Efficiency of Heat Engines
Efficiency of a heat engine is defined as the ratio of work output to heat input, expressed as a percentage. This metric illustrates how effectively a heat engine converts the thermal energy it receives into mechanical work. According to the second law of thermodynamics, it’s impossible for any engine to achieve complete efficiency, indicating that some energy will always be lost in the conversion process.
Mathematically, efficiency (η) can be calculated as:
Given that the work done (W) is the difference between the heat input (Q1) and the heat rejected (Q2):
W=Q1-Q2
Substituting this into the equation for efficiency yields:
η = (Q1-Q2)/Q1 = 1- (Q2/Q1)
Hence, if Q2 =0, implying no heat is rejected, the efficiency would theoretically reach 100%. However, such a scenario is unattainable in practice due to inevitable energy losses within any real system. Consequently, every engine’s efficiency is inherently capped.
Carnot Efficiency
Carnot engine represents a theoretical model of a perfectly efficient engine that operates on a reversible, closed thermodynamic cycle. Within this cycle, the working fluid undergoes four distinct stages: isothermal expansion, adiabatic (or isentropic) expansion, isothermal compression, and adiabatic compression. This idealized cycle serves as a foundational concept for understanding other thermodynamic cycles widely applied across various industries, notably in Carnot heat engines and refrigeration systems.
While the Carnot engine sets the standard for maximal theoretical efficiency, no practical engine can fully attain this efficiency due to inevitable losses, primarily from friction. The efficiency of a Carnot engine is determined solely by the temperatures of the hot and cold reservoirs it operates between.
In essence, the Carnot engine operates by absorbing heat (Q1) from a high-temperature source, converting part of that heat into work (W) by exploiting the difference in heat content (W=Q1-Q2), and then discharging the remaining heat (Q2) to a low-temperature sink.
Mathematically, Carnot efficiency (η) can be calculated as:
η = 1 – (Q2/Q1)
which is the efficiency of the heat engine.
If Q2 = 0, then efficiency = 100% . Carnot engine is known for this.
Heat Engine – Definition, Working, PV Diagram, Efficiency, Types
Heat engines are devices that turn heat energy into motion or mechanical work. Heat engines are based on the principles of thermodynamics, specifically the conversion of heat into work according to the first and second laws of thermodynamics. They are found everywhere, from our cars, power plants to even old trains. Despite their wide use, they all share a common limitation that they can’t be 100% efficient.
In this article we will learn in detail about Heat Engines, its working, diagram, efficiency, applications and limitations.