Carnot's Theorem Principle Thermodynamics

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Carnot's Theorem Principle

With the practice of using reversible processes, Sadi Carnot in 1824 advanced the study of the second law by disclosing a principle consisting of the following propositions.

1. No engine can be more efficient than a reversible engine operating between the same high temperature and low temperature reservoirs. Here the term heat reservoir is taken to mean either a heat source or a heat sink.
2. The efficiencies of all reversible engines operating between the same constant temperature reservoirs are the same.
3. The efficiency of a reversible engine depends only upon the temperatures of the heat source and heat receiver.

Carnot's theorem states:

• All heat engines between two heat reservoirs are less efficient than a Carnot engine operating between the same reservoirs.
• Every Carnot engine between a pair of heat reservoirs is equally efficient, regardless of the working substance employed or the operation details.

The formula for this maximum efficiency is

n_max= n_carnot = 1 - T_c/T_H

where T C is the absolute temperature of the cold reservoir, T H is the absolute temperature of the hot reservoir, and the efficiency "n" is the ratio of the work done by the engine to the heat drawn out of the hot reservoir.

Based on modern thermodynamics, Carnot's theorem is a result of the second law of thermodynamics . Historically, however, it was based on contemporary caloric theory and preceded the establishment of the second law.