History of Thermodynamics

Table of Contents

Introduction

The historical development of thermodynamics represents not only one of the most fascinating chapters but also one of the most significant episodes in the intellectual evolution of humanity. Originating from a purely practical investigation related to the economic aspects of engineering, it has evolved into a doctrine of profound philosophical importance. Its implications extend across a broad spectrum of human thought, encompassing both highly practical applications and the expansive queries of cosmology. The field has encountered challenges throughout its progression due to misconceptions from our incomplete understanding of Heat’s nature and matter’s structure. The individuals responsible for its foundational advancements, who significantly contribute to Gibbs’ intellectual lineage, were of varied and intriguing backgrounds, drawn from diverse professions, including the military, engineering, medicine, and academia. This diversity is unparalleled in all of physics, except electricity, in terms of its profound impact on human thought and its widespread influence.

As a scientific discipline, thermodynamics was initially confined to studying Heat’s relationship with mechanical work, as suggested by its name. However, mainly owing to the contributions of Willard Gibbs, its scope has significantly broadened to encompass the entire spectrum of energy transformations across all possible manifestations—thermal, mechanical, electrical, chemical, and radiant. For those looking to explore further into the chemical aspects of thermodynamics, a comprehensive list of Chemical Suppliers can provide the necessary resources for experimental and industrial applications. The theoretical evolution within its initially narrow scope can be delineated into two major advancements.

The Impact of Carnot’s Work

The first significant leap was made in 1824 by Nicolas Leonard Sadi Carnot, a young French military engineer who aimed to maximize the mechanical work derived from a given amount of Heat. His resolution to this engineering challenge introduced two of the most generative concepts to science and a methodological approach that has since become emblematic. Within his work, Carnot acknowledged for the first time the necessity of returning a system to its initial state to accurately account for its transformations. Furthermore, he introduced the concept of reversible processes—those in which a tiny adjustment in external conditions can invert the direction of the process.

Utilizing these novel concepts, he embarked on arguably one of the most ingenious intellectual endeavours in the annals of scientific inquiry. He demonstrated that, given a heat source at a specific temperature capable of imparting Heat to a working medium and another reservoir at a lower temperature capable of receiving expelled Heat, the maximum conceivable amount of mechanical work is achievable when the processes the working medium undergoes are entirely reversible.

The reasoning is brief as follows: Consider an engine with a working medium, for instance, steam, which absorbs a quantity of Heat (H) from a high-temperature source (like a steam boiler), performs work (W) on an external burden, discharges a quantity of Heat (h) to a cooler reservoir, and is subsequently restored to its initial state, allowing the cycle to perpetuate indefinitely. If these operations are conceived to be reversible, the engine, upon receiving work (W) from an external force in each cycle, would operate in reverse, extracting heat (h) from the cooler reservoir and transferring heat (H) back to the hotter source in every cycle.

Foundations of Carnot’s Principle

Therefore, if any engine (whether reversible or not) operating between these two reservoirs is hypothesized to perform the same work (W) utilizing less Heat than (H), implying a higher efficiency, it could potentially reverse the operation of the reversible engine. Consequently, in each operational cycle, the amalgamated engines would return more Heat to the high-temperature reservoir than what was extracted, leading to a continuous transfer of Heat from a cooler to a warmer body without external intervention. Such an outcome contradicts empirical evidence, leading to the deduction that no engine can surpass the efficiency of a reversible engine operating within the same temperature range. Alternatively, it posits that the maximal work output from a given heat source is exclusively attainable through a reversible engine. This pivotal conclusion is recognized as “Carnot’s principle,” which, although derived from theoretical considerations, is irrespective of the working medium’s nature or the specific cycle it undergoes. The foundational aspects crucial to this conclusion include, firstly, the presence of temperature variances between the reservoirs; secondly, the reversible nature of the working medium’s processes; and thirdly, the refutation of the notion that Heat can spontaneously transfer from a colder to a warmer body without external assistance.

This third fundamental component of the argument is celebrated as the “Second Law of Thermodynamics.” While implicit in the derivation of Carnot’s principle, he did not explicitly articulate it as a law. It was not until over twenty-five years later that Clausius and William Thomson (Lord Kelvin) formally established it as a cornerstone of thermodynamic science. The other two critical elements of Carnot’s rationale—the concept of reversibility and the assertion that mechanical work cannot be derived from Heat in the absence of a temperature gradient—are also integral to thermodynamics. Despite Carnot’s seminal role in founding this new scientific field, he did not advance to quantifying the ideal efficiency’s magnitude, hindered by the then-prevailing confusion in the scientific community regarding Heat’s essence. Evidence from the “Reflexions” and further in his posthumously published papers by his brother suggests Carnot’s skepticism towards the then-dominant “caloric” theory of Heat and his inclination towards the kinetic theory.

Carnot Efficiency

Clapeyron’s Mathematical Formulation

Nevertheless, the individual who notably advanced this second step and significantly disseminated Carnot’s findings, Benoit Pierre Emile Clapeyron, was a staunch proponent of Heat being a material “fluid.” In his work “Memoire sur la puissance de la chaleur,” published in the Journal de l’Ecole Polytechnique, he mathematically formulated Carnot’s principle, asserting that a reversible engine’s efficiency depends solely on the temperatures of the two reservoirs (Carnot’s function). He endeavoured to ascertain its value by examining a specific reversible cycle pertinent to a substance’s state change (from liquid to vapour or solid to liquid). Despite the accuracy of his outcomes, his derivation was based on the caloric hypothesis assumption—that the Heat absorbed from the hot reservoir (H) was equivalent to that expelled to the cooler reservoir (h), with the work being generated through a temperature drop, akin to the operation of a water wheel propelled by the elevation difference between its intake and discharge points.

The Emergence of the Energy Concept

As experimental evidence began to amass—from the investigations conducted by Benjamin Thomson (Count Rumford) and Sir Humphrey Davy around the turn of the 19th century to those of Robert Mayer and James Prescott Joule in the 1840s—it became evident that heat and mechanical work are merely two different forms of the same entity, energy. This recognition led to the understanding that the conversion between these forms is governed by a constant ratio, encapsulating the essence of the First Law of Thermodynamics. This law posits that when external heat energy is supplied to a body, it generally results in expansion (manifesting as work) and an increase in temperature (augmenting its “internal” or “intrinsic” energy).

Therefore, if these three energy forms are quantified using the same units, with increases marked as positive, the First Law dictates that any energy transformation results in a change in intrinsic energy equal to the difference between the heat energy supplied to the body and the work it performs. In scenarios where no heat energy is supplied, the work executed depletes the intrinsic energy, maintaining the total mechanical energy (both external and internal) unchanged or conserved. During a cyclic process that periodically returns a body to its initial state, no alteration in its intrinsic energy occurs. Consequently, the net heat energy supplied must equal the work performed, signifying the body’s total energy conservation in both forms. Therefore, The First Law can be viewed as articulating the “conservation of energy” principle, applicable to transformations between Heat and mechanical energy.

Correction of the Carnot Function

With the definitive establishment of the First Law in the late 1840s, it became necessary to rectify Clapeyron’s erroneous derivation of the Carnot function. Contrary to the hydraulic analogy that posited equal amounts of heat energy being absorbed and expelled by a working substance, the First Law mandates that their difference equates to the thermal equivalent of the external work done, formulated as: W = H – h

Leveraging this principle, Thomson (in 1848) demonstrated that by selecting a sequence of heat reservoirs with gradually decreasing temperatures and operating reversible engines (each performing the same external work) between them in a manner where the Heat expelled by one engine is absorbed by the next, a point is eventually reached where no heat remains to be expelled. The temperature at this juncture would represent the lowest conceivable limit—the absolute zero.

This approach to temperature scaling, which considers the work performed by a series of reversible engines, introduces the reciprocal of the temperature of the hottest reservoir as the Carnot function value, leading to an efficiency expression for a reversible engine as: Work done/Heat received = (Heat rejected – Heat received)/Heat received

Simplifying, we get: Work done/Heat received = Trej – Trec/Trec; where Trec represents the temperature of heat absorption, and Trej denotes the temperature of heat expulsion. This method of temperature measurement is known by several names: the “work,” the “absolute,” the “thermodynamic,” or the “Kelvin” scale. Temperatures are based on this scale, with its “zero point” set approximately 273 degrees below the centigrade scale or about 460 degrees below the Fahrenheit scale. Thus, twenty-four years after Carnot’s principle was articulated, its precise quantitative expression was determined, and another two years before, Clausius solidified its foundation with an accurate rendition of the Second Law of Thermodynamics.

Integration of Thermodynamic Laws

The subsequent advancement of the theory involves interpreting the equation above and integrating the expressions of the two laws into a singular equation. Clausius, drawing from an alternative efficiency expression for a reversible engine, Heat rejected/Temp. of rejection = Heat received/Temp. of reception, conceived the notion of “entropy.” This concept, indicative of a substance’s state just as its temperature or pressure, volume or intrinsic energy, is defined as the ratio of the reversible heat energy exchange to the absolute temperature at which it occurs. An alternative, perhaps more elucidative definition, is also offered.

Given that no real engine can achieve the efficiency of an ideal reversible engine, it is inferred that in all practical transformations of Heat into mechanical energy, there is an inevitable loss of energy. This energy loss in such transformations can be quantified by the change in entropy, which serves as a measure of this unavoidable dissipation, or entropy can be defined as the quantity that, when multiplied by the lowest accessible temperature, yields the magnitude of the irrecoverably lost energy.

While immensely useful in physics, entropy presents challenges in conceptual visualization primarily due to the absence of direct sensory perception, unlike other physical properties such as temperature or volume. Nevertheless, entropy is one of the most instrumental concepts introduced into physics. It facilitates a considerable simplification in articulating Carnot’s principle, comparable to the conceptual breakthrough of “absolute” temperature. The aforementioned alternate expression of the principle simplifies that within the system comprising the two reservoirs and the working substance, the change in entropy is null, or in reversible cycles, entropy remains conserved. Further illustrating the utility of this concept, Clausius deduced (most evidently from the second definition) that entropy invariably increases in all irreversible processes or natural changes. This principle, encapsulated in his formulation of the second law as “The entropy of the world strives towards a maximum,” along with his rendition of the first law as “The energy of the world is constant,” was prominently placed by Gibbs at the commencement of his seminal monograph. These principles aptly encapsulate the foundational elements upon which his work was constructed.

The Prime Fundamental Equation of Thermodynamics

Another testament to the value of the entropy concept is its contribution to integrating and simplifying the two laws of thermodynamics into what can be described as the “prime” fundamental equation of the discipline. For reversible processes, where the work performed can be quantified as the product of pressure and the resultant change in volume—applicable to fluids (gases, vapours, and liquids) as well as to non-crystalline and unstrained solids—the equation manifests as: Change in intrinsic energy equals: (a) Change in heat energy minus Change in mechanical energy, (b) Temperature times Change in entropy minus Pressure times Change in volume.

This equation is deemed fundamental in that, given experimental data on how a substance’s change in energy is contingent upon changes in entropy and volume, it is sufficient to determine the substance’s thermal and mechanical properties. However, this equation is strictly applicable to substances uniform in composition.

Gibbs’ Contribution and Legacy

This fundamental equation was the cornerstone for Gibbs’ elaboration and expansion of thermodynamics. It encapsulates the entirety of his indebtedness to his forerunners. None had even remotely anticipated the direction of his further exploration of the subject. Before him, no one had envisioned that the equation could be extended to encompass non-homogeneous bodies, nor had it been recognized that such an extension would unlock the vast domain of chemical equilibrium.

The narrative of Gibbs’ methodical and logically inevitable progression towards his grand generalization and the thoroughness with which he examined its outcomes and implications stands as a nearly unparalleled account in scientific history. “On the Equilibrium of Heterogeneous Substances,” which emerged in the scientific community in the 1870s as unexpectedly as Carnot’s Reflexions in the 1820s, did not require subsequent enhancement to achieve its potential, unlike Carnot’s work. Gibbs’ contribution constitutes a complete entity, within which the advancements over the following seventy-five years in the encompassed fields primarily appear as direct and unavoidable outcomes. Comparable to Sir Isaac Newton’s Principia, Gibbs’ work remains a monumental testament to the potency of abstract thought and logical reasoning in the trajectory of human intellectual advancement.

Concluding Thoughts

First Law of Thermodynamics

The First Law of Thermodynamics, also known as the Law of Conservation of Matter/Energy, provides a fundamental cornerstone for understanding how energy and matter interact within the universe. This law posits that within a closed system undergoing adiabatic processes—where no heat is exchanged with the surroundings—the total amount of work done during a transition from one state to another remains constant across all possible pathways between these two states.

Breaking it down into simpler terms, the First Law asserts that energy or matter can change form but cannot be created out of nothing or annihilated into nothingness. It underscores the principle that energy and matter cannot emerge spontaneously without a cause, nor can they disappear without a trace.

The significance of the First Law extends far beyond its scientific definition; it underpins the very foundation of scientific inquiry. Science relies on establishing clear cause-and-effect relationships. Without the First Law, the unpredictability of matter or energy appearing out of nowhere would cast doubt on these relationships, making scientific observations unreliable. Essentially, the First Law reinforces the principle of causality, ensuring that scientific conclusions are built on solid ground.

Implications of the First Law

The philosophical implications of the First Law are profound. It suggests that the universe must either have always existed in some form, never emerging from or dissolving into nothingness or originated from a transcendent creator outside the realm of our universal laws. This introduces a fascinating paradox when discussing the universe’s origins or a supreme creator. Critics often challenge the concept of a creator by questioning its origin, inadvertently attributing to causality—a principle dependent on interactions within the universe—a self-existent nature they deny a supreme being. This line of reasoning fails to acknowledge that a creator existing beyond our universal laws wouldn’t be bound by these laws, including causality, which presupposes interactions within the universe.

Furthermore, the argument against a self-existent universe while denying a self-existent creator overlooks the unity principle in science: a law that applies in one context should be universally applicable. Thus, denying the universe’s spontaneous emergence while questioning a creator’s existence presents a logical inconsistency with the First Law.

In conclusion, the First Law of Thermodynamics provides a framework for understanding physical processes and invites deep philosophical contemplation about the universe’s origins. It posits that the most consistent standpoint with scientific principles and causality is the existence of a self-existing, external agent, not confined by the universe’s laws, as the source of all creation.

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