On the Available Work Limits at Constant Heat and Entropy Production


  • Saeed Shahsavari Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran
  • Mehran Moradi Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran
  • Morteza Esmaeilpour Department of Civil Engineering, Geo and Environmental Sciences, Karlsruhe Institute of Technology, Kralsruhe, Germany




Thermodynamic cycle; Maximum work; Minimum work; Production Entropy; Maximum irreversibility


In this paper, using the combination of the first and second laws of thermodynamics, the work bounds in thermodynamic cycles are investigated generally and, to show the application, the results are extracted for some physical systems. Also, a new concept on the available work limits is extracted. To provide information on the maximum or minimum amount of work to be done during a thermodynamic cycle, energy balance, as well as irreversibility, should be considered. Entropy production during a thermodynamic cycle as a limiting criterion for work to be done is expressed as Clausius inequality. Therefore an inequality extracted from the first and second laws of thermodynamic to obtain lower and upper bounds of available work. The obtained upper bound of the work to be done is in agreement with Carnot’s rule. The lower bound is obtained at the maximum possible irreversibility during the respective cycle.




Erlichson, Herman. "Sadi Carnot,Founder of the Second Law of Thermodynamics'." European journal of physics 20.3 (1999): 183.

Sheehan, D. P. "The second law of thermodynamics: Foundations and status." Foundations of Physics 37.12 (2007): 1653-1658.

Ponter, A. R. S. "General displacement and work bounds for dynamically loaded bodies." Journal of the Mechanics and Physics of Solids 23.2 (1975): 151-163.

Wolff, Ronald W. "Upper bounds on work in system for multichannel queues." Journal of applied probability 24.2 (1987): 547-551.

Reinhardt, William P., and John E. Hunter III. "Variational path optimization and upper and lower bounds to free energy changes via finite time minimization of external work." The Journal of chemical physics 97.2 (1992): 1599-1601.

Ponter, Alan RS, and Jeffrey John Williams. "Work bounds and associated deformation of cyclically loaded creeping structures." (1973): 921-927.

WILLIAMS, JJ. "Work Bounds and Associated Deformation of Cyclically Loaded Creeping Structures."

Siirtola, Antti. "Bounds: from parameterised to finite-state verification." 2011 Eleventh International Conference on Application of Concurrency to System Design. IEEE, 2011.

Danes, Florin, and Bertrand Garnier. "Effective conductivity bounds by inserting adiabatic or isothermal surfaces." International journal of heat and mass transfer 54.15-16 (2011): 3523-3535.

Carter, Peter. "Analysis of cyclic creep and rupture. Part 1: Bounding theorems and cyclic reference stresses." International journal of pressure vessels and piping 82.1 (2005): 15-26.

Layton, W. J. "Energy dissipation bounds for hear flows for a model in large eddy simulation." Mathematical and Computer Modelling 35.13 (2002): 1445-1451.

Srivastava, Saket, Sudeep Sarkar, and Sanjukta Bhanja. "Estimation of upper bound of power dissipation in QCA circuits." IEEE transactions on nanotechnology 8.1 (2008): 116-127.

Laugesen, Richard S. "New dissipated energies for the thin fluid film equation." Communications on Pure & Applied Analysis 4.3 (2005): 613.

Bryant, Samuel J., and Benjamin B. Machta. "Energy dissipation bounds for autonomous thermodynamic cycles." Proceedings of the National Academy of Sciences 117.7 (2020): 3478-3483.

Bryant, Samuel J., and Benjamin B. Machta. "Energy Dissipation Bounds in Autonomous Thermodynamic Systems." arXiv preprint arXiv:1903.06780 (2019).

Burbury, S. H. "LVII. The second law of Thermodynamics." The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 37.229 (1894): 574-578.

Carnot, Sadi, Rudolf Clausius, and William Thomson Baron Kelvin. The Second Law of Thermodynamics. American Book Company, 1899.




How to Cite

Shahsavari, S., Mehran Moradi, & Esmaeilpour, M. (2020). On the Available Work Limits at Constant Heat and Entropy Production. Asian Journal of Applied Sciences, 8(6). https://doi.org/10.24203/ajas.v8i6.6374