A First Law Thought Experiment With A Second Law Result For Heat Engines Based On A Self-Contained Modified Carnot Cycle

  • Richard D Kaufman Independent Researcher

Abstract

The first law of thermodynamics does not forbid heat engines with 100% thermodynamic efficiency; it is the second law of thermodynamics which states that heat engines cannot obtain 100% efficiency. Can the first law ever show this second law result? Yes. We show that the first law alone can show that some heat engines cannot achieve efficiencies of 100% when self-contained cycles (which we define) are considered for some temperature reservoirs. Self-contained cycles do not rely on the surroundings for anything but heat transfer to the cycle. Self-contained cycles require that any work input required by the cycle must come from previously stored energy from the cycle (such as, by potential energy in a weight previously lifted by the engine when performing work). Also, any regenerative heat output must occur before it is used as regenerative heat input. Using an example of a self-contained modified Carnot cycle that utilizes an ideal gas, the first law shows that efficiencies of 100% are not possible for T_h < 2 T_c, where T_h is at a hotter temperature than T_c, a colder temperature. These cycles, which could operate through a finite temperature difference ∆T in some regions of a PV diagram, are not possible in other regions.

References

Baierlein, R. (1994). Entropy and the second law: A pedagogical alternative. American Journal of Physics, 62, 15-26.
Cengel, Y. A., & Boles, M. A. (1994). Thermodynamics an Engineering Approach (2nd ed.), McGraw-Hill, NY.
Lemons, D. S., & Penner, M. K. (2008). Sadi Carnot’s contribution to the second law of thermodynamics. American Journal of Physics, 76, 21-25.
Marcella, T. V. (1992), Entropy production and the second law of thermodynamics: An introduction to second law analysis. American Journal of Physics, 60, 888-895.
Reese, R. L. (2000). University Physics (Vol. 1). Brooks/Cole, Pacific Grove.
Samiullah, M. (2007). What is a reversible process? American Journal of Physics, 75, 608-609.
Wu, J. (2015). Three factors causing the thermal efficiency of a heat engine to be less than unity and their relevance to daily life. European Journal of Physics, 36, 015008.
Zemansky, M. W., & Dittman, R. H. (1997). Heat and thermodynamics (7th ed.). McGraw-Hill, NY.
Published
2019-04-02
How to Cite
KAUFMAN, Richard D. A First Law Thought Experiment With A Second Law Result For Heat Engines Based On A Self-Contained Modified Carnot Cycle. European Journal of Physics Education, [S.l.], v. 10, n. 1, p. 24-37, apr. 2019. ISSN 1309-7202. Available at: <http://eu-journal.org/index.php/EJPE/article/view/222>. Date accessed: 27 june 2019. doi: https://doi.org/10.20308/ejpe.v10i1.222.
Section
Classroom Physics