Spontaneity of nuclear fusion: a qualitative analysis via classical thermodynamics

Tosti, Silvano

doi:10.12688/openreseurope.13738.3

Cited by 3 publications

(2 citation statements)

References 25 publications

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“…The distribution of the average binding energy per nucleon (neutron or proton) vs. the mass number (see also Ref. [22]).…”

Section: Theorymentioning

confidence: 99%

“…By applying the classical thermodynamics, it results that the entropic contribution to the reaction spontaneity plays a different role in the fission and fusion reactions [22,23]. The operation of the plasmas at a very high temperature, adopted to increase the reaction rates in magnetically confined fusion machines, may significantly reduce the thermodynamic spontaneity of these processes.…”

Section: Introductionmentioning

confidence: 99%

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Classical Thermodynamic Analysis of D-Based Nuclear Fusion Reactions: The Role of Entropy

Tosti

2023

Energies

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In this work, the feasibility of nuclear processes is studied via classical thermodynamics by assessing the change in entropy, a parameter that has so far been neglected in the analysis of these reactions. The contribution of the entropy to the reaction spontaneity plays a different role in the fission and fusion reactions. In particular, in fusion reactions the temperature acts as a very powerful amplifier of the entropic term (−T ΔS) that, at the temperature of tokamaks (millions Kelvin), may significantly reduce the thermodynamic spontaneity of these processes. A new approach is followed for assessing the feasibility of the D-based reactions of interest for the magnetically confined nuclear fusion through the investigation of the effect of the temperature on both kinetics and thermodynamics. The results confirm that the deuterium–tritium reaction is the most promising fusion reaction to be realized in tokamak devices. At the temperature of 1.5 × 108 K (≈13 keV), the DT reaction exhibits a large thermodynamic spontaneity (ΔG = 16.0 MeV) and its reactivity is of the order of 10−22 m3/s, a value capable of guaranteeing the tritium burning rate needed to operate the nuclear plants under tritium self-sufficiency conditions and with a net energy production. The other results show that at the tokamaks’ temperature the two branches of the DD reaction exhibit a modest spontaneity (ΔG around −2 MeV) coupled to very low reactivity values (10−24 m3/s). The temperature rise that could be aimed to increase the reactivity is however ineffective to improve the reaction feasibility since it would augment the entropic term as well, thus shifting the ΔG towards positive values. The D3He reaction is soundly spontaneous at the tokamaks’ temperature (ΔG values of −17.2 MeV) while its kinetics is close to that of the DD reactions, which are at least two orders of magnitude lower than that of the DT reaction.

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“…The distribution of the average binding energy per nucleon (neutron or proton) vs. the mass number (see also Ref. [22]).…”

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Classical Thermodynamic Analysis of D-Based Nuclear Fusion Reactions: The Role of Entropy

Tosti

2023

Energies

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Assessment of Nuclear Fusion Reaction Spontaneity via Engineering Thermodynamics

Tosti

2024

Entropy

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This work recalls the basic thermodynamics of chemical processes for introducing the evaluation of the nuclear reactions’ spontaneity. The application and definition of the thermodynamic state functions of the nuclear processes have been described by focusing on their contribution to the chemical potential. The variation of the nuclear binding potentials involved in a nuclear reaction affects the chemical potential through a modification of the internal energy and of the other state functions. These energy changes are related to the mass defect between reactants and products of the nuclear reaction and are of the order of magnitude of 1 MeV per particle, about six orders of magnitude larger than those of the chemical reactions. In particular, this work assesses the Gibbs free energy change of the fusion reactions by assuming the Qvalue as the nuclear contribution to the chemical potential and by calculating the entropy through the Sackur–Tetrode expression. Then, the role of the entropy in fusion processes was re-examined by demonstrating the previous spontaneity analyses, which assume a perfect gas of DT atoms in the initial state of the fusion reactions, are conservative and lead to assessing more negative ΔG than in the real case (ionized gas). As a final point, this paper examines the thermodynamic spontaneity of exothermic processes with a negative change of entropy and discusses the different thermodynamic spontaneity exhibited by the DT fusion processes when conducted in a controlled or uncontrolled way.

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Classical Thermodynamic Analysis of Deuterium-Based Fusion Reactions

Tosti

Marrelli

2022

Hydrogen

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The fusion reactions involving deuterium are of great interest for the exploitation of the fusion energy via magnetic-confinement devices. In classical thermodynamics, the spontaneity of a process is established through the assessment of the change in Gibbs free energy. So far, the feasibility of nuclear reactions has been characterized in terms of cross section and Q-value while the entropic term (T ΔS) has been neglected. Such an assumption is always justified for fission reactions where the term ΔS is positive. In the case of fusion reactions that operate at very high temperatures (106–107 K) and where ΔS is negative, the change in Gibbs free energy may be positive, making the reaction non-spontaneous. This paper proposes a classical thermodynamic analysis of D-based reactions of interest for the magnetic-confinement fusion applications. The entropy contribution was evaluated via the Sackur–Tetrode equation while the change in enthalpy was considered constant and as corresponding to the Q-value of the fusion reaction. The results of the thermodynamic analysis are compared with nuclear reaction feasibility criteria based on the reaction reactivity. The DT and D3He reactions show a high degree of spontaneity although the second one presents a lower reactivity. An increase in temperature could enhance the reactivity of the D3He reaction at the cost of decreasing its thermodynamic spontaneity. Both branches of the DD reaction are characterized by a much lower thermodynamic spontaneity than that of the DT and D3He reactions. Furthermore, at the temperature of their maximum cross section, the DD reactions exhibit a largely positive change in Gibbs free energy and, therefore, are not spontaneous. At the temperature of magnetic-confinement fusion machines (1.5 × 108 K), among the D-based reactions studied, the DT one exhibits the highest degrees of spontaneity and reactivity.

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Spontaneity of nuclear fusion: a qualitative analysis via classical thermodynamics

Cited by 3 publications

References 25 publications

Classical Thermodynamic Analysis of D-Based Nuclear Fusion Reactions: The Role of Entropy

Classical Thermodynamic Analysis of D-Based Nuclear Fusion Reactions: The Role of Entropy

Assessment of Nuclear Fusion Reaction Spontaneity via Engineering Thermodynamics

Classical Thermodynamic Analysis of Deuterium-Based Fusion Reactions

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