Question

what is carnot theorem

Answer 1

arnot's theorem, developed in 1824 by Nicolas Léonard Sadi Carnot, also calledCarnot's rule, is a principle that specifies limits on the maximum efficiency any heat engine can obtain, which thus solely depends on the difference between the hot and cold temperature reservoirs.

Answer 2

Carnot theorem states that

   All reversible engines operating between the same two temperatures (infinite heat reservoirs) have equal efficiency and no engine operating between the same two temperatures (infinite heat reservoirs) can have an efficiency greater than this.
 
   A Carnot engine is a reversible engine, that does work by taking in energy.

  This theorem is a direct consequence of the 2nd law of thermodynamics.

  The efficiency of energy transfer can be calculated also as

$\eta = \frac{work\ done\ by\ engine}{Heat\ absorbed\ by\ system}=1-\frac{T_C}{T_H}\\\\T_c=temperature\ of \ cold\ reservoir\\T_H=temperature\ of\ hot\ reservoir$

This principle is used practically in many heat transfer based applications like a refrigerator, AC, in vehicles, heating furnaces etc.