Carnot Efficiency

Carnot efficiency, abbreviated a \( \eta_c \) (Greek symbol eta), a dimensionless number, is the theroetical maximum efficiency of any heat engine depending only on the temperatures it operates between.  The Carnot efficiency is applicable to both ideal and real heat engines, and it's used as a benchmark to compare the performance of actual heat engines against the theoretical maximum efficiency that can be achieved.  The efficiency is expressed as a ratio of the work output to the heat input, and it depends solely on the temperatures of the heat source and heat sink.

In the Carnot cycle, which is a theoretical thermodynamic cycle that operates between two temperature reservoirs, the efficiency is maximized when the heat transfer occurs isothermally (at constant temperature) during both the heat addition and heat rejection processes.  The Carnot efficiency represents the upper limit of efficiency for any heat engine operating between the given temperature limits.

Real world heat engines, such as internal combustion engines and steam turbines, operate with efficiencies lower than the Carnot efficiency due to factors like friction, heat loss, and irreversibilities within the engine.  The Carnot efficiency serves as a reference point to evaluate the performance of these real engines and to highlight the inherent limitations imposed by the laws of thermodynamics.

 

Carnot efficiency formula
\( \eta_c \;=\;  ( T_h - T_c \;/\; T_h ) \;100 \)     (Carnot Efficiency) \( T_h \;=\;  -100 \; T_c   \;/\;  \eta_c \; -100   \) \( T_c \;=\;   T_h  -  [\;( \eta_c \; T_h ) \;/\; 100 \;] \)
Symbol	English	Metric
\( \eta_c \) (Greek symbol eta) = Carnot Efficiency	\(dimensionless\)	\(dimensionless\)
\( T_h \) = Hot Source Absolute Temperature	\(F\)	\(K\)
\( T_c \) = Cold Source Absolute Temperature	\(F\)	\(K\)