Heat Engine

Heat engines function on the principles of thermodynamics, converting thermal energy into mechanical work through a cyclic process.
This article will give a comprehensive overview of heat engines and present different equations for considering heat engines.
Heat engines include a range of technologies, including internal combustion engines, steam engines, and gas turbines. They adhere to the principles of the first and second laws of thermodynamics, focusing on the controlled transfer of heat from a high-temperature reservoir to a low-temperature reservoir.
Working substance (gas) absorbs heat from the source, performs work on the surroundings and rejects a part of it to the sink.
Check out our Heat Engine calculator to run these calcs!
DefinitionsHere are some important definitions to keep in mind for heat engines!
Efficiency: performance measure.
Sink: a reservoir that absorbs heat energy.
Source: a reservoir that supplies heat energy.
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Figure 1: Diagram of Heat Engines
The following are the variables for the equations
η = efficiency, i.e. efficiency of a heat engine.
Q1 = the heat supplied to the engine
Q2 = the heat rejected from the engine
T = the temperature. i.e. T(1) is the temperature at state 1. For the equations below, the T1 (source) and T2 (sink) temperatures must be in kelvin.
W = work done by the system, the net heat absorbed.
From energy conservation:
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Q1=Q2+WQ_1=Q_2+WQ1​=Q2​+W
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∴ W=Q1−Q2\therefore\ W=Q_1-Q_2∴ W=Q1​−Q2​
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Efficiency % η =Total Work DoneTotal Heat Supplied × 100Efficiency\  \%\  \eta\ =\frac{Total\ Work\ Done}{Total\ Heat\ Supplied}\ \times\ 100Efficiency % η =Total Heat SuppliedTotal Work Done​ × 100
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=WQ1×100=Q1−Q2Q1×100=(1−Q2Q1)×100=(1−T2T1)×100=\frac{W}{Q_1}\times100=\frac{Q_1-Q_2}{Q_1}\times100=(1-\frac{Q_2}{Q_1})\times100=(1-\frac{T_2}{T_1})\times100=Q1​W​×100=Q1​Q1​−Q2​​×100=(1−Q1​Q2​​)×100=(1−T1​T2​​)×100
The efficiency of a heat engine is a function of the heat supplied and expelled from the engine and the total work done by the system over the total heat supplied.
If an ideal engine works between t1 (degrees Celsius) and t2 (degrees Celsius):
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Efficiency % η =(1−T2T1)×100=(1−t2+273t1+273)×100Efficiency\  \%\  \eta\ =(1-\frac{T_2}{T_1})\times100=(1-\frac{t_2+273}{t_1+273})\times100Efficiency % η =(1−T1​T2​​)×100=(1−t1​+273t2​+273​)×100
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Here's a calculator to actually run these equations! 
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Heat Engine Calculator
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Heat engines are a large part of modern industrial civilisation, playing a critical role in various applications, from transportation to electricity generation.
Understanding heat engines is important not only for technological advancements but also for combatting environmental concerns and energy efficiency, as these devices have a significant impact on energy and the environment.
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Additional ResourcesIf you liked this, check out our other articles and resources!
Check out our library of templates here.
Diesel Cycle
Duel Combustion Cycle
Brayton Cycles
Power Cycles
Introduction to Thermodynamics
Importance of Mechanical Engineering Calculation Templates
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ReferencesHyperphysics. 2000. Heat Engine Cycle. [ONLINE] Available at: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heaeng.html. [Accessed 31 October 2023].
LinkedIn. 2023. Important Thermodynamic Concepts. [ONLINE] Available at: https://www.linkedin.com/feed/update/urn:li:activity:7095576421120548864?utm_source=share&utm_medium=member_desktop. [Accessed 24 October 2023].
Wikipedia. 2023. https://en.wikipedia.org/wiki/Heat_engine. [ONLINE] Available at: https://en.wikipedia.org/wiki/Heat_engine. [Accessed 31 October 2023].
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