Free Expansion

3 Key excerpts on "Free Expansion"

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  eBook - ePub

  Elements of Gasdynamics

  • H. W. Liepmann, A. Roshko, A. Roshko(Authors)
  • 2013(Publication Date)
  • Dover Publications

    (Publisher)

  ; if γ is constant, the relations become very simple indeed:

  We shall later see that an adiabatic, reversible process is isentropic: i.e., a process for which the entropy S remains constant.

  These examples do not exhaust, of course, the applications of the first law to reversible processes. But they outline the general procedure. 1.8 The First Law Applied to Irreversible Processes

  The first typical irreversible process that we shall discuss is the adiabatic expansion of a gas . The system of interest consists of a vessel with heat-insulated, rigid walls. A diaphragm divides the vessel into two volumes V 1 and V 2 (Fig. 1.3 ). Both volumes are filled with the same gas at the same temperature T . The pressures p 1 and p 2 , however, are different. The theory of the flow under such conditions will occupy us in later chapters; here we are interested only in the thermodynamics of the setup.

  FIG . 1.3 Heat-insulated vessel with dividing diaphragm.

  Let the diaphragm be ruptured at a time t = 0. A violent flow of the gas ensues; a shock wave propagates into the low-pressure side, an expansion wave into the high-pressure side, and by reflection and refraction a complicated wave system is set up. This subsides under the action of viscosity and internal heat conductivity, and eventually the gas is at rest again, in a new state of thermodynamic equilibrium. We now apply the first law to the change from the initial state to the final one.

  No heat has left the surroundings, and no work has been performed by the surroundings. Hence from Eq. 1.5 we have

  The internal energy in an expansion process is conserved .

  If the gas can be approximated by a perfect gas, then E = E (T ) and hence Eq. 1.32 yields:

  In the adiabatic, irreversible expansion of a perfect gas, initial and final state have the same temperature. Historically Gay Lussac performed a similar experiment; he measured the initial and final temperature and, since he found them equal, reasoned that E = E (T

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  Biomolecular Thermodynamics

  From Theory to Application

  • Douglas Barrick(Author)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  Problem 3.11 ).

  The Work Associated with the Irreversible Expansion of an Ideal Gas

  So far, we have only analyzed reversible transformations. As discussed at the beginning of the chapter, analysis of irreversible changes is challenging, because variables that are important for calculations tend not to be well defined. These include pressure and temperature. One approach to analyzing irreversible thermodynamic changes is to assume that the surroundings are very large, and adjust quickly in response to changes in the system. Although this “reservoir” case is a limiting approximation, it can highlight the differences between reversible and irreversible changes. Here we will use the reservoir approach to analyze irreversible gas expansions. We will postpone discussion of irreversible heat flow until Chapter 4 , where we develop entropy and its relation to reversible and irreversible processes.

  Passage contains an image Adiabatic irreversible expansion of a small system against a mechanical reservoir

  Irreversible expansion occurs when the pressure of the surroundings is significantly lower† than the pressure of the system. If the surroundings is vast (compared to the system), and if its pressure equilibrates quickly in the surroundings, then the pressure of the surroundings can be regarded as constant (i.e., it acts as a mechanical reservoir). The work done on the surroundings is given by

  w s u r r = ∫ V i V f p s u r r d V = p s u r r Δ V	(3.57)

  where Δ V refers to the system volume change. If this volume change is adiabatic, dw = dU . Combined with the fact that energy is conserved, this adiabatic constraint allows us to write Equation 3.57

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  BIOS Instant Notes in Physical Chemistry

  • Gavin Whittaker, Andy Mount, Matthew Heal(Authors)
  • 2000(Publication Date)
  • Taylor & Francis

    (Publisher)

  i ). Heat capacityWhen a system takes up or gives out energy in the form of heat, the temperature change in the system is directly proportional to the amount of heat. At constant pressure, The heat capacity at constant pressure, C p and at constant volume, C v , are approximately equal for solids and liquids, but the difference for gases is given by C p =C v +nR . Related topics Enthalpy (B2 )Entropy and change (B5 ) Thermochemistry (B3 )Free energy (B6 ) Entropy ()Statistical thermodynamics (G8 )

  Thermodynamics

  Thermodynamics is a macroscopic science, and at its most fundamental level, is the study of two physical quantities, energy and entropy. Energy may be regarded as the capacity to do work, whilst entropy (see Topics and G8 ) may be regarded as a measure of the disorder of a system. Thermodynamics is particularly concerned with the interconversion of energy as heat and work. In the chemical context, the relationships between these properties may be regarded as the driving forces behind chemical reactions. Since energy is either released or taken in by all chemical and biochemical processes, thermodynamics enables the prediction of whether a reaction may occur or not without need to consider the nature of matter itself. However, there are limitations to the practical scope of thermodynamics which should be borne in mind. Consideration of the energetics of a reaction is only one part of the story. Although hydrogen and oxygen will react to release a great deal of energy under the correct conditions, both gases can coexist indefinitely without reaction. Thermodynamics determines the potential for chemical change, not the rate of chemical change—that is the domain of chemical kinetics (see Topics F1 to F6 ). Furthermore, because it is such a common (and confusing) misconception that the potential for change depends upon the release of energy, it should also be noted that it is not energy, but entropy which is the final arbiter of chemical change (see Topic B5

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