The statement "The efficiency of all reversible heat engines operating between the same temperature levels is the same" is known as:

Explanation:

​Carnot's theorem:

• Carnot's theorem implies that the efficiency of a reversible heat engine depends only on the temperature levels between which it operates and not on the working substance or the design of the engine. Reversible heat engines are idealized systems that operate without dissipative losses like friction or heat leakage, ensuring maximum efficiency.

Mathematical Representation: The efficiency (η) of a reversible heat engine is given by:

η = 1 - (T₂/T₁)

Where:

• T₁: Temperature of the hot reservoir (higher temperature).
• T₂: Temperature of the cold reservoir (lower temperature).

This formula shows that the efficiency is dependent only on the absolute temperatures of the reservoirs. Any reversible heat engine operating between the same T₁ and T₂ will have the same efficiency.

Importance of Carnot Theorem:

• Provides a benchmark for the maximum efficiency achievable by heat engines.
• Establishes the concept of reversibility as a theoretical limit in thermodynamic processes.
• Forms the basis for the second law of thermodynamics, emphasizing that no heat engine can be more efficient than a Carnot engine operating between the same temperature levels.