant temperature or pressure. For example, the Helmholtz and Gibbs energies are the energies available in a system to do useful work when the temperature and volume or the pressure and temperature are fixed, respectively.

The five most well known potentials are:

Name Symbol Formula Natural variables
Internal energy
Helmholtz free energy
Gibbs free energy
Landau Potential (Grand potential) ,

where  is the temperature,  the entropy,  the pressure,  the volume,  the chemical potential, the number of particles in the system, and  is the count of particles types in the system.

Thermodynamic potentials can be derived from the energy balance equation applied to a thermodynamic system. Other thermodynamic potentials can also be obtained through Legendre transformation.

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