Abstract
This article explores some interesting relations between Pythagorean means (arithmetic, geometric, and harmonic means) and the coefficients of performance of reversible Carnot machines (heat engine, refrigerator, and heat pump).
Similar content being viewed by others
Suggested Reading
Sir Thomas Heath, A History of Greek Mathematics, Vol.1, Oxford: Clarendon Press, 1921.
P T Landsberg, A Thermodynamic Proof of the Inequality Between Arithmetic and Geometric mean, Phys. Lett., Vol.67A, No.1, 1978.
M A B Deakin and G J Group, The Logical Status of Thermodynamic Proofs of Mathematical Theorems, Phys. Lett., Vol.83A, p.239, 1981.
R J Tykodi, Using Model Systems to Demonstrate Instances of Mathematical Inequalities, Am. J. Phys., Vol. 64, p.644, 1996.
R S Johal, Optimal Performance of Heat Engines With a Finite Source or Sink and Inequalities Between Means, Phys. Rev., E 94, 012123, 2016.
Author information
Authors and Affiliations
Corresponding author
Additional information
Ramandeep Johal explores the foundations of thermodynamics through investigations on finite-time thermodynamics, inference and quantum thermodynamics. His first book of poems The Sea of Tranquility has been published by the Writers Workshop, Kolkata, in 2016.
Rights and permissions
About this article
Cite this article
Johal, R.S. Pythagorean means and Carnot machines. Reson 22, 1193–1203 (2017). https://doi.org/10.1007/s12045-017-0581-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12045-017-0581-z