The Carnot cycle with the van der Waals equation of state

Agrawal, D. C.; Menon, V. J.

doi:10.1088/0143-0807/11/2/004

Cited by 11 publications

(26 citation statements)

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“…From the derivation using the Redlich-Kwong gas equation of state, we show that the derivation procedure succeeds even if the specific heat at constant volume C v is the function of volume and temperature -the difficulty encountered by Agrawal and Menon [1] while deriving Carnot efficiency using equation of state with On the contrary of Agrawal-Menon's discussion in Ref. [1] that it is difficult to apply the procedure stated in Section 1 for a finite Carnot cycle when the working substance is arbitrary, our results in Section 4 show that it is technically possible to derive the Carnot efficiency (I.1) from the general thermodynamic properties discussed in Section 2. However, since the thermodynamic properties are derived from the Maxwell's relations where the concept of entropy is used, the results in Section 4 are hence not surprising.…”

Section: Discussionmentioning

confidence: 97%

The efficiency of the Carnot cycle with arbitrary gas equations of state

Tjiang¹,

Sutanto²

2006

Eur. J. Phys.

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Abstract. The derivation of the efficiency of Carnot cycle is usually done by calculating the heats involved in two isothermal processes and making use of the associated adiabatic relation for a given working substance's equation of state, usually the ideal gas. We present a derivation of Carnot efficiency using the same procedure with Redlich-Kwong gas as working substance to answer the calculation difficulties raised by Agrawal and Menon [1]. We also show that using the same procedure, the Carnot efficiency may be derived regardless of the functional form of the gas equation of state.

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Section: Discussionmentioning

confidence: 97%

The efficiency of the Carnot cycle with arbitrary gas equations of state

Tjiang¹,

Sutanto²

2006

Eur. J. Phys.

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“…For example, equation (1) reproduces the ideal gas equation when ; and reproduces the Van der Waals equation for and , where and are the usual Van der Waals parameters. In 1990, Agrawal and Menon showed how the Van der Waals equation verifies the Carnot efficiency [5]. Later, in 2006 Tjiang and Sutanto [6] made the same verification for the Redlich-Kwong state equation.…”

Section: A Somewhat General State Equation For Gasesmentioning

confidence: 89%

“…Equation (3) with , and any other gives equation (2). In the same way, many equations can be constructed, as for example, when , and (hereafter is not the Van der Waals parameter referred above), and every other results in (4) Similarly, with , and and every other we obtain (5) and with , and and every other then (6) in all these cases and are constants with proper units. It should be said that Eq.…”

Section: A Somewhat General State Equation For Gasesmentioning

confidence: 99%

“…In Figure 2 we depict a diagram of adiabatic processes (figure 2a), isothermal processes (figure 2b) and a Carnot cycle (figure 2c) for a substance described by equation (2). Obviously, we can construct Carnot cycles for equations (4), (5) and (6) (see figures (2), (3) and (4), respectively). In particular, equations (2), (5) and (6) represent unconventional substances, which do not fulfil the T-H criterion as they do not reproduce the ideal gas equation for diluted gases ( ).…”

Section: On the Tykodi-hummel Criterionmentioning

confidence: 99%

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The universality of the Carnot theorem

González-Ayala¹,

Angulo‐Brown²

2013

Eur. J. Phys.

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Abstract. It is common in many thermodynamic textbooks to illustrate the Carnot theorem through the usage of diverse state equations for gases, paramagnets, and other simple thermodynamic systems. As it is well-known, the universality of the Carnot efficiency is easily demonstrated in a temperature-entropy diagram, which means that is independent of the working substance. In this present work we remark that the universality of the Carnot theorem goes beyond the conventional state equations, and it is fulfilled by gas state equations that do not behave as ideal gas in the dilution limit namely Some of these unconventional state equations have certain thermodynamic "anomalies" that nonetheless do not forbid them from obeying the Carnot theorem. We discuss how this very general behaviour arises from the Maxwell relations, which are connected with a geometrical property expressed through preserving area transformations. A rule is proposed to calculate the Maxwell relations associated with a thermodynamic system by using the preserving area relationships. In this way it is possible to calculate the number of possible preserving area mappings by giving the number of possible Jacobian identities between all pairs of thermodynamic variables included in the corresponding Gibbs equation. This work is intended for undergraduate and specialists in thermodynamics and related areas.

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“…However, in a real context, a thermal engine works with a non-ideal gas. The performannce of a finite time cycle with a van der Waals gas as working fluid was analyzed among others by Agrawal & Menon (1990), and more recently by Ladino-Luna (2005). Fig.…”

Section: Introductionmentioning

confidence: 99%