The 2nd law of thermodynamics is a conjecture about the efficiency of a heat engine that deviates from reality and has become witchcraft.
Comparing the first and second laws of thermodynamics when studying heat engines, you will find that the second law of thermodynamics is purely speculative.See the picture for details.
Hi. First law presents energy as the state function that deponds to thermodynamic parameters such as T, V, N,....
The second law corresponds to entropy as the state function which is related to the collective behavior of the particles of the system, not to thermodynamic parameters.
The efficiency is resulted from our observation in nature, not by mathematical calculations.
The question highlights the difference between how Carnot efficiency is studied in the second law of thermodynamics and how engineers approach practical thermal systems.
Writing:
The second law of thermodynamics provides a theoretical framework for understanding how thermal systems work and sets the upper limit for efficiency in converting heat into work. This theoretical limit is called "Carnot efficiency," which represents the maximum possible efficiency a heat engine can achieve when operating between two thermal reservoirs (a hot and a cold reservoir). Carnot efficiency does not require detailed knowledge of the relationships between pressure, volume, and temperature. It simply depends on the absolute temperatures of the reservoirs and is calculated as:
\[
\eta_{Carnot} = 1 - \frac{T_2}{T_1}
\]
where T₁ is the temperature of the hot reservoir and T₂ is the temperature of the cold reservoir. This equation represents the theoretical upper bound on efficiency, assuming the engine operates in an ideal, reversible manner without any energy loss.
However, this theoretical picture often differs from the practical reality that engineers face. In real-world applications, engineers need to go beyond just knowing the theoretical limits of efficiency; they must also understand how the system behaves in terms of detailed thermodynamic properties. They use equations like \( P = P(V, T) \) (pressure as a function of volume and temperature) and \( E = E(V, T) \) (energy as a function of volume and temperature) to design systems that approach these limits while accounting for real-world inefficiencies and material behavior.
In short, while the second law and Carnot efficiency provide the theoretical limits, engineers must deal with the practical aspects of system design, using detailed relationships between pressure, energy, volume, and temperature to optimize the system within those theoretical constraints.
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