On thermodynamical work and heat definitions and their consistency regarding the second law

Anacleto, Joaquim; Pereira, Mário; Gonçalves, Norberto Jorge

doi:10.1590/s1806-11172010000200004

Cited by 2 publications

(4 citation statements)

References 15 publications

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“…Both irreversible components are non-negative as expected from the second law. We thus see that expressing the first law in terms of internal fields is consistent with irreversible entropy production, contrary to a recent claim [9].…”

Section: General Consideration and Clausius Relationcontrasting

confidence: 99%

“…Our approach to incorporate viscous dissipation results in expressing the first law in terms of internal fields and provides an elegant formulation of non-equilibrium thermodynamics in which the Clausius inequality turns into an equality in all cases, which is a remarkable result in its own right. It has been recently suggested [9] that use of internal fields is not always consistent with the second law. We find no such problem in our approach.…”

Section: σ0mentioning

confidence: 99%

“…However, there is some truth to their critique, which was motivated by an earlier paper by Bertrand [2], who revisited the confusion first noted by Bauman [3] about different formulation of work dW = P 0 dV or dW = P dV in terms of internal (P ) and external (P 0 ) pressures [4], see Fig. 1, and discussed by many others [5][6][7][8][9][10] since then. Different formulation of work from the first law obviously results in different heat.…”

Section: σ0mentioning

confidence: 99%

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Generalized Non-equilibrium Heat and Work and the Fate of the Clausius Inequality

Gujrati¹

2011

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By generalizing the traditional concept of heat dQ and work dW to also include their time-dependent irreversible components diQ and diW allows us to express them in terms of the instantaneous internal temperature T (t) and pressure P (t), whereas the conventional form uses the constant values T0 and P0 of the medium. This results in an extremely useful formulation of non-equilibrium thermodynamics so that the first law turns into the Gibbs fundamental relation and the Clausius inequality becomes an equality dQ(t)/T (t) ≡ 0 in all cases, a quite remarkable but unexpected result. We determine the irreversible components diQ ≡ diW and discuss how they can be determined to obtain the generalized dW (t) and dQ(t).

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Section: General Consideration and Clausius Relationcontrasting

confidence: 99%

Section: σ0mentioning

confidence: 99%

Section: σ0mentioning

confidence: 99%

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Generalized Non-equilibrium Heat and Work and the Fate of the Clausius Inequality

Gujrati¹

2011

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“…The Clausius inequality [44] turns into an equality in all cases as dQ(t)/T (t) becomes a state variable, the work is expresssed as an equality, as if we are dealing with equilibrium processes, a quite remarkable result in its own right, even though there is irreversible entropy generation. It has been recently suggested [32] that the use of internal fields is not always consistent with the second law. We find no such problem in our approach.…”

Section: New Resultsmentioning

confidence: 99%

Nonequilibrium Thermodynamics. Symmetric and Unique Formulation of the First Law, Statistical Definition of Heat and Work, Adiabatic Theorem and the Fate of the Clausius Inequality: A Microscopic View

Gujrati

2012

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The status of heat and work in nonequilibrium thermodynamics is quite confusing and nonunique at present with conflicting interpretations even after a long history of the first law dE(t) = d e Q(t) − dW e (t) in terms of exchange heat and work, and is far from settled. Moreover, the exchange quantities lack certain symmetry (see text). By generalizing the traditional concept to also include their time-dependent irreversible components d i Q(t) and d i W (t) allows us to express the first law in a symmetric form dE(t) = dQ(t) − dW (t) in which dQ(t) and work dW (t) appear on equal footing and possess the symmetry. We prove that d i Q(t) ≡ d i W (t); as a consequence, irreversible work turns into irreversible heat. Statistical analysis in terms of microstate probabilities p i (t) uniquely identifies dW (t) as isentropic and dQ(t) as isometric (see text) change in dE(t), a result known in equilibrium. We show that such a clear separation does not occur for d e Q(t)and dW e (t). Hence, our new formulation of the first law provides tremendous advantages and results in an extremely useful formulation of non-equilibrium thermodynamics, as we have shown recently [Phys. Rev. E 81, 051130 (2010); ibid 85, 041128 and 041129 ( 2012)]. We prove that an adiabatic process does not alter p i . All these results remain valid no matter how far the system is out of equilibrium. When the system is in internal equilibrium, dQ(t) ≡ T (t)dS(t) in terms of the instantaneous temperature T (t) of the system, which is reminiscent of equilibrium, even though, neither d e Q(t) ≡ T (t)d e S(t) nor d i Q(t) ≡ T (t)d i S(t). Indeed, d i Q(t) and d i S(t) have very different physics. We express these quantities in terms of d e p i (t) and d i p i (t), and demonstrate that p i (t) has a form very different from that in equilibrium. The first and second laws are no longer independent so that we need only one law, which is again reminiscent of equilibrium. The traditional formulas like the Clausius inequality d e Q(t)/T 0 < 0, ∆ e W < −∆ [E(t − T 0 S(t))], etc. become equalities dQ(t)/T (t) ≡ 0, ∆W = −∆ [E(t − T (t)S(t)], etc, a quite remarkable but unexpected result in view of the fact that ∆ i S(t) > 0. We identify the uncompensated transformation N (t, τ ) during a cycle. We determine the irreversible components in two simple cases to show the usefulness of our approach; here, the traditional formulation is of no use. Our extension bring about a very strong parallel between equilibrium and non-equilibrium thermodynamics, except that one has irreversible entropy generation d i S(t) > 0 in the latter.

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On thermodynamical work and heat definitions and their consistency regarding the second law

Cited by 2 publications

References 15 publications

Generalized Non-equilibrium Heat and Work and the Fate of the Clausius Inequality

Generalized Non-equilibrium Heat and Work and the Fate of the Clausius Inequality

Nonequilibrium Thermodynamics. Symmetric and Unique Formulation of the First Law, Statistical Definition of Heat and Work, Adiabatic Theorem and the Fate of the Clausius Inequality: A Microscopic View

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