Glossary

12.1 Thermodynamic cycles for heat engines

3 min read•july 23, 2024

Heat engines are the workhorses of energy conversion, turning heat into mechanical power. They're behind everything from car engines to power plants. These machines rely on clever cycles of heating, expanding, cooling, and compressing a working fluid to extract useful work.

The sets the gold standard for efficiency, but real engines like Otto, Diesel, and Rankine cycles make practical trade-offs. They may not be perfect, but they get the job done, powering our world with the heat-to-work conversion magic of thermodynamics.

Heat Engines and Thermodynamic Cycles

Purpose of heat engines

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  • Convert thermal energy (heat) into mechanical work by operating in a cyclic manner with a working fluid undergoing changes in temperature, pressure, and volume
  • Harness energy from a high-temperature heat source to power various machines (vehicles, generators, industrial equipment)
  • Rely on thermodynamic principles where energy is converted from one form to another (first law) and efficiency is limited by the necessity to reject some heat to a low-temperature sink (second law)

Components of heat engine cycles

  • Working fluid undergoes thermodynamic processes (air, steam, gas mixture)
  • High-temperature reservoir supplies heat to the working fluid (heat source)
  • Low-temperature reservoir receives rejected heat from the working fluid (heat sink)
  • Mechanical components facilitate conversion of thermal energy to mechanical work (pistons, cylinders, turbines)
  • Heat addition: heat transferred from high-temperature source to working fluid, increasing temperature and pressure
  • Expansion: high-temperature, high-pressure working fluid expands, performing mechanical work (pushing a piston, rotating a turbine)
  • Heat rejection: working fluid rejects some heat to low-temperature sink, decreasing temperature and pressure
  • Compression: working fluid compressed back to initial state, ready to start cycle again

Carnot cycle and efficiency limits

  • Idealized, reversible heat engine cycle operating between two thermal reservoirs at constant temperatures
    • Four reversible processes: isothermal expansion, adiabatic expansion, isothermal compression, adiabatic compression
    • Working fluid typically an ideal gas
  • Sets upper limit for of any heat engine operating between two thermal reservoirs
    • Thermal efficiency (η)(\eta): ratio of net (Wnet)(W_{net}) to heat input (Qin)(Q_{in}), η=WnetQin\eta = \frac{W_{net}}{Q_{in}}
    • Carnot efficiency depends only on hot (TH)(T_H) and cold (TC)(T_C) reservoir temperatures: ηCarnot=1−TCTH\eta_{Carnot} = 1 - \frac{T_C}{T_H}
  • No real heat engine can achieve thermal efficiency higher than Carnot efficiency when operating between same temperature limits (consequence of )
  • Serves as benchmark for evaluating performance of real heat engines and understanding fundamental limitations imposed by thermodynamics

Comparison of practical engine cycles

  • Practical heat engine cycles (Otto, Diesel, Rankine) approximate ideal Carnot cycle while accounting for real-world constraints and limitations
  • used in spark-ignition internal combustion engines (gasoline engines)
    • Four processes: , , ,
    • Thermal efficiency depends on compression ratio (r)(r) and specific heat ratio (γ)(\gamma): ηOtto=1−1rγ−1\eta_{Otto} = 1 - \frac{1}{r^{\gamma-1}}
  • used in compression-ignition internal combustion engines (diesel engines)
    • Four processes: isentropic compression, , isentropic expansion, constant-volume heat rejection
    • Thermal efficiency depends on compression ratio (r)(r), cutoff ratio (ρ)(\rho), and specific heat ratio (γ)(\gamma): ηDiesel=1−1rγ−1(ργ−1γ(ρ−1))\eta_{Diesel} = 1 - \frac{1}{r^{\gamma-1}}\left(\frac{\rho^\gamma-1}{\gamma(\rho-1)}\right)
  • used in steam power plants
    • Four processes: isentropic compression (pump), constant-pressure heat addition (boiler), isentropic expansion (turbine), (condenser)
    • Thermal efficiency depends on temperature and pressure limits of steam, efficiency of turbine, pump, and boiler
  • Practical heat engine cycles have lower thermal efficiencies than Carnot efficiency due to irreversibilities (friction, heat loss, combustion inefficiencies)
  • Designed to optimize performance within constraints of available materials, technology, and economic considerations

Key Terms to Review (24)

Adiabatic process: An adiabatic process is a thermodynamic process in which no heat is exchanged between the system and its surroundings. This means that any change in the internal energy of the system is entirely due to work done on or by the system, making it a critical concept in understanding various thermodynamic cycles and processes.
Brayton Cycle: The Brayton Cycle is a thermodynamic cycle that describes the operation of a gas turbine engine, where air is compressed, heated, and then expanded to produce work. It consists of two main processes: isentropic compression and isentropic expansion, with a constant pressure heat addition phase. This cycle is fundamental to understanding the efficiency and performance of jet engines and power plants that utilize gas turbines.
Carnot Cycle: The Carnot cycle is an idealized thermodynamic cycle that represents the most efficient way to convert heat into work, consisting of two isothermal and two adiabatic processes. This cycle serves as a benchmark for all real heat engines, highlighting the limits of efficiency based on the temperatures of the heat reservoirs involved.
Constant-pressure heat addition: Constant-pressure heat addition refers to the process where heat is added to a system at a constant pressure, typically during the operation of heat engines. This process is crucial for understanding thermodynamic cycles, as it affects how energy is transferred within the engine and influences its efficiency and work output. During this phase, the working fluid absorbs heat while expanding, leading to an increase in temperature and energy content.
Constant-pressure heat rejection: Constant-pressure heat rejection refers to the process in thermodynamic cycles where heat is expelled from a system at a constant pressure. This process is crucial for heat engines as it helps to convert thermal energy into mechanical work efficiently. During this stage, the working fluid loses energy while maintaining pressure, which can influence the overall performance and efficiency of the engine cycle.
Constant-volume heat addition: Constant-volume heat addition is a thermodynamic process where heat is added to a system while maintaining a constant volume. This means that the system does not expand or contract during the heat addition phase, leading to a rise in temperature and pressure. This concept is crucial in understanding how heat engines operate, particularly in cycles such as the Otto cycle, where fuel combustion occurs at constant volume.
Constant-volume heat rejection: Constant-volume heat rejection is a thermodynamic process in which heat is removed from a system while maintaining a constant volume. This process is significant in the context of heat engines, as it occurs during the rejection of heat to the cold reservoir, impacting the engine's efficiency and performance.
Diesel cycle: The diesel cycle is a thermodynamic cycle that describes the functioning of diesel engines, where combustion occurs at constant pressure and the compression ratio is higher than in Otto engines. This cycle is characterized by its efficiency and ability to use various fuels, which connects it to the broader concepts of heat engine cycles and distinguishes it from the Otto cycle.
First Law of Thermodynamics: The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. This principle emphasizes the conservation of energy within a closed system, illustrating how energy transfers and transformations impact thermodynamic processes and systems.
Heat reservoir: A heat reservoir is a large system that can absorb or supply heat without undergoing a significant change in temperature. It acts as a source or sink of thermal energy for other systems involved in energy transfer processes. This concept is crucial for understanding how heat engines operate, as they rely on the interactions between the working substance and heat reservoirs to convert thermal energy into work.
Indicator Diagram: An indicator diagram is a graphical representation that illustrates the pressure and volume relationship within a thermodynamic cycle of an engine, particularly during the power stroke. It shows how the pressure of the working fluid changes with respect to the displacement of the piston, providing insight into the efficiency and performance of the engine's operation. This diagram is crucial for analyzing thermodynamic cycles because it highlights the work done by or on the system during each phase of the cycle.
Isentropic compression: Isentropic compression is a thermodynamic process in which a fluid is compressed without any heat transfer, maintaining constant entropy throughout the process. This means that the compression occurs in an idealized manner, typically represented in cycles for heat engines, where it contributes to the efficiency of the overall system by minimizing energy losses due to heat exchange.
Isentropic expansion: Isentropic expansion is a thermodynamic process in which a gas expands without any change in entropy, meaning that the process is both adiabatic and reversible. This type of expansion is idealized and serves as a benchmark for evaluating real processes in heat engines, allowing for more efficient performance under certain conditions. Understanding isentropic expansion helps in analyzing the efficiency of thermodynamic cycles and the work output from expanding gases.
Isothermal process: An isothermal process is a thermodynamic process in which the temperature of the system remains constant while heat is exchanged with the surroundings. This constant temperature implies that any internal energy changes in the system are fully compensated by heat transfer, making it an essential concept in understanding how systems behave under thermal equilibrium and the laws governing energy conservation.
Mechanical efficiency: Mechanical efficiency is a measure of how effectively a machine converts input energy into useful work output. It is expressed as a ratio of the useful work output to the total energy input, usually represented as a percentage. This concept is crucial in understanding thermodynamic cycles, where the goal is to maximize work output while minimizing energy losses.
Otto Cycle: The Otto Cycle is a thermodynamic cycle that describes the functioning of a gasoline engine, consisting of two adiabatic and two isochoric processes. It is crucial in understanding how heat engines convert thermal energy into mechanical work, highlighting the relationship between pressure, volume, and temperature during the engine's operation.
Pressure-volume diagram: A pressure-volume diagram is a graphical representation that illustrates the relationship between the pressure and volume of a thermodynamic system during various processes. This diagram is crucial in analyzing thermodynamic cycles, especially for heat engines, as it visually depicts how the system's state changes through compression, expansion, and heat transfer. By examining the area within the closed loop of the cycle on this diagram, one can determine the work done by or on the system, which is a key factor in assessing the efficiency of heat engines.
Rankine Cycle: The Rankine Cycle is a thermodynamic cycle that converts heat into work, typically used in steam power plants. It involves the processes of heating, phase change, and cooling of a working fluid, usually water, to generate mechanical energy that can be converted into electricity. This cycle is vital in understanding how energy is transformed and utilized in various applications, linking thermal efficiency and energy conversion principles.
Second law of thermodynamics: The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time, and it dictates the direction of thermodynamic processes. This principle establishes that energy transformations are not 100% efficient, highlighting the inherent tendency for systems to move towards a state of greater disorder or randomness, affecting heat transfer, the performance of engines, and various processes in nature.
Temperature-entropy diagram: A temperature-entropy diagram, often referred to as a T-S diagram, is a graphical representation that shows the relationship between temperature and entropy in thermodynamic processes. This diagram is crucial for visualizing how heat engines operate, as it illustrates the changes in both temperature and entropy throughout various stages of a thermodynamic cycle, helping to identify efficiencies and losses in the process.
Thermal Efficiency: Thermal efficiency is a measure of how well a system converts heat energy into useful work. It's expressed as a ratio of the work output of the system to the heat input, highlighting how effectively a thermal system operates. Understanding thermal efficiency is crucial for evaluating energy performance in various thermodynamic applications, including engines and power cycles.
Thermal efficiency formula: The thermal efficiency formula quantifies the effectiveness of a heat engine in converting thermal energy into work, expressed as the ratio of the useful work output to the heat input. This measure is crucial for understanding how well a heat engine operates, providing insight into its performance and sustainability. A higher thermal efficiency indicates that a greater portion of the input energy is being transformed into useful work, which is a key consideration in the design and operation of heat engines.
Work Output: Work output refers to the useful energy or mechanical work produced by a thermodynamic system, such as a heat engine, during its operation. It is a crucial measure of efficiency, illustrating how much of the energy input is converted into useful work rather than lost as waste heat. The work output can be analyzed in terms of thermodynamic cycles and is influenced by the second law of thermodynamics, which sets limits on the conversion efficiency of heat to work.
Working substance: The working substance is the medium or material through which energy is transferred or transformed in a heat engine. This substance undergoes phase changes, temperature fluctuations, and pressure variations as it absorbs and releases heat, enabling the engine to convert thermal energy into mechanical work. Understanding the characteristics and behavior of the working substance is crucial in analyzing the efficiency and performance of heat engines.
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