Thermoelectric Cycle and the Second Law of Thermodynamics

Abstract

In 2019, Schilling et al. claimed that they achieved the supercooling of a body without external intervention in their thermoelectric experiments, thus arguing that the second law of thermodynamics was bent. Kostic suggested that their claim lacked full comprehension of the second law of thermodynamics. A review of history shows that what Clausius referred to as the second law of thermodynamics is the theorem of the equivalence of transformations (unfairly ignored historically) in a reversible heat–work cycle, rather than “heat can never pass from a cold to a hot body without some other change” that was only viewed by Clausius as a natural phenomenon. Here, we propose the theorem of the equivalence of transformations for reversible thermoelectric cycles. The analysis shows that the supercooling phenomenon Schilling et al. observed is achieved by a reversible combined power–refrigeration cycle. According to the theorem of equivalence of transformations in reversible thermoelectric cycles, the reduction in body temperature to below the ambient temperature requires the body itself to have a higher initial temperature than ambient as compensation. Not only does the supercooling phenomenon not bend the second law, but it provides strong evidence of the second law.

Thermodynamic Derivation of the Reciprocal Relation of Thermoelectricity

“…Thus, for this thermoelectric circuit that does not take into account any irreversible factors, the contributions to heat from the Peltier effect and from the Thomson effect cancel each other out [ 17 ]: where I is the electric current and σ is the Thomson coefficient. Based on Equation (33), together with the energy conservation law, Kelvin derived the well-known Kelvin relation for the first time [ 18 ]. In fact, Equation (33) expresses that the net change in entropy for a reversible thermoelectric cycle is zero [ 19 ]: Therefore, Equation (33) was referred to as the “Clausius equality” in the thermoelectric cycle [ 18 ].…”

“…Based on Equation (33), together with the energy conservation law, Kelvin derived the well-known Kelvin relation for the first time [ 18 ]. In fact, Equation (33) expresses that the net change in entropy for a reversible thermoelectric cycle is zero [ 19 ]: Therefore, Equation (33) was referred to as the “Clausius equality” in the thermoelectric cycle [ 18 ]. The cyclic integral of entropy equal to zero is a reflection of its state property.…”

“…where I is the electric current and σ is the Thomson coefficient. Based on Equation ( 33), together with the energy conservation law, Kelvin derived the well-known Kelvin relation for the first time [18]. In fact, Equation (33) expresses that the net change in entropy for a reversible thermoelectric cycle is zero [19]:…”

“…Therefore, Equation ( 33) was referred to as the "Clausius equality" in the thermoelectric cycle [18]. The cyclic integral of entropy equal to zero is a reflection of its state property.…”

A Symmetric Form of the Clausius Statement of the Second Law of Thermodynamics

“…Nonetheless, Xue et al [4][5][6] reviewed the history of Clausius's establishment of thermodynamics in the mid-19 th century to find that, in fact, the second law of thermodynamics claimed by Clausius has nothing to do with irreversibility. Clausius incorporated the two laws of thermodynamics into a symmetrical theoretical framework, where he regarded the theorem of equivalence between heat and work as the first law and the theorem of equivalence of "transformations" (TET) as the second law and considered them to be of the same kind [2,3].…”