Isentropic Process

9 Key excerpts on "Isentropic Process"

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  Advanced Thermodynamics

  • (Author)
  • 2014(Publication Date)
  • Library Press

    (Publisher)

  Temperature is the thermodynamic conjugate variable to entropy, thus the conjugate process would be an isothermal process in which the system is thermally connected to a constant-temperature heat bath. Isentropic flow An isentropic flow is a flow that is both adiabatic and reversible. That is, no heat is added to the flow, and no energy transformations occur due to friction or dissipative effects. For an isentropic flow of a perfect gas, several relations can be derived to define the pressure, density and temperature along a streamline. Note that energy can be exchanged with the flow in an isentropic transformation, as long as it doesn't happen as heat exchange. An example of such an exchange would be an isentropic expansion or compression, with entail work done on or by the flow. Derivation of the isentropic relations For a closed system, the total change in energy of a system is the sum of the work done and the heat added, The work done on a system by changing the volume is, where p is the pressure and V is the volume. The change in enthalpy ( ) is given by, ________________________ WORLD TECHNOLOGIES ________________________ Since a reversible process is adiabatic (i.e. no heat transfer occurs), so . This leads to two important observations, , and or => The heat capacity ratio can be written as, For an ideal gas is constant. Hence on integrating the above equation, assuming a perfect gas, we get i.e. Using the equation of state for an ideal gas, , also, for constant C p = C v + R (per mole), and Thus for Isentropic Processes with an ideal gas, or Table of isentropic relations for an ideal gas

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  Advances in Thermodynamics and Thermal Engineering

  • (Author)
  • 2014(Publication Date)
  • Academic Studio

    (Publisher)

  Derivation of the isentropic relations For a closed system, the total change in energy of a system is the sum of the work done and the heat added, The work done on a system by changing the volume is, where p is the pressure and V is the volume. The change in enthalpy ( ) is given by, ____________________ WORLD TECHNOLOGIES ____________________ Since a reversible process is adiabatic (i.e. no heat transfer occurs), so . This leads to two important observations, , and or => The heat capacity ratio can be written as, For an ideal gas is constant. Hence on integrating the above equation, assuming a perfect gas, we get i.e. Using the equation of state for an ideal gas, , also, for constant C p = C v + R (per mole), and Thus for Isentropic Processes with an ideal gas, or ____________________ WORLD TECHNOLOGIES ____________________ Table of isentropic relations for an ideal gas Derived from: Where: = Pressure = Volume = Ratio of specific heats = = Temperature = Mass = Gas constant for the specific gas = = Universal gas constant = Molecular weight of the specific gas = Density = Specific heat at constant pressure = Specific heat at constant volume Thermodynamic potentials Isenthalpic process An isenthalpic process or isoenthalpic process is a process that proceeds without any change in enthalpy, H ; or specific enthalpy, h . ____________________ WORLD TECHNOLOGIES ____________________ In a steady-state, steady-flow process, significant changes in pressure and temperature can occur to the fluid and yet the process will be isenthalpic if there is no transfer of heat to or from the surroundings, no work done on or by the surroundings, and no change in the kinetic energy of the fluid. (If a steady-state, steady-flow process is analysed using a control volume everything outside the control volume is considered to be the surroundings. ) The throttling process is a good example of an isenthalpic process. Consider the lifting of a relief valve or safety valve on a pressure vessel.

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  Thermodynamics Made Simple for Energy Engineers

  • S. Bobby Rauf(Author)
  • 2021(Publication Date)
  • River Publishers

    (Publisher)

  Compression of vapor, therefore, is an adiabatic process. As discussed later in this text, the compression segment of the refrigeration cycle is not just adiabatic but also an Isentropic Process. Isenthalpic or Isoenthalpic Process An isenthalpic, or isoenthalpic, process is a thermodynamic pro-cess in which no change in enthalpy occurs, or ∆h = 0, or h 1 = h 2 . A steady-state, steady-fow process, would be isenthalpic if the follow-ing conditions are met: 1) The thermodynamic process is adiabatic—meaning, no heat is ex-changed with the environment. 2) Work is neither performed by the system onto the surroundings 153 Thermodynamic Processes nor is it performed by the surroundings onto the system. 3) There is no change in the kinetic energy of the system or fuid. Isenthalpic Process Example— Throttling Process in a Refrigeration System Refrigeration system throttling process is an example of an isen-thalpic process. See Figure 8-3. Throttling of a high pressure liquid re-frigerant to a low pressure liquid phase is an adiabatic process; i.e. no heat is exchanged with the environment. Moreover, no work is done on or by the surroundings, and there is no change in the kinetic energy of the fuid. Note that during the throttling process shown in Figure 8-3, the process adopts a vertical downward path, dropping the pres-sure precipitously while the enthalpy stays unchanged, thus, render-ing the process isenthalpic. In other words, all three requirements or conditions, stated above, for an isenthalpic process are met during the throttling segment of the refrigeration cycle. Other examples of practical isoenthalpic processes include lifting of a relief valve or safety valve on a pressurized vessel. The specifc en-thalpy of the fuid inside the pressure vessel is the same as the specifc Figure 8-3. Thermodynamic Processes in a Typical Refrigeration Cycle 154 Thermodynamics Made Simple for Energy Engineers enthalpy of the same fuid immediately after it escapes the vessel.

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  Thermodynamics Made Simple for Energy Engineers

  & Engineers in Other Disciplines

  • S. Bobby Rauf(Author)
  • 2023(Publication Date)
  • River Publishers

    (Publisher)

  8 Thermodynamic Processes

  Topics

  • Thermodynamic processes
  • Heat engine cycles
  • Steam turbines
  • Temperature-enthalpy diagrams
  • Pressure-enthalpy diagrams
  • Pressure-volume diagrams
  • Temperature-entropy diagrams
  • Practical examples and associated case study.

  8.1 Introduction

  This chapter explores some of the mainstream thermodynamic processes, heat engines and heat engine cycles. Fundamentals of thermodynamic processes, heat engines, heat engine cycles and associated systems are explained and illustrated through process flow diagrams, graphs, tables and pictures. Practical significance, application, analytical methods, and computational techniques associated with heat engine cycles and thermodynamic processes are demonstrated through case study, examples and self-assessment problems.

  8.2 Thermodynamic Processes

  Thermodynamic processes are processes that entail heat, internal energy, enthalpy, entropy, work, pressure, temperature and volume. In this section, we will explore the following thermodynamic processes and illustrate these processes with practical examples:

  1. Adiabatic Process
  2. Isenthalpic Process
  3. Isochoric Process
  4. Isothermal Process
  5. Isobaric Process
  6. Isentropic Process

  8.2.1 Adiabatic process

  Adiabatic process is a thermodynamic process in which no heat either enters or leaves the thermodynamic system boundary. An adiabatic process can also be explained through the following mathematical statements or equations:

  (8.1)

  Δ U = − W

  (8.2)

  Δ Q = 0

  Equations 8.1 and 8.2 essentially state that in an adiabatic process, wherein no heat is gained or lost, any work performed on the system or by the system is transformed into a net change in the internal energy of the system. As specifically stated above, Eq. 8.1

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  Radial Flow Turbocompressors

  Design, Analysis, and Applications

  • Michael Casey, Chris Robinson(Authors)
  • 2021(Publication Date)
  • Cambridge University Press

    (Publisher)

  111 4.3 Isentropic Efficiency The reference Isentropic Process is both reversible and adiabatic. The denominator in the equation is the change in static enthalpy, but if the change in kinetic energy is negligible, then this is the same as the change in the total enthalpy, which is the proper definition of the shaft work. The isentropic efficiency is also referred to as the adiabatic efficiency, although this terminology could be misleading as an adiabatic process is not necessarily isentropic. Isentropic efficiency is easy to understand and can be straightforwardly applied to real gases as well as ideal gases. Furthermore, the reversible work of the reference Isentropic Process is a function of the inlet temperature and the pressure ratio; it is not affected by the actual performance of the machine. This means that knowledge of the end state of the real process is not required in order to calculate the reversible aerodynamic work. In connection with thermodynamic cycle calculations, the isen- tropic efficiency leads to simple expressions, and is therefore generally used in relation to processes in single-stage turbochargers, refrigeration cycles and gas turbine cycles, as shown in Sections 18.9.1 and 18.10.1. Making use of the isentropic relations for a perfect gas from Section 2.7.1, the static–static isentropic stage efficiency can be written as η ss s ¼ T 2s  T 1 T 2  T 1 ¼ T 2s =T 1 ð Þ  1 T 2 =T 1 ð Þ  1 ¼ p 2s =p 1 ð Þ γ1 γ  1 T 2 =T 1 ð Þ  1 ¼ p 2 =p 1 ð Þ γ1 γ  1 T 2 =T 1 ð Þ  1 : (4.9) The difference in enthalpy between states 2s and 2, shown in Figure 4.2, at the pressure level p 2 , can be obtained by integration of the Gibbs equation for a constant pressure process, dp ¼ 0, (dh) p ¼ Tds, between states 2s and 2, which shows that h 2  h 2s ¼ ð 2 2s dh p ¼ ð 2 2s Tds: (4.10) This indicates that the measure of the detrimental effect of real irreversibilities on the isentropic efficiency is the integral of Tds from 2 to 2s.

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  Thermodynamics and Heat Power

  • Irving Granet, Maurice Bluestein(Authors)
  • 2014(Publication Date)
  • CRC Press

    (Publisher)

  Using the energy equation for a reversible, nonflow process enabled us to derive some general rela-tions among entropy, enthalpy, and internal energy. Key Terms Terms used for the first time in this chapter are as follows: absolute thermodynamic temperature: An arbitrary temperature function used with the Carnot cycle. For practical purposes, it is identical to the absolute temperature scales of Kelvin or Rankine. Carnot cycle: A reversible cycle proposed by Sadi Carnot in 1824 that consists of two constant-temperature and two adiabatic processes. cycle: A series of thermodynamic processes during which the working fluid can be made to undergo changes involving energy transitions and is subsequently returned to its original state. 174 Thermodynamics and Heat Power entropy: A property of a substance; also a measure of the unavailability that occurs in an irreversible process. heat engine: A continuously operating system across whose boundaries flow only heat and work. isentropic: A process carried out at constant entropy. A reversible adiabatic process is isentropic. isothermal: A process carried out at constant temperature. principle of the increase of entropy: The entropy of an isolated system increases or in the limit remains the same. reversible process: Any process performed so that the system and all its surroundings can be restored to their initial states by performing the process in reverse. second law of thermodynamics: Heat cannot, of itself, pass from a lower temperature to a higher temperature. thermal efficiency: The ratio of the net work of a cycle to the heat added to the cycle.

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  Thermodynamics

  A Smart Approach

  • Ibrahim Dinçer(Author)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  In some cases, a reversible, poly-tropic process may be used as the ideal process for compression applications. Then, a polytropic efficiency may be defined as: η pol , c = W pol W a 4 17 where the subscript pol refers to polytropic process and W a = m h 2 a -h 1 . Furthermore, the work input rate for a reversible, polytropic process is given for an ideal gas with constant specific heats as: 4.9 Isentropic Efficiencies for Ideal Gases 195 W pol = m nR T 2 -T 1 n -1 = m nRT 1 n -1 P 2 P 1 n -1 n -1 4 18 Here, n is the polytropic exponent, which is similar to adiabatic exponent ( k ), but its value is slightly higher than k . (c) Pump While discussing ideal gases, we insert the subsection on a pump here, particularly for liquids. A pump is used to increase the pressure of a liquid. A mechanical work input is needed for this process. The liquid may be considered to be an incompressible fluid and the power input for the isentropic case may be determined from specific volume and pres-sure data. A schematic diagram of a pump is shown in Figure 4.19. When the changes in potential and kinetic energies of a liquid are negligible, the isen-tropic efficiency of a pump is defined as: η is , p = W s W a = mv P 2 -P 1 m h 2 a -h 1 4 19 where v is the specific volume of the liquid; it is usually taken at the pump inlet and the subscript p refers to pump. (d) Nozzle A nozzle is essentially an adiabatic device, as shown in Figure 4.20, because of the negligible heat transfer and is used to accelerate a fluid or gas. Therefore, the isentropic (i.e. reversible State 1 at T 1 and P 1 State 2 at T 2 and P 2 Pump W in Figure 4.19 Schematic diagram of a pump. V 2 >> V 1 V 1 Nozzle Figure 4.20 Nozzles are shaped so that they can convert pressure energy into kinetic energy. 196 4 Entropy and Exergy and adiabatic) process serves as a suitable model for nozzles.

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  Physical Principles of Chemical Engineering

  International Series of Monographs in Chemical Engineering

  • Peter Grassmann, H. Sawistowski(Authors)
  • 2013(Publication Date)
  • Pergamon

    (Publisher)

  It should be noted in particular that the terms isentropic and isochoric in the case of an open system always relate to the change of state taking place, but t To distinguish change of state from process, cf. H. D. Baehr, Thermodynamics (Thermodynamik) Springer-Verlag, Berlin-Göttingen-Heidelberg, 1962, § 1.31. §2.3] Changes of State 71 not to the entire entropy contained in the balance region or the total volume. For example, in the case of every steady-state process the density of the working medium, its temperature, and its pressure at all points remain constant with time, so that also the total entropy S B of the working medium enclosed by a fixed balance shell remains constant, i.e. dS B = 0. Nevertheless, this need not necessarily be an Isentropic Process. We can only speak of this process when the entropy of each mass particle Am passing through the balance region and undergoing the change of state there, i.e., for example, expanding or con-tracting, remains constant. Thus isentropic means that the specific entropy s referred to any unit of mass, e.g. kilogram, remains constant. Only when we proceed from this definition does a line s = const, in the diagram correspond to an isentropic change of state, for this also represents the change of specific entropy, i.e. the entropy related to the kilogram, or the molar entropy, i.e. the entropy related to the kilomole. Thus the relations found for the closed process can be converted to the open process relatively simply. Here we imagine the mass particle Am enclosed in a balance shell moving with the particle, as passing through our large balance region, e.g. the compressor in question, like a document packed in a case and dispatched through the pneumatic postal equipment. The case enclosing the mass particle should here be assumed to be completely elastic, so that it can follow all the volume changes of the mass Am brought about by variations in the temperature and pressure.

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  Physics, Volume 1

  • Robert Resnick, David Halliday, Kenneth S. Krane(Authors)
  • 2016(Publication Date)
  • Wiley

    (Publisher)

  In a truly reversible process, there would be no losses of energy due to turbulence, friction, or other dissipative effects. Clearly the reversible process is an abstraction, be- cause all natural processes will result in these types of en- ergy losses and hence be irreversible. For example, if there is friction in the piston of Fig. 21-13, the system will not return to its original configuration when we return the lead shot to the container. However, by improving the apparatus and making other experimental refinements, we can ap- proach arbitrarily close to reversibility. More importantly, the strictly reversible process is a simple and useful abstraction that helps us to analyze and understand more complex processes, just as the ideal gas concept is an ab- straction that helps us to understand the behavior of real gases. We begin our discussion of entropy by simply stating the definition of entropy change for a reversible process and then examining its consequences. The definition is (24-1) Here dQ is the increment of heat energy that is transferred into or out of the (closed) system at (Kelvin) temperature T, and the integral is evaluated from the initial state i of the system to its final state f. Both the heat transferred and the temperature at which the transfer takes place are equally important in defining the entropy change. If the process is isothermal, so that the heat transfer takes place at a constant temperature T, then Eq. 24-1 re- duces to (24-2) Because the (Kelvin) temperature T is always positive, it follows from Eqs. 24-1 and 24-2 that the entropy change has the same algebraic sign as the heat Q. That is, if heat energy is added (reversibly) to a closed system the entropy of that system increases and con- versely. The unit of entropy that follows from its defining equation is the joule/kelvin. (S  0) (Q  0), S  Q T (reversible, isothermal). S   f i dQ T (reversible). 546 Chapter 24 / Entropy and the Second Law of Thermodynamics

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