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

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.

SUBMITTER: Kennedy IR

PROVIDER: S-EPMC8304742 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:The heat capacity, C p, of synthetic hydroxyapatite [Ca5(PO4)3OH-OH-Ap], as well as of ten compositions along the OH-Ap-chlorapatite (Cl-Ap) join and 12 compositions along the OH-Ap-fluorapatite (F-Ap) join have been measured using relaxation calorimetry (heat capacity option of the Physical Properties Measurement System-PPMS) and differential scanning calorimetry (DSC) in the temperature range of 5-764 K. Apatites along the Cl-OH and F-OH joins were synthesized at 1100 °C and 300 MPa in an internally heated gas pressure vessel via an exchange process between synthetic fluorapatite or chlorapatite crystals (200-500 μm size) and a series of Ca(OH)2-H2O solutions with specific compositions and amounts relative to the starting apatite. The standard third-law entropy of OH-Ap, derived from the low-temperature heat capacity measurements, is S° = 386.3 ± 2.5 J mol-1 K-1, which is ~ 1% lower than that resulting from low-temperature adiabatic calorimetry data on OH-Ap from the 1950's. The heat capacity of OH-Ap above 298.15 K shows a hump-shaped anomaly centred around 442 K. Based on published structural and calorimetric work, this feature is interpreted to result from a monoclinic to hexagonal phase transition. Super ambient C p up to this transition can be represented by the polynomial: CpOH - Ap298K-442KJ mol-1K-1=1013.7-13735.5T-0.5+2.616718107T-2-3.551381109T-3. . The DSC data above this transition were combined with heat capacities computed using density functional theory and can be given by the C p polynomial: CpOH - Ap>442KJ mol-1K-1=877.2-11393.7T-0.5+5.452030107T-2-1.3941251010T-3 . Positive excess heat capacities of mixing, ∆C p ex, in the order of 1-2 J mol-1 K-1, occur in both solid solutions at around 70 K. They are significant at these conditions exceeding the 2σ-uncertainty of the data. This positive ∆C p ex is compensated by a negative ∆C p ex of the same order at around 250 K in both binaries. At higher temperatures (up to 1200 K), ∆C p ex is zero within error for all solid solution members. As a consequence, the calorimetric entropies, Scal, show no deviation from ideal mixing behaviour within a 2σ-uncertainty for both joins. Excess entropies of mixing, ∆Sex, are thus zero for the OH-Ap-F-Ap, as well as for the OH-Ap-Cl-Ap join. The C p-T behaviour of the OH-Ap endmember is discussed in relation to that of the F- and Cl-endmembers.Supplementary informationThe online version contains supplementary material available at 10.1007/s00269-021-01167-1.

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

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