Comparison:
1）The first law of thermodynamics calculates the Carnot efficiency；
2）the second law of thermodynamics predicts: η= 1-T1/T2.
Method:
1）The first law: P=P (V, T), E=E (V, T) DE=Q-W==>η，Efficiency needs to be calculated and determined.
2）Second Law: Anti perpetual motion machine, guessing==>1-T1/T2.
Effect:
1）The first law: E, P, W, Q ，η of the cyclic process can be obtained,
2）Second Law: Only efficiency can be obtained：η= 1-T1/T2.
- The uniqueness of natural science requires scientists to make choices.
- The second law of thermodynamics can only yield a single conclusion: η= 1-T1/T2（Meaningless--- lacking support from E, P, W, Q results.）Like an island in the ocean.
Principles of Physics must be understood free from Mathematics. The first and second Law of Thermodynamics are the most general and fundamental Laws of Nature.
1. Law: "Von Nichts kommt nichts."
2. Law: "Ein bisschen Verlust ist immer."
best wishes
M.
If you use the second Law applied to Newton-Einsteins Equation of Motion you come up with the Sommerfeld FSC - by the way. (The power of the second law was the reason! Not me.)
It seems like you're discussing the efficiency (η) of a heat engine based on the second law of thermodynamics. The equation you've provided, η = 1 - T1/T2, is indeed an oversimplified expression for the efficiency of a heat engine, where T1 and T2 represent the absolute temperatures of the hot and cold reservoirs, respectively. However, this equation doesn't account for all the factors involved in a real-world thermodynamic process.
In reality, the efficiency of a heat engine depends on various factors, including the nature of the working substance, the specific thermodynamic cycle being used (e.g., Carnot cycle, Rankine cycle), and the presence of irreversibilities and losses. The complete expression for the efficiency of a heat engine involves entropy changes, work (W) done by or on the engine, and heat transfer (Q) between the reservoirs.
Efficiency = 1 - (Qc / Qh)
Where:
Qc is the heat transferred to the cold reservoir.
Qh is the heat transferred from the hot reservoir.
This equation takes into account the energy balance and the concept of entropy, which is a fundamental aspect of the second law of thermodynamics. The efficiency of a real heat engine will always be less than the idealized expression you've mentioned due to factors like friction, heat losses, and non-ideal behavior of working substances.
So, while η = 1 - T1/T2 provides a simplified conceptual understanding, a comprehensive analysis of real-world heat engines requires consideration of all relevant factors, as described by the complete efficiency formula.
Efficiency = 1 - (Qc / Qh)
Where:
Qc is the heat transferred to the cold reservoir.
Qh is the heat transferred from the hot reservoir.
Apply it to gravity and you come up with (GR+TD)
Preprint Conclusions from the Principles of Thermodynamics
Bo Miao: "The first law of thermodynamics calculates the Carnot efficiency" -- no, not at all. The first law only states that heat and work (i) are forms of energy, and (ii) they are the ways energy is transferred from one system to another. How could there be any efficiency included in this law? Please explain.
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