Glossary

engines are marvels of engineering that convert thermal energy into mechanical . They operate between high and low- reservoirs, using a to harness the power of flow. Understanding their components and principles is crucial for grasping thermodynamic concepts.

Efficiency is key in performance. The sets the theoretical maximum, while real-world factors like friction and heat loss reduce actual efficiency. Various cycles, such as Otto and Diesel, offer different approaches to harnessing thermal energy in practical applications.

Heat Engines

Components of heat engines

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  • Convert thermal energy (heat) into mechanical energy () by operating between a () and a ()
  • Heat flows from the high-temperature reservoir to the low-temperature reservoir, with some of the heat converted into work during this process
  • undergoes the (gas or steam)
  • Heat source provides heat to the working substance
  • Heat sink absorbs heat from the working substance
  • Mechanical components convert the expansion and contraction of the working substance into useful work
    • Pistons
    • Turbines

Factors in heat engine efficiency

  • Efficiency is the ratio of work output to heat input, calculated using the formula η=WQH\eta = \frac{W}{Q_H}
    • η\eta represents efficiency
    • WW represents work output
    • QHQ_H represents heat input from the high-temperature reservoir
  • Carnot efficiency is the maximum theoretical efficiency of a heat engine operating between two temperatures, calculated using the formula ηCarnot=1−TCTH\eta_{Carnot} = 1 - \frac{T_C}{T_H}
    • TCT_C represents the temperature of the (heat sink)
    • THT_H represents the temperature of the (heat source)
    • A larger temperature difference between the heat source and heat sink leads to higher efficiency
  • Irreversibilities and losses reduce the actual efficiency of heat engines below the Carnot efficiency
    • Friction
    • Heat loss
    • Incomplete combustion

Efficiency calculations for ideal gas engines

  • Thermodynamic cycles represent the series of processes that the working substance undergoes in a heat engine, returning to its initial state after completing a cycle
  • (constant volume heat addition)
    • Efficiency calculated using the formula η=1−1rγ−1\eta = 1 - \frac{1}{r^{\gamma-1}}
      • rr represents the
      • γ\gamma represents the of the gas
  • (constant pressure heat addition)
    • Efficiency calculated using the formula η=1−1rγ−1(rcγ−1γ(rc−1))\eta = 1 - \frac{1}{r^{\gamma-1}} \left(\frac{r_c^{\gamma}-1}{\gamma(r_c-1)}\right)
      • rr represents the compression ratio
      • rcr_c represents the
      • γ\gamma represents the specific heat ratio of the gas
  • (constant pressure heat addition and rejection)
    • Efficiency calculated using the formula η=1−1rpγ−1γ\eta = 1 - \frac{1}{r_p^{\frac{\gamma-1}{\gamma}}}
      • rpr_p represents the
      • γ\gamma represents the specific heat ratio of the gas

Thermodynamic principles and analysis

  • The first law of thermodynamics relates the change in of a system to heat added and work done
  • Pressure-volume diagrams are used to visualize and analyze thermodynamic cycles
  • An is an idealized thermodynamic process that is and reversible
  • The of the states that it is impossible to construct a heat engine that operates in a cycle and produces no effect other than the extraction of heat from a reservoir and the performance of an equivalent amount of work

Key Terms to Review (43)

Absolute temperature scale: An absolute temperature scale is a thermodynamic temperature scale that uses absolute zero as its null point. The two most common absolute temperature scales are Kelvin and Rankine.
Adiabatic: Adiabatic refers to a process or system in which there is no transfer of heat or mass between the system and its surroundings. In other words, an adiabatic process occurs without any exchange of heat with the environment.
Adiabatic compressions: Adiabatic compression is a process in which a gas is compressed without any heat exchange with its surroundings. The internal energy of the gas increases, resulting in an increase in temperature.
Brayton cycle: The Brayton cycle is a thermodynamic cycle that describes the operation of a gas turbine engine, where air is compressed, mixed with fuel, ignited, and then expanded to produce work. It is fundamental in understanding how heat engines convert thermal energy into mechanical energy, showcasing the processes of compression, combustion, and expansion that are key to efficient energy conversion.
Carnot Efficiency: Carnot efficiency is a fundamental concept in thermodynamics that describes the maximum possible efficiency of a heat engine operating between two temperature reservoirs. It establishes a theoretical limit on the conversion of heat into work, providing a benchmark for the performance of real-world heat engines.
Carnot's Theorem: Carnot's theorem is a fundamental principle in thermodynamics that establishes the maximum efficiency of a heat engine operating between two thermal reservoirs at different temperatures. It provides the theoretical limit for the conversion of heat into work, which is an important concept in understanding the performance and limitations of various types of heat engines.
Clausius statement of the second law of thermodynamics: The Clausius statement of the second law of thermodynamics asserts that it is impossible for a self-acting machine, unaided by any external force, to transfer heat from a cooler body to a hotter one. This principle underlines the unidirectional nature of spontaneous heat transfer.
Cold reservoir: A cold reservoir is a system or environment that absorbs heat from a working substance in a thermodynamic cycle, allowing the process to continue. It maintains low temperature and facilitates the removal of waste heat from heat engines.
Compression Ratio: Compression ratio is a fundamental parameter in the operation of heat engines, particularly internal combustion engines. It refers to the ratio of the maximum to minimum volume within the engine's cylinders, which directly impacts the efficiency and power output of the engine.
Cutoff Ratio: The cutoff ratio, in the context of heat engines, is a measure of the efficiency of a heat engine's operation. It represents the ratio of the actual work output to the maximum possible work output that could be obtained from a given amount of heat input.
Diesel Cycle: The Diesel cycle is a thermodynamic cycle that describes the operation of a Diesel engine. It is characterized by the compression ignition of fuel, where the fuel is injected into the engine's cylinders and ignited by the high temperatures generated during the compression stroke.
Efficiency (e): 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.
Entropy: Entropy is a measure of the disorder or randomness in a system. It quantifies the number of possible microscopic configurations that correspond to a thermodynamic system's macroscopic state.
Heat: Heat is a form of energy transfer between systems or objects with different temperatures. It flows from the hotter object to the cooler one until thermal equilibrium is reached.
Heat: Heat is a form of energy that is transferred from a hotter object to a cooler object due to a temperature difference. It is a fundamental concept in thermodynamics that describes the flow of thermal energy and its effects on matter.
Heat engine: A heat engine is a device that converts thermal energy into mechanical work by undergoing cyclic processes. It operates between two reservoirs at different temperatures, absorbing heat from the hot reservoir and partially converting it into work while expelling the remaining heat to the cold reservoir.
Heat Sink: A heat sink is a passive heat exchanger that transfers thermal energy from a hotter object, such as a microprocessor or power transistor, to a cooler surrounding environment, thereby reducing the temperature of the hotter object. Heat sinks are commonly used in electronic devices to dissipate excess heat and prevent overheating of sensitive components.
Heat source: A heat source is any system or object that provides thermal energy to another system, usually to produce work or facilitate a process. In the context of heat engines, heat sources are crucial as they supply the necessary energy to convert thermal energy into mechanical work, allowing engines to perform useful tasks. These sources can be fuels, solar energy, or other materials that release heat through combustion or other processes.
High-Temperature Reservoir: A high-temperature reservoir is a critical component in the operation of heat engines, which are devices that convert thermal energy into mechanical work. It refers to a source of high-temperature heat that serves as the input for the heat engine, providing the necessary energy to drive the engine's thermodynamic cycle.
Hot reservoir: A hot reservoir is a source of thermal energy at a relatively high temperature that supplies heat to a heat engine. It is essential for the conversion of thermal energy into work.
Internal combustion engine: An internal combustion engine (ICE) is a heat engine where the combustion of fuel occurs with an oxidizer in a combustion chamber. The expansion of the high-temperature and high-pressure gases produced by combustion applies direct force to components, such as pistons or turbine blades.
Internal energy: Internal energy is the total energy contained within a system due to both the random motions of its particles and the potential energies of their interactions. It encompasses kinetic and potential energy at the microscopic level.
Internal Energy: Internal energy is the total energy contained within a thermodynamic system, consisting of the kinetic energy of the system's particles and the potential energy associated with the configuration of the particles. It is a fundamental concept in thermodynamics that describes the energy stored within a system, which can be altered through the processes of work and heat transfer.
Isentropic Process: An isentropic process is a thermodynamic process that occurs without any change in the entropy of the system. In other words, it is a reversible and adiabatic process where no heat is exchanged with the surroundings, and the system's internal energy changes solely due to work done on or by the system.
Isothermal: Isothermal refers to a process or condition in which the temperature remains constant while heat is transferred into or out of a system. In an isothermal process, the system's internal energy does not change because any heat added to the system is balanced by an equal amount of work done by the system, allowing it to maintain a steady temperature throughout.
Kelvin-Planck statement: The Kelvin-Planck statement is a formulation of the second law of thermodynamics that describes the fundamental limitations on the operation of heat engines. It states that it is impossible for any device that operates on a cycle to produce net positive work from a single thermal reservoir.
Low-temperature reservoir: A low-temperature reservoir is a thermal energy source that absorbs heat from a heat engine during its operation, typically at a lower temperature than the engine's working fluid. This reservoir plays a critical role in the thermodynamic cycles of heat engines by providing a pathway for waste heat to escape, allowing the engine to perform work efficiently. The performance of a heat engine depends significantly on the temperature difference between the high-temperature source and this low-temperature sink.
Otto Cycle: The Otto cycle is a thermodynamic cycle that describes the operation of a four-stroke internal combustion engine, which is the most common type of engine used in automobiles. The cycle is named after Nikolaus Otto, who invented the four-stroke engine in 1876.
Piston: A piston is a cylindrical component that moves back and forth within a cylinder, often used in engines and pumps to transfer energy and perform work. The movement of the piston compresses gases or fluids, enabling work to be done through mechanical processes. This motion is crucial in understanding how energy is converted from one form to another, particularly in systems involving work, heat, and internal energy.
Pressure Ratio: Pressure ratio is a dimensionless quantity that represents the relationship between two different pressures within a system, typically in the context of heat engines. It is a crucial parameter in understanding the performance and efficiency of these engines.
Pressure-Volume Diagram: A pressure-volume diagram, also known as a PV diagram, is a graphical representation of the relationship between the pressure and volume of a system, typically in the context of thermodynamic processes. It is a fundamental tool used to analyze and understand the behavior of heat engines and other thermodynamic systems.
Reversibility: Reversibility is a fundamental concept in thermodynamics that describes the ability of a process to be reversed without causing any changes to the surrounding environment. In the context of heat engines, reversibility is a crucial characteristic that determines the efficiency and performance of these systems.
Sadi Carnot: Sadi Carnot was a French physicist and engineer known as the father of thermodynamics, particularly recognized for his foundational work on the efficiency of heat engines. He developed the concept of the Carnot cycle, which is a theoretical model that describes the most efficient possible engine operating between two temperature reservoirs. His insights laid the groundwork for understanding how heat can be converted into work, influencing the development of modern thermodynamics.
Second Law of Thermodynamics: The Second Law of Thermodynamics is a fundamental principle that describes the natural tendency of energy to dissipate and become less useful over time. It establishes the directional nature of various processes and the limits on the efficiency of energy conversion within a system.
Specific Heat Ratio: The specific heat ratio, also known as the adiabatic index or the heat capacity ratio, is a dimensionless quantity that represents the ratio of the specific heat capacity at constant pressure to the specific heat capacity at constant volume for a given substance. This ratio is a fundamental property that governs the behavior of gases in various thermodynamic processes, particularly in the context of heat engines.
Temperature: Temperature is a measure of the average kinetic energy of the particles (atoms or molecules) in a substance. It quantifies the degree of hotness or coldness of an object and is a fundamental concept in thermodynamics that is closely related to the transfer of heat energy.
Thermal Efficiency: Thermal efficiency is a measure of the effectiveness of a heat engine in converting the heat energy input into useful work output. It represents the ratio of the useful work done by the engine to the total heat energy supplied to it, and is a key performance metric for evaluating the efficiency of heat-based power systems.
Thermodynamic Cycle: A thermodynamic cycle is a series of thermodynamic processes undergone by a system that ultimately returns the system to its initial state. These cycles are central to the operation of heat engines and other thermodynamic devices, as they allow for the conversion of heat into useful work.
Turbine: A turbine is a rotary mechanical device that extracts energy from a fluid flow and converts it into useful work. It is a key component in various heat engine systems, including those used in power generation and transportation.
Work: Work is the energy transferred to or from an object via a force acting upon it over a displacement. In physics, work is mathematically expressed as $W = F \cdot d \cdot \cos(\theta)$, where $F$ is the force, $d$ is the displacement, and $\theta$ is the angle between them.
Work: Work is a fundamental concept in physics that describes the transfer of energy due to the application of a force over a distance. It is a measure of the energy expended or transferred during a physical process and is a crucial factor in understanding the behavior of thermodynamic systems, electric potential, and the storage of energy in capacitors.
Working substance: A working substance is the material or fluid within a heat engine that undergoes a thermodynamic cycle, absorbing and rejecting heat to produce work. It is essential for the conversion of thermal energy into mechanical energy.
Working Substance: The working substance in a heat engine is the material, typically a gas or fluid, that undergoes a cyclic process to convert thermal energy into mechanical work. It is the medium through which the heat engine operates, absorbing heat from a high-temperature source, performing work, and rejecting heat to a low-temperature sink.
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