1st and 2nd laws of thermodynamics

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SUMMARY

The discussion centers on the relationship between the 1st and 2nd laws of thermodynamics, particularly in the context of ideal gases undergoing reversible processes. The reasoning presented suggests that the 2nd law may be derived from the 1st law, utilizing concepts such as Mayer's relation, the dependence of internal energy on temperature, and Carnot's theorem. Participants express skepticism about the validity of this reasoning, highlighting potential flaws due to reliance on assumptions that may already incorporate the 2nd law. The conversation emphasizes the need for a deeper understanding of thermodynamic principles.

PREREQUISITES
  • Understanding of the 1st and 2nd laws of thermodynamics
  • Familiarity with ideal gas law and Mayer's relation
  • Knowledge of Carnot's theorem and its implications
  • Basic concepts of reversible processes in thermodynamics
NEXT STEPS
  • Study the derivation of Mayer's relation in detail
  • Explore the implications of Carnot's theorem on thermodynamic cycles
  • Investigate the assumptions underlying the ideal gas law
  • Learn about statistical thermodynamics and its relation to classical thermodynamics
USEFUL FOR

Students of physics, engineers in renewable energy sectors, and anyone seeking to deepen their understanding of thermodynamic laws and their interrelationships.

fabius53
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While refreshing some thermodynamics for a personal interest in renewable energies, I drafted a reasoning that apparently leads from the 1st law to the 2nd law of thermodynamics, so that the latter, at least for ideal gases undergoing reversible processess, would seem to be just a consequence of the former.
Shortly, the reasoning starts from 1st law and ideal gas law, through Mayer's relation, the dependence of internal energy on just temperature, a general expression of the heat exchange \deltaQ, adiabatic slope, Carnot's theorem and finally 2nd law; in detail, it is included here (1stlaw-2ndlaw.pdf).
As far as I remember, 1st law and 2nd law of thermodynamics are basic laws (at least without involving statistical thermodynamics), so I tend to think that there must be some flaw in my reasoning.
Can anyone help me spot any flaws ? Or is the reasoning correct only under very restrictive hypotheses ? Can anyone maybe help me understand more deeply thermodynamics laws ?
I appreciate any contribution
 

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You use relations for ideal gases that were derived assuming the second law of thermodynamics in one way or another. It is not surprising that you can extract it again from these relations.
 

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