[Paper Review] Dissipative heat engine is thermodynamically inconsistent

Anastassia M. Makarieva, V. G. Gorshkov|arXiv (Cornell University)|Oct 5, 2009

Advanced Thermodynamics and Statistical Mechanics18 references18 citations

TL;DR

This paper demonstrates that the concept of a dissipative heat engine—where work from a Carnot cycle is internally dissipated and reused to increase output—is thermodynamically inconsistent. It shows that such a model violates both the first and second laws of thermodynamics by implying infinite work output at low temperatures, and that the energy input must decrease as dissipation increases, limiting work to Carnot levels. The model's physical interpretation is flawed because it ignores the need for an external dynamic system to drive expansion and compression in a heat engine.

ABSTRACT

A heat engine operating on the basis of the Carnot cycle is considered, where the mechanical work performed is dissipated within the engine at the temperature of the warmer isotherm and the resulting heat is added to the engine together with an external heat input. The resulting work performed by the engine per cycle is increased at the expense of dissipated work produced in the previous cycle. It is shown that such a dissipative heat engine is thermodynamically inconsistent violating the first and second laws of thermodynamics. The existing physical models employing the dissipative heat engine concept, in particular, the heat engine model of hurricane development, are physically invalid.

Motivation & Objective

• To challenge the physical validity of the dissipative heat engine model used in meteorological literature.
• To identify the thermodynamic inconsistencies in the assumption that internal dissipation of work can increase engine output beyond Carnot limits.
• To clarify that a heat engine requires an external dynamic system to perform work, not internal dissipation.
• To demonstrate that the apparent entropy balance in the model is mathematically identical to the Carnot cycle but physically invalid due to energy conservation violations.
• To argue that atmospheric circulation patterns like hurricanes cannot be explained by Carnot-like heat engines or their dissipative variants.

Proposed method

• Analyzes the Carnot cycle as a reversible process requiring external mechanical work to drive expansion and compression.
• Models a Carnot engine with an ideal spring as the auxiliary dynamic system to perform mechanical work.
• Derives energy and entropy balances for both standard and dissipative heat engines.
• Shows that in the dissipative model, the external heat input Qsd must decrease as work dissipation Ad increases, violating the assumption of constant Qsd.
• Uses the Kelvin-Planck statement of the second law to prove that regenerating work from heat at the same temperature is impossible.
• Compares the entropy balance of the dissipative model to the Carnot cycle, showing mathematical identity without physical consistency.

Experimental results

Research questions

• RQ1 Can internal dissipation of work within a heat engine increase its net work output beyond the Carnot limit?
• RQ2 Is the dissipative heat engine model consistent with the first and second laws of thermodynamics?
• RQ3 Does the assumption of constant external heat input Qsd in the dissipative model hold under energy conservation?
• RQ4 Can a heat engine operating in thermal equilibrium with a heat reservoir spontaneously initiate heat transfer and expansion at a finite rate?
• RQ5 Do atmospheric vortices like hurricanes result from Carnot-like heat engines or from other dynamic processes?

Key findings

• The dissipative heat engine model violates the first law of thermodynamics because it implies work output Ad > Qsd while assuming constant external heat input Qsd, which is impossible as Qsd must decrease with increasing Ad.
• The model violates the second law of thermodynamics by suggesting that work Ad can be dissipated and then fully reconverted into work at the same temperature Ts, which is forbidden by the Kelvin-Planck statement.
• The effective efficiency εd = (Ts − T0)/T0 becomes infinite as T0 → 0, implying infinite work output, which is physically impossible.
• The total heat input Qs = Qsd + Ad remains constant, so the work output Ad is limited to the Carnot value A = εQs, even with internal dissipation.
• The apparent entropy balance Sd = Qs/Ts − Q0/T0 = 0 is mathematically identical to the Carnot cycle, but the physical interpretation is invalid because it ignores the need for an external dynamic system to drive the cycle.
• The paper concludes that atmospheric circulation cannot be explained by heat engine models, including dissipative ones, and that moisture condensation and potential energy release are the true drivers of storms.