Action and Entropy in Heat Engines: An Action Revision of the Carnot Cycle.

Ivan R Kennedy,Migdat Hodzic

doi:10.3390/e23070860

Abstract

Despite the remarkable success of Carnot’s heat engine cycle in founding the discipline of thermodynamics two centuries ago, false viewpoints of his use of the caloric theory in the cycle linger, limiting his legacy. An action revision of the Carnot cycle can correct this, showing that the heat flow powering external mechanical work is compensated internally with configurational changes in the thermodynamic or Gibbs potential of the working fluid, differing in each stage of the cycle quantified by Carnot as caloric. Action (@) is a property of state having the same physical dimensions as angular momentum (mrv = mr2ω). However, this property is scalar rather than vectorial, including a dimensionless phase angle (@ = mr2ωδφ). We have recently confirmed with atmospheric gases that their entropy is a logarithmic function of the relative vibrational, rotational, and translational action ratios with Planck’s quantum of action ħ. The Carnot principle shows that the maximum rate of work (puissance motrice) possible from the reversible cycle is controlled by the difference in temperature of the hot source and the cold sink: the colder the better. This temperature difference between the source and the sink also controls the isothermal variations of the Gibbs potential of the working fluid, which Carnot identified as reversible temperature-dependent but unequal caloric exchanges. Importantly, the engine’s inertia ensures that heat from work performed adiabatically in the expansion phase is all restored to the working fluid during the adiabatic recompression, less the net work performed. This allows both the energy and the thermodynamic potential to return to the same values at the beginning of each cycle, which is a point strongly emphasized by Carnot. Our action revision equates Carnot’s calorique, or the non-sensible heat later described by Clausius as ‘work-heat’, exclusively to negative Gibbs energy (−G) or quantum field energy. This action field complements the sensible energy or vis-viva heat as molecular kinetic motion, and its recognition should have significance for designing more efficient heat engines or better understanding of the heat engine powering the Earth’s climates.

Highlights

Carnot cycle with specified heat inputs per molecule, using the action mechanics described in Section 3 to calculate entropy, Gibbs potential, and other properties of state at
Carnot cycle with specified heat inputs per molecule, using the action mechanics described namic or quantum states of the molecules in the working fluid—not to the external work in Section 3 to calculate entropy, Gibbs potential, and other properties of state at each being done, the maximum external work possible is shown in Table 1 as well
“The maximum of motive power resulting from the employment of steam is the maximum of motive power realizable by any means whatever . . . there should not occur any change of temperature which may not be due to a change of volume.”

Summary

Introduction

The fully reversible cycle for ideal gases as working fluid in a heat engine, proposed by Carnot in 1824 [1,2], led to a revolution in our understanding of heat, energy, entropy, and their relationships. All heat input to the cycle is considered to be at the temperature of the source, while heat rejected is considered to be at the temperature of the sink. Carnot proposed that the motive power of the engine is a function of product of the volume of the working vapor and its pressure at the extremes of temperature Note that his cycle estimates the maximum work possible thermodynamically rather than the motive power or rate of work

Results

Discussion

Conclusion