College Physics III – Thermodynamics, Electricity, and Magnetism
Definition
Efficiency (e) is the ratio of useful energy output to the total energy input, expressed as a percentage. It measures how well a system converts energy from one form to another without losses.
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The efficiency of a heat engine is given by $e = \frac{W_{out}}{Q_{in}}$, where $W_{out}$ is the work output and $Q_{in}$ is the heat input.
Efficiency can never be 100% due to the second law of thermodynamics, which states that some energy will always be lost as waste heat.
A real engine's efficiency is always less than its Carnot efficiency, which represents the maximum possible efficiency between two temperature reservoirs.
The Carnot efficiency is calculated using $e_{Carnot} = 1 - \frac{T_C}{T_H}$, where $T_C$ is the absolute temperature of the cold reservoir and $T_H$ is the absolute temperature of the hot reservoir.
Improving efficiency often involves minimizing friction, reducing heat losses, and optimizing system components.
Review Questions
How do you calculate the efficiency of a heat engine?
Why can no heat engine achieve 100% efficiency?
What factors influence the actual efficiency of a real-world heat engine?
Related terms
Second Law of Thermodynamics: A fundamental principle stating that entropy in an isolated system always increases over time; it implies that energy transformations are not perfectly efficient.
Heat Engine: A device that converts thermal energy into mechanical work by exploiting temperature differences between two reservoirs.
Carnot Cycle: An idealized thermodynamic cycle proposed by Sadi Carnot, representing the most efficient possible heat engine cycle operating between two temperatures.