Glossary

6.3 Entropy generation and irreversibility

3 min read•july 23, 2024

quantifies irreversibility in thermodynamic processes. It's always non-negative, with zero for reversible processes and positive for irreversible ones. Understanding generation helps assess process efficiency and identify areas for improvement.

Calculating entropy generation involves rates, temperatures, and system entropy changes. Factors like heat transfer, , , and contribute to entropy generation. Minimizing entropy generation reduces and improves system efficiency in real-world applications.

Entropy Generation and Irreversibility

Entropy generation and irreversibility

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  • Entropy generation quantifies entropy produced within a system during a process due to irreversibilities caused by friction, heat transfer through a finite temperature difference, mixing, and chemical reactions
  • states entropy generation is always non-negative for any real process
    • Reversible processes have zero entropy generation
    • Irreversible processes always have positive entropy generation
  • Entropy generation measures the irreversibility of a process greater entropy generation indicates a more

Calculation of entropy generation

  • Entropy generation for a process calculated using the equation: S˙gen=∑Q˙T−dSdt\dot{S}_{gen} = \sum \frac{\dot{Q}}{T} - \frac{dS}{dt}
    • S˙gen\dot{S}_{gen} represents the
    • Q˙\dot{Q} represents the heat transfer rate
    • TT represents the at which the heat transfer occurs
    • dSdt\frac{dS}{dt} represents the rate of change of entropy of the system
  • For a closed system undergoing a process, entropy generation calculated as: Sgen=ΔStotal−QTS_{gen} = \Delta S_{total} - \frac{Q}{T}
    • ΔStotal\Delta S_{total} represents the of the system and its surroundings
    • QQ represents the heat transfer between the system and its surroundings
    • TT represents the absolute temperature at which the heat transfer occurs
  • In the case of an (no heat transfer), entropy generation equals the change in entropy of the system: Sgen=ΔSsystemS_{gen} = \Delta S_{system}

Factors in entropy generation

  • Heat transfer through a finite temperature difference
    • Entropy generated when heat transferred between two reservoirs at different temperatures (hot reservoir and cold reservoir)
    • Entropy generation proportional to heat transfer and inversely proportional to temperature at which transfer occurs
  • Friction in moving parts
    • Friction converts mechanical work into heat, increasing system entropy
    • Entropy generation due to friction proportional to work lost to friction and inversely proportional to absolute temperature
  • Mixing of fluids
    • Entropy generated when two or more fluids mix due to irreversible nature of mixing process (oil and water)
    • Entropy generation depends on fluid properties and mixing process
  • Chemical reactions
    • Chemical reactions can generate entropy due to irreversible nature of reaction (combustion)
    • Entropy generation depends on extent of reaction and temperature at which it occurs

Lost work from irreversibility

  • Lost work represents the difference between maximum theoretical work obtainable from a process and actual work obtained
    • Maximum theoretical work obtainable if process were reversible
    • Actual work always less than maximum theoretical work due to irreversibilities
  • Lost work directly related to entropy generation of the process: Wlost=T0⋅SgenW_{lost} = T_0 \cdot S_{gen}
    • T0T_0 represents the absolute temperature of the surroundings
    • SgenS_{gen} represents the entropy generation of the process
  • Presence of lost work reduces system efficiency
    • Greater lost work leads to lower system efficiency ()
    • Minimizing entropy generation helps reduce lost work and improve system efficiency
  • In real-world systems, important to identify and minimize sources of irreversibility to maximize efficiency and minimize lost work (power plants, refrigerators)

Key Terms to Review (21)

Absolute temperature: Absolute temperature is a measure of temperature that is referenced from absolute zero, the point where all molecular motion ceases, and is measured in Kelvin (K). This scale provides a fundamental framework for thermodynamic calculations and allows for the description of thermal energy in a consistent manner across various scientific contexts. Absolute temperature is crucial in understanding the behavior of gases, calculating changes in entropy, and analyzing irreversibility in thermodynamic processes.
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.
Carnot Efficiency: Carnot efficiency is the maximum theoretical efficiency of a heat engine operating between two temperature reservoirs, derived from the second law of thermodynamics. This concept sets an upper limit on the efficiency of all real heat engines, emphasizing the importance of reversible processes and the temperature difference between the heat source and sink in achieving optimal performance.
Chemical Reactions: Chemical reactions are processes that involve the transformation of reactants into products through the breaking and forming of chemical bonds. These reactions are essential in understanding energy changes, especially in relation to entropy, as they can lead to variations in disorder and influence the direction and spontaneity of a process.
Clausius Inequality: The Clausius inequality is a fundamental principle in thermodynamics that relates to the change in entropy of a system, stating that the change in entropy for any process is greater than or equal to the heat transferred divided by the temperature at which the transfer occurs. This inequality highlights the directionality of spontaneous processes and indicates that real processes cannot occur with 100% efficiency. It establishes a connection between irreversible processes and entropy, serving as a cornerstone for understanding the Second Law of Thermodynamics.
Disorder: Disorder refers to the level of randomness or chaos in a system, often associated with the concept of entropy. In thermodynamics, higher disorder corresponds to higher entropy, which signifies a greater number of microstates or arrangements available to a system. Understanding disorder is crucial in analyzing how energy is distributed and transformed in various processes, revealing insights about the direction of spontaneous changes and the efficiency of energy conversions.
Entropy: Entropy is a measure of the degree of disorder or randomness in a system, reflecting the number of microscopic configurations that correspond to a thermodynamic system's macroscopic state. It connects to various principles of thermodynamics, indicating how energy disperses and the direction of spontaneous processes.
Entropy generation: Entropy generation refers to the production of entropy within a thermodynamic system due to irreversible processes. It quantifies the degree of disorder or randomness that increases as energy is transformed or transferred, reflecting the inherent inefficiencies in real-world processes. Understanding entropy generation helps illustrate the relationship between energy conversions and the second law of thermodynamics, emphasizing that some energy will always be lost as waste heat or increase in entropy during any transformation.
Exergy: Exergy is a measure of the maximum useful work possible from a system as it reaches equilibrium with its environment. It represents the quality of energy and indicates how much of that energy can be converted into work. Understanding exergy is crucial when assessing the efficiency of processes, especially in systems that involve heat and energy transfer, revealing insights about irreversibilities and how to optimize energy use.
Friction: Friction is a force that opposes the relative motion of two surfaces in contact. It plays a significant role in the conversion of energy and affects the efficiency of various processes, particularly in mechanical systems, by contributing to entropy generation and irreversibility. Understanding friction is crucial for analyzing energy losses and ensuring effective performance in thermal systems.
Heat Engines: Heat engines are devices that convert thermal energy into mechanical work by taking in heat from a high-temperature source and releasing some of that heat to a lower temperature sink. This process is governed by the principles of thermodynamics, particularly the first and second laws, which dictate the efficiency and limitations of how heat can be transformed into work.
Heat Transfer: Heat transfer is the process of thermal energy moving from one object or system to another due to a temperature difference. This fundamental concept connects various phenomena, including how systems reach thermodynamic equilibrium and how energy is conserved in different processes.
Irreversible process: An irreversible process is a type of thermodynamic process that cannot be reversed to restore the system and its surroundings to their original states without an increase in entropy. These processes often involve dissipative factors like friction, turbulence, or unrestrained expansion, which lead to a net change that cannot simply be undone. In understanding these processes, it's crucial to consider their role in defining thermodynamic equilibrium, how they differ from reversible processes, and their implications for concepts like entropy generation.
Lost Work: Lost work refers to the amount of mechanical energy that is not available for useful work due to irreversible processes in a thermodynamic system. This concept is closely related to the idea of entropy generation, where irreversibility leads to a degradation of energy quality, making it impossible to completely convert thermal energy into work without some loss.
Mixing: Mixing refers to the process of combining two or more substances to create a homogeneous mixture. This process is important because it can lead to changes in the properties of the individual components and can result in an increase in entropy, which is a measure of disorder in a system. Mixing is closely related to concepts of entropy generation and irreversibility, as it often involves irreversible changes in the state of the materials involved, thereby contributing to the overall increase in a system's entropy.
Rate of entropy generation: The rate of entropy generation is a measure of the production of entropy in a thermodynamic system over time, often associated with irreversible processes. It quantifies how much disorder or randomness is created as energy is transformed from one form to another, particularly when there are losses due to friction, heat transfer, or mixing. Understanding this concept is crucial for analyzing the efficiency of thermodynamic cycles and the performance of engines and refrigerators, where minimizing entropy generation can lead to improved efficiency.
Reversible Process: A reversible process is an idealized thermodynamic process that can be reversed without leaving any change in the system or its surroundings. In this type of process, both the system and the environment can return to their original states, making it an important concept for understanding efficiency and performance in thermodynamic cycles.
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.
Thermodynamic cycles: Thermodynamic cycles refer to a series of processes that a working substance undergoes, returning to its initial state at the end of the cycle. These cycles are fundamental in understanding how energy is converted from one form to another and are crucial for the efficiency of engines and refrigeration systems. In analyzing thermodynamic cycles, relationships like those expressed in Maxwell's equations help in understanding the properties of the working substance, while concepts of entropy generation and irreversibility highlight the inefficiencies present in real-world applications.
Thermodynamic Efficiency: Thermodynamic efficiency is a measure of how well a system converts energy from one form to another, specifically the ratio of useful work output to the total energy input. It is important because it helps evaluate the performance of various processes and systems, indicating how much energy is conserved and how much is wasted. Understanding this concept is crucial for optimizing systems in various applications, including mechanical engines, biological processes, and assessing the irreversibility in thermodynamic cycles.
Total change in entropy: Total change in entropy refers to the overall increase in disorder or randomness in a system and its surroundings as a result of energy transformations. This concept is critical when discussing the second law of thermodynamics, which states that the total entropy of an isolated system can never decrease over time, emphasizing the irreversibility of natural processes and the generation of entropy during energy exchanges.
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