A simplified analysis of the Feynman pallet and ratchet mechanism considering different forms of generated power
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Delfino Ladino-Luna
,
Juan C. Chimal-Eguía
Abstract
In this paper, we analyze the advanced Feynman’s mechanism from the well-known Feynman’s Lectures on Physics, under the maximum power output, maximum efficient power, and maximum power density criterion. Considering this mechanism like a thermal engine, and using a simplified model, the physical existence regions for these objective functions are shown. We also show their comparison for given values of a defined dimensionless parameter. The behavior for each case of both the general and the normalized forms of the objective functions is compared graphically and the existence of certain intervals of values for the variable parameter used, in which the relation of these objective functions change, is determined. Additionally, it is shown that as the numerical value of the mentioned variable parameter used approaches zero, the area of the region of physical existence of the objective functions is greater. The results of the mentioned comparison are discussed, and appropriate conclusions are included.
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: This research was partially supported by the Consejo Nacional de Ciencia y Tecnología (CONACyT, Mexico). Juan Carlos Chimal-Eguía also thank COFAA-IPN and EDI-IPN.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
Nomenclature
- C
-
coefficient of heat leakage, W/(K)
- F
-
applied force, N
- k
-
dimensionless heat leakage coefficient
- k B
-
Boltzmann’s constant
-
-
quantity of molecules
- N A
-
Avogadro’s number
- P *
-
dimensionless power output
- p
-
pressure
-
-
rate of heat Flow, W
- T
-
temperature of the heat reservoir, K
- t
-
time, s
- V
-
volume, m3
- z
-
dimensionless internal parameter
- Z
-
toque for the sprocket
- Greek symbols
- α
-
defined internal parameter
- ε
-
energy required to overcome the spring force
- η
-
efficiency
- θ
-
angle of rotation of the axle
- τ
-
temperature ratio
- Superscripts
- *
-
dimensionless value
- Subscripts
- 0
-
quantity at zero value of any parameter
- max
-
maximum value
- C
-
quantity at low temperature
- H
-
quantity at high temperature
References
[1] R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics, vol. I, Massachusetts, USA, Addison-Wesley Pub., 1963, pp. 46.1–46.12.Suche in Google Scholar
[2] M. O. Magnasco, “Forced thermal ratchets,” Phys. Rev. Lett., vol. 71, no. 10, pp. 1477–1481, 1993. https://doi.org/10.1103/physrevlett.71.1477.Suche in Google Scholar PubMed
[3] J. M. R. Parrondo, “Criticism of Feynman’s analysis of the ratchet as an engine,” Am. J. Phys., vol. 64, no. 9, pp. 1125–1130, 1996. https://doi.org/10.1119/1.18393.Suche in Google Scholar
[4] M. O. Magnasco, “Feynman’s ratchet and pawl,” J. Stat. Phys., vol. 93, nos. 3/4, pp. 615–632, 1998. https://doi.org/10.1023/b:joss.0000033245.43421.14.10.1023/B:JOSS.0000033245.43421.14Suche in Google Scholar
[5] S. Velasco, J. M. M. Rocco, A. Medina, and A. Calvo-Hernández, “Feynman’s ratchet optimization: maximum power and maximum efficiency regimes,” J. Phys. D: Appl. Phys., vol. 34, pp. 1000–1006, 2001. https://doi.org/10.1088/0022-3727/34/6/323.Suche in Google Scholar
[6] T. Munakata and D. Suzuki, “Rectification efficiency of Feynman ratchet,” J. Phys. Soc. Jpn., vol. 74, no. 2, pp. 550–553, 2005. https://doi.org/10.1143/jpsj.74.550.Suche in Google Scholar
[7] L. Chen, Z. Ding, and F. Sun, “Optimum performance analysis of Feynman’s engine as cold and hot ratchets,” J. Non-Equilibrium Thermodyn., vol. 36, pp. 155–177, 2011. https://doi.org/10.1515/jnet.2011.011.Suche in Google Scholar
[8] R. Long, B. Li, and W. Liu, “Performance analysis for Feynman’s ratchet as a refrigerator with heat leak under different figure of merits,” Appl. Math. Model., vol. 40, pp. 10437–10446, 2016. https://doi.org/10.1016/j.apm.2016.07.027.Suche in Google Scholar
[9] V. Singh and R. S. Johal, “Feynman’s ratchet, and pawl with ecological criterion: optimal performance versus estimation with prior information,” Entropy, vol. 19, pp. 576–586, 2017. https://doi.org/10.3390/e19110576.Suche in Google Scholar
[10] P. Chambadal, Les Centrales Nucleares, Paris, France, Armand Colin, 1957, pp. 41–58.Suche in Google Scholar
[11] I. I. Novikov, “The efficiency of atomic power station (a review),” J. Nuclear Energy II, vol. 7, pp. 125–128, 1957. https://doi.org/10.1016/0891-3919(58)90244-4.Suche in Google Scholar
[12] F. L. Curzon and B. Ahlborn, “Efficiency of a Carnot engine at maximum power output,” Am. J. Phys., vol. 43, pp. 22–24, 1975. https://doi.org/10.1119/1.10023.Suche in Google Scholar
[13] B. Andresen, P. Salamon, and B. Berry, “Thermodynamic in finite time: extremals for imperfect heat engines,” J. Chem. Phys., vol. 66, pp. 1571–1577, 1977. https://doi.org/10.1063/1.434122.Suche in Google Scholar
[14] D. Gutkowicz-Krusin, I. Procaccia, and J. Ross, “On the efficiency of rate processes. Power and efficiency of heat engines,” J. Chem. Phys., vol. 69, pp. 3898–3906, 1978. https://doi.org/10.1063/1.437127.Suche in Google Scholar
[15] M. O. Ondrechen, M. H. Rubin, and Y. B. Band, “The generalized Carnot cycle: a working fluid operating in finite time between finite heat sources and sinks,” J. Chem. Phys., vol. 78, pp. 4721–4727, 1983. https://doi.org/10.1063/1.445318.Suche in Google Scholar
[16] A. Bejan, “Entropy generation minimization: the new thermodynamics of finite-size devices and finite-time processes,” J. Appl. Phys., vol. 79, pp. 1191–1218, 1996. https://doi.org/10.1063/1.362674.Suche in Google Scholar
[17] A. Sahim, A. Kodal, and H. Yavuz, “Maximum power density for an endoreversible Carnot heat engine,” Energy, vol. 21, pp. 1219–1225, 1996. https://doi.org/10.1016/0360-5442(96)00068-0.Suche in Google Scholar
[18] A. Kodal, B. Sahin, and T. Yilmaz, “A comparative performance analysis of irreversible Carnot heat engine under maximum power density and maximum power conditions,” Energy Convers. Manag., vol. 41, pp. 235–248, 2000. https://doi.org/10.1016/s0196-8904(99)00107-7.Suche in Google Scholar
[19] T. Yilmaz and Y. Dormusoglu, “Efficient power analysis for an irreversible Carnot heat engine,” Int. J. Energy Res., vol. 32, pp. 623–628, 2008. https://doi.org/10.1002/er.1377.Suche in Google Scholar
[20] D. Ladino-Luna, R. T. Páez-Hernández, J. C. Chimal-Eguía, and N. Sánchez-Salas, “A simplified analysis of the generated power in the Feynman pallet and ratchet mechanism,” in Proceedings 4o Congreso Multidisciplinario de Ciencias Aplicadas en Latinoamérica (COMCAPLA 2018), México, 2018, pp. 87–94.Suche in Google Scholar
[21] D. Ladino-Luna, R. T. Páez-Hernández, and J. C. Chimal-Eguía, “Análisis de la eficiencia para el mecanismo de Feynman maximizando diversas formas de potencia,” in Proceedings XXXIII Congreso Nacional de Termodinámica, México, 2019, pp. 538–547.Suche in Google Scholar
[22] W. Muschik and K. H. Hoffmann, “Endoreversible thermodynamics: a tool for simulating and comparing processes of discrete systems,” J. Non-Equilibrium Thermodyn., vol. 31, pp. 293–317, 2006. https://doi.org/10.1515/jnet.2006.013.Suche in Google Scholar
[23] Y. Yohei Nakayama, K. Kawaguchi, and N. Nakagawa, “Unattainability of Carnot efficiency in thermal motors: coarse graining and entropy production of Feynman-Smoluchowski ratchets,” Phys. Rev. E., vol. 98, p. 022102, 2018. https://doi.org/10.1103/physreve.98.022102.Suche in Google Scholar
[24] M. Santillán, G. Maya, and F. Angulo-Brown, “Local stability analysis of an endoreversible Curzon-Ahlborn-Novikov engine working in a maximum-power-like regime,” J. Phys. D: Appl. Phys., vol. 34, pp. 2068–2072, 2001. https://doi.org/10.1088/0022-3727/34/13/318.Suche in Google Scholar
[25] R. Páez-Hernández, F. Angulo-Brown, and M. Santillán, “Dynamic robustness, and thermodynamic optimization in a non-endoreversible Curzon and Ahlborn engine,” J. Non-Equilibrium Thermodyn., vol. 31, pp. 173–188, 2006.10.1515/JNETDY.2006.008Suche in Google Scholar
[26] Z. Ding, Y. Ge, L. Chen, H. Feng, and S. Xia, “Optimal performance regions of Feynman’s ratchet engine with different optimization criteria,” J. Non-Equilibrium Thermodyn., vol. 45, no. 2, pp. 191–207, 2020. https://doi.org/10.1515/jnet-2019-0102.Suche in Google Scholar
© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Original Research Articles
- The Onsager–Machlup theory of fluctuations and time-dependent generalized normal distribution
- Impact of wavy porous layer on the hydrodynamic forces and heat transfer of hybrid nanofluid flow in a channel with cavity under the effect of partial magnetic field
- Natural convection of a viscoelastic Cattaneo–Christov fluid bounded by thick walls with finite thermal conductivity
- A simplified analysis of the Feynman pallet and ratchet mechanism considering different forms of generated power
- Energy production in one-qubit quantum Agrawal machines
- The optimization of heat transfer in thermally convective micropolar-based nanofluid flow by the influence of nanoparticle’s diameter and nanolayer via stretching sheet: sensitivity analysis approach
- A practical upper-bound efficiency model for solar power plants
- Generalized Onsager fluxes based on inexact differential 1-form
Artikel in diesem Heft
- Frontmatter
- Original Research Articles
- The Onsager–Machlup theory of fluctuations and time-dependent generalized normal distribution
- Impact of wavy porous layer on the hydrodynamic forces and heat transfer of hybrid nanofluid flow in a channel with cavity under the effect of partial magnetic field
- Natural convection of a viscoelastic Cattaneo–Christov fluid bounded by thick walls with finite thermal conductivity
- A simplified analysis of the Feynman pallet and ratchet mechanism considering different forms of generated power
- Energy production in one-qubit quantum Agrawal machines
- The optimization of heat transfer in thermally convective micropolar-based nanofluid flow by the influence of nanoparticle’s diameter and nanolayer via stretching sheet: sensitivity analysis approach
- A practical upper-bound efficiency model for solar power plants
- Generalized Onsager fluxes based on inexact differential 1-form
