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"Carnot"
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Carnot Theorem Revisited: A Critical Perspective
After a brief review of Carnot’s everlasting contributions to the foundations of thermodynamics, we critically examine the consequences of the Carnot theorem, which leaves behind some lingering questions and confusion that persist even today. What is the one significant aspect of the Carnot cycle that leads to this theorem? When does the working substance play an important role for an engine and what is its correlation with the protocol of operational details? Do all reversible engines working between the same two temperatures have the same maximum efficiency of the Carnot engine as Fermi has suggested? Are all heat engines equivalent to a Carnot engine in disguise? Our new perspective allows for the clarification of these questions with a positive answer for the last question. Recognizing that Carnot eventually abandoned the caloric theory, we use a result by Carnot and simple dimensional analysis to show how the first law, the concept of entropy, and the efficiency of the Carnot engine could have been germinated by Carnot in his time. This then demonstrates that Carnot had good understanding of entropy before its invention by Clausius. We suggest that both should be credited with inventing entropy by calling it Carnot–Clausius entropy. We also clarify some fundamental misconceptions plaguing reversible regenerators and their irreversible replacement by heat exchangers in the field.
Journal Article
2024 ‘Key Reflections’ on Sadi Carnot’s 1824 ‘Réflexions’ and 200 Year Legacy
This author is not a philosopher nor a historian of science, but an engineering thermodynamicist. In that regard, and in addition to various philosophical “why and how” treatises and existing historical analyses, the physical and logical “what it is” reflections, as sequential Key Points, where a key Sadi Carnot reasoning infers the next one, along with novel contributions and original generalizations, are presented. We need to keep in mind that in Sadi Carnot’s time (early 1800s), steam engines were inefficient (below 5%, so the heat in and out was comparable within experimental uncertainty, as if caloric were conserved), the conservation of caloric flourished (might be a fortunate misconception leading to the critical analogy with the waterwheel), and many critical thermal concepts, including the conservation of energy (The First Law), were not even established. If Clausius and Kelvin earned the title “Fathers of thermodynamics”, then Sadi Carnot was ‘the ingenious’ “Forefather of thermodynamics-to-become”.
Journal Article
A Contemporary View on Carnot’s Réflexions
Entropy and energy had not yet been introduced to physics by the time Carnot wrote his seminal Réflexions. Scholars continue to discuss what he really had in mind and what misconceptions he might have had. Actually, his work can be read as a correct introduction to the physics of heat engines when the term calorique is replaced by entropy and entropy is used as the other fundamental thermal quantity besides temperature. Carnot’s concepts of falling entropy as an analogy to the waterfall, and the separation of real thermal processes into reversible and irreversible processes are adopted. Some details of Carnot’s treatise are ignored, but the principal ideas are quoted and assumed without modification. With only two thermal quantities, temperature and entropy, modern heat engines can be explained in detail. Only after the principal function of heat engines is developed is energy introduced as physical quantity in order to compare thermal engines with mechanical and electrical engines and, specifically, to calculate efficiency.
Journal Article
Thermodynamic theory of highly multimoded nonlinear optical systems
Lately, there has been a resurgence of interest in nonlinear multimode optical systems. The sheer complexity emerging from the presence of a multitude of nonlinearly interacting modes has led not only to new opportunities in observing a host of novel optical effects but also to new theoretical challenges in understanding their collective dynamics. Here, we present a consistent thermodynamical framework capable of describing in a universal fashion the exceedingly intricate behaviour of such photonic configurations. In this respect, we derive new equations of state and show that both the ‘internal energy’ and optical power always flow in accord to the second law of thermodynamics. The laws governing isentropic processes are derived and the prospect for realizing Carnot-like cycles is presented. In addition to shedding light on fundamental issues, our work may pave the way towards a new generation of high-power multimode optical structures and could have ramifications in other disciplines, such as Bose–Einstein condensates and optomechanics.
Journal Article
Conformal Graph Directed Markov Systems on Carnot Groups
We develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped
with a sub-Riemannian metric. In particular, we develop the thermodynamic formalism and show that, under natural hypotheses, the limit
set of an Carnot conformal GDMS has Hausdorff dimension given by Bowen’s parameter. We illustrate our results for a variety of examples
of both linear and nonlinear iterated function systems and graph directed Markov systems in such sub-Riemannian spaces. These include
the Heisenberg continued fractions introduced by Lukyanenko and Vandehey as well as Kleinian and Schottky groups associated to the
non-real classical rank one hyperbolic spaces.
eBook
Quantum signatures in the quantum Carnot cycle
The Carnot cycle combines reversible isothermal and adiabatic strokes to obtain optimal efficiency, at the expense of a vanishing power output. Quantum Carnot-analog cycles are constructed and solved, operating irreversibly with positive power. Swift thermalization is obtained in the isotherms utilizing shortcut to equilibrium protocols and the adiabats employ frictionless unitary shortcuts. The working medium in this study is composed of a particle in a driven harmonic trap. For this system, we solve the dynamics employing a generalized canonical state. Such a description incorporates both changes in energy and coherence. This allows comparing three types of Carnot-analog cycles, Carnot-shortcut, Endo-shortcut and Endo-global. The Carnot-shortcut engine demonstrates the trade-off between power and efficiency. It posses a maximum in power, a minimum cycle-time where it becomes a dissipator and for a diverging cycle-time approaches the ideal Carnot efficiency. The irreversibility of the cycle arises from non-adiabatic driving, which generates coherence. To study the role of coherence we compare the performance of the shortcut cycles, where coherence is limited to the interior of the strokes, with the Endo-global cycle where the coherence never vanishes. The Endo-global engine exhibits a quantum signature at a short cycle-time, manifested by a positive power output while the shortcut cycles become dissipators. If energy is monitored the back action of the measurement causes dephasing and the power terminates.
Journal Article
Rankine Carnot Batteries with the Integration of Thermal Energy Sources: A Review
This paper provides an overview of a novel electric energy storage technology. The Thermally Integrated Pumped Thermal Electricity Storage (TI-PTES) stores electric energy as thermal exergy. Compared to standard PTES, TI-PTES takes advantage of both electric and low-temperature heat inputs. Therefore, TI-PTES is a hybrid technology between storage and electric production from low-temperature heat. TI-PTES belongs to a technology group informally referred to as Carnot Batteries (CBs). As the TI-PTES grows in popularity, several configurations have been proposed, with different claimed performances, but no standard has emerged to date. The study provides an overview of the component and operating fluid selection, and it describes the configurations proposed in the literature. Some issues regarding the performance, the ratio between thermal and electrical inputs, and the actual TI-PTES utilisation in realistic scenarios are discussed. As a result, some guidelines are defined. The configurations that utilise high-temperature thermal reservoirs are more extensively studied, due to their superior thermodynamic performance. However, low-temperature TI-PTES may achieve similar performance and have easier access to latent heat storage in the form of water ice. Finally, to achieve satisfactory performance, TI-PTES must absorb a thermal input several times larger than the electric one. This limits TI-PTES to small-scale applications.
Journal Article
Review of Carnot Battery Technology Commercial Development
Carnot batteries are a quickly developing group of technologies for medium and long duration electricity storage. It covers a large range of concepts which share processes of a conversion of power to heat, thermal energy storage (i.e., storing thermal exergy) and in times of need conversion of the heat back to (electric) power. Even though these systems were already proposed in the 19th century, it is only in the recent years that this field experiences a rapid development, which is associated mostly with the increasing penetration of intermittent cheap renewables in power grids and the requirement of electricity storage in unprecedented capacities. Compared to the more established storage options, such as pumped hydro and electrochemical batteries, the efficiency is generally much lower, but the low cost of thermal energy storage in large scale and long lifespans comparable with thermal power plants make this technology especially feasible for storing surpluses of cheap renewable electricity over typically dozens of hours and up to days. Within the increasingly extensive scientific research of the Carnot Battery technologies, commercial development plays the major role in technology implementation. This review addresses the gap between academia and industry in the mapping of the technologies under commercial development and puts them in the perspective of related scientific works. Technologies ranging from kW to hundreds of MW scale are at various levels of development. Some are still in the stage of concepts, whilst others are in the experimental and pilot operations, up to a few commercial installations. As a comprehensive technology review, this paper addresses the needs of both academics and industry practitioners.
Journal Article
Realization of a micrometre-sized stochastic heat engine
An optically trapped colloidal particle serves as the first realization of a stochastic thermal engine, extending our understanding of the thermodynamics behind the Carnot cycle to microscopic scales where fluctuations dominate.
The conversion of energy into mechanical work is essential for almost any industrial process. The original description of classical heat engines by Sadi Carnot in 1824 has largely shaped our understanding of work and heat exchange during macroscopic thermodynamic processes
1
. Equipped with our present-day ability to design and control mechanical devices at micro- and nanometre length scales, we are now in a position to explore the limitations of classical thermodynamics, arising on scales for which thermal fluctuations are important
2
,
3
,
4
,
5
. Here we demonstrate the experimental realization of a microscopic heat engine, comprising a single colloidal particle subject to a time-dependent optical laser trap. The work associated with the system is a fluctuating quantity, and depends strongly on the cycle duration time,
τ
, which in turn determines the efficiency of our heat engine. Our experiments offer a rare insight into the conversion of thermal to mechanical energy on a microscopic level, and pave the way for the design of future micromechanical machines.
Journal Article