Technology & Engineering
Isobaric Process
An isobaric process is a thermodynamic process in which the pressure remains constant. This means that work is done on or by the system without changing the pressure. In practical terms, this could occur in systems such as a constant-pressure heat exchanger or a gas expanding in a cylinder with a movable piston.
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8 Key excerpts on "Isobaric Process"
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Library Press(Publisher)
We conclude with: ________________________ WORLD TECHNOLOGIES ________________________ Isochoric Process in the Pressure volume diagram. In this diagram, pressure increases, but volume remains constant. On a pressure volume diagram, an isochoric process appears as a straight vertical line. Its thermodynamic conjugate, an Isobaric Process would appear as a straight horizontal line. Ideal gas If an ideal gas is used in an isochoric process, and the quantity of gas stays constant, then the increase in energy is proportional to an increase in temperature and pressure. Take for example a gas heated in a rigid container: the pressure and temperature of the gas will increase, but the volume will remain the same. Ideal Otto cycle The ideal Otto cycle is an example of an isochoric process when it is assumed that the burning of the gasoline-air mixture in an internal combustion engine car is instantaneous. There is an increase in the temperature and the pressure of the gas inside the cylinder while the volume remains the same. ________________________ WORLD TECHNOLOGIES ________________________ Temperature - entropy Isothermal process An isothermal process is a change of a system, in which the temperature remains constant: Δ T = 0. This typically occurs when a system is in contact with an outside thermal reservoir (heat bath), and the change occurs slowly enough to allow the system to continually adjust to the temperature of the reservoir through heat exchange. In contrast, an adiabatic process is where a system exchanges no heat with its surroundings ( Q = 0). In other words, in a n isothermal process, the value Δ T = 0 but Q ≠ 0, while in an adiabatic process, Δ T ≠ 0 but Q = 0. Details for an ideal gas Several isotherms of an ideal gas on a p-V diagram ________________________ WORLD TECHNOLOGIES ________________________ For the special case of a gas to which Boyle's law applies, the product pV is a constant if the gas is kept at isothermal conditions.
- S. Bobby Rauf(Author)
- 2021(Publication Date)
- River Publishers(Publisher)
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. In such a scenario, the temperature and velocity of the escaping fuid can be calculated if the enthalpy is known. In Figures 8-1 and 8-2, an isenthalpic process follows the isotherm line at a specifc temperature, and along the isotherm the following re-lationship between enthalpy, temperature and specifc heat holds true: dh = c p dT = 0 Additional examples of isenthalpic process are referenced later in this chapter, under the heat engine cycle discussion. Constant Pressure or Isobaric Process An Isobaric Process is a thermodynamic process in which the pressure remains constant. See Figure 8-4, where the curve represents an isobar. Even though the temperature varies as a function of the en-tropy in this graph, the pressure stays constant. Isobaric Process Example I: Evaporation Stage of a Refrigeration Cycle Evaporation stage of a refrigeration cycle represents an Isobaric Process in that the pressure remains constant as the low pressure liq-uid system evaporates or changes phases from liquid to gaseous by ab-sorbing the heat energy from the air passing through the heat exchang-er. This absorption of heat by the system—refrigerant or the working fuid— from the surroundings (ambient air) is shown in Figure 8-4 as the shaded area under the isobar, between entropies s 1 and s 2 . In an Isobaric Process: Δp = 0 and, Q = ΔH The latter mathematical statement, Q = ∆H, implies that in this Isobaric Process, the heat absorbed by the refrigerant, during the evap-oration phase, results in a net increase in the enthalpy of the refriger-ant. Some of the equations with practical applications in closed sys-tem Isobaric Processes are listed below:
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
We conclude with: ____________________ WORLD TECHNOLOGIES ____________________ Isochoric Process in the Pressure volume diagram. In this diagram, pressure increases, but volume remains constant. On a pressure volume diagram, an isochoric process appears as a straight vertical line. Its thermodynamic conjugate, an Isobaric Process would appear as a straight horizontal line. Ideal gas If an ideal gas is used in an isochoric process, and the quantity of gas stays constant, then the increase in energy is proportional to an increase in temperature and pressure. Take for example a gas heated in a rigid container: the pressure and temperature of the gas will increase, but the volume will remain the same. Ideal Otto cycle The ideal Otto cycle is an example of an isochoric process when it is assumed that the burning of the gasoline-air mixture in an internal combustion engine car is instantaneous. There is an increase in the temperature and the pressure of the gas inside the cylinder while the volume remains the same. ____________________ WORLD TECHNOLOGIES ____________________ Temperature - entropy Isothermal process An isothermal process is a change of a system, in which the temperature remains constant: Δ T = 0. This typically occurs when a system is in contact with an outside thermal reservoir (heat bath), and the change occurs slowly enough to allow the system to continually adjust to the temperature of the reservoir through heat exchange. In contrast, an adiabatic process is where a system exchanges no heat with its surroundings ( Q = 0). In other words, in a n isothermal process, the value Δ T = 0 but Q ≠ 0, while in an adiabatic process, Δ T ≠ 0 but Q = 0. Details for an ideal gas Several isotherms of an ideal gas on a p-V diagram ____________________ WORLD TECHNOLOGIES ____________________ For the special case of a gas to which Boyle's law applies, the product pV is a constant if the gas is kept at isothermal conditions.
eBook - PDF- Donald Olander(Author)
- 2007(Publication Date)
- CRC Press(Publisher)
Application of the First and Second Laws to Processes in Closed Systems 89 Many processes do not fit the simple restraints of constant volume, temperature, or pressure. These are considered in Problems 3.2 and 3.4. 3.5 THE ISENTROPIC PROCESS The last of the important “iso” processes are those taking place at constant entropy. Figure 3.4 shows a simple version of this type of state change. A less evident example of an isentropic process is the blowdown of gas from a high-pressure cylinder, as illustrated in Figure 1.8. As emphasized on the diagram, such a process must be both adiabatic and reversible. No real process can be perfectly reversible, so isentropic analyses of adiabatic processes are idealizations. However, nearly isentropic processes include the following: expansion or compression of gases (except through a valve or an orifice); liquid-vapor phase changes of water encountered in practical devices such as turbines of power plants; compression of liquids by efficient pumps. Entropy changes accompanying reversible and irreversible processes in gases and liquids are treated in Problems 3.1 and 3.8. The starting point for thermodynamic calculations involving this particular restraint is the pair of formulas relating entropy changes in a process to changes in pressure, temperature and specific volume. These are rearranged forms of Equations (1.15a) and (1.16a): (3.7a) and (3.8a) FIGURE 3.4 An isentropic process. Pressure Specific Volume V 1 V 2 Slow Expansion or Compression Adiabatic Cylinder and Piston ds du T p T dv = + ds dh T v T dp = −
- Keith Stowe(Author)
- 2007(Publication Date)
- Cambridge University Press(Publisher)
Special processes 227 Figure 12.1 (a) Processes throughout vast regions of space are isobaric and/or isothermal. The gravitational collapse of interstellar clouds, which forms stars, is nearly adiabatic. (Courtesy of NASA) (b) A thunderhead is the result of the rapid adiabatic cooling of air as it rises and expands. (Plymouth State University photograph, courtesy of Bill Schmitz) (c) The physical and chemical processes carried out through marine plankton are isobaric and isothermal. (Courtesy of Mark Moline, California Polytechnic State University) (b) 228 Introduction to thermodynamics and statistical mechanics (c) Figure 12.1 ( cont .) We choose our variables to be N , p , T because N and p are constant and we are measuring changes in T . The change in internal energy is given by the first law, 1 d E = T d S − p d V = T ∂ S ∂ T p d T − p ∂ V ∂ T p d T . With the help of Table 11.1 we can convert these partial derivatives to give d E = ( C p − pV β )d T (Isobaric Processes) . (12.1) This is what we wanted. If we know how the properties C p , p , V , and β depend on T then we can integrate equation 12.1 to find the relationship for finite changes. B Isothermal processes Isothermal nondiffusive processes also operate under two constraints, d N = d T = 0. So again, there is just one remaining independent variable, which we are free to choose. 1 Note the convention that we usually display only two variables for nondiffusive (d N = 0) processes. Special processes 229 Example 12.2 How does a system’s internal energy vary with volume for isother-mal, nondiffusive, processes (d T = d N = 0)? We choose our variables to be T , N , V because T and N are constant and we are measuring changes in V . The change in internal energy is given by the first law: d E = T d S − p d V = T ∂ S ∂ V T d V − p d V . Again, we use Table 11.1 to convert the partial derivative to easily measured properties: d E = T β κ − p d V (isothermal processes) .
- Lucien Borel, Daniel Favrat(Authors)
- 2010(Publication Date)
- PPUR(Publisher)
CHAPTER 8 Thermodynamic processes and diagrams 8.1 TYPICAL THERMODYNAMIC PROCESSES 8.1.1 Generalities In Subsection 2.3.1, we defined the following typical thermodynamic processes: • isochoric process; • Isobaric Process; • isothermal process; • isoenergy process; • isenthalpic process; • isentropic process; • and polytropic process. We will now provide, for each of these processes concerning fluids, the most useful thermodynamic relations, in their integral forms. The relations are derived directly from those given in differential form in the previous chapters, particularly in Sections 2.4 through 2.6. Their construction relies on elementary mathematics and is easy to reproduce. For this, it is sufficient to observe that, for a factor that is fixed, • for real fluids, all entities , , , , , , , , , and depend on only two state functions, e.g., P and T ; • for ideal gases and the entities , , , , , , and only depend on T ; • for perfect gases, and the entities , , , , , , and are constant. 8.1.2 Thermodynamic relations Tables 8.1 through 8.7 systematically give the most useful thermodynamic relations for the isochoric, isobaric, isothermal, isoenergy, isenthalpic and polytropic proc- esses. For real fluids, the integrations have been performed by assuming that the thermal factors , and , as well as the specific heats and , are constant and equal to their mean values , , , and . In a first approximation, one could also consider the values corresponding to the arithmetic average of the pres- sure and of the temperature. Take, for instance, σ α v β p γ t α σ β σ γ σ c v c p c σ γ Γ α β γ v = = = p t 1 α σ β σ γ σ c v c p c σ γ Γ α β γ v = = = p t 1 α σ β σ γ σ c v c p c σ γ Γ α v β p γ t c v c p α v β p γ t c v c p 342 Thermodynamics and Energy Systems Analysis: from Energy to Exergy Table 8.1 Isochoric process ( ). * For ideal gases, we consider average values of and . Table 8.2 Isobaric Process ( ). * For ideal gases, we consider average values of and .
eBook - PDF- P.F. Kelly(Author)
- 2014(Publication Date)
- CRC Press(Publisher)
Isothermic Processes Isothermic processes occur at constant temperature. The terms appearing in the First Law, specialised to isothermic ideal gas systems, are enumerated below. Δ U Owing to the constancy of the temperature, the internal energy of the system remains unchanged, i.e., Δ U = 0. Q Thus, according to the First Law, the flows of work and heat must cancel: 0 = Δ U = Q − W = ⇒ Q = W. W The work done by an ideal gas expanding isothermically from an initial volume, V i , to a final volume, V f , was computed in Chapter 10: W if bracketleftbig P bracketrightbig = nRT ln bracketleftbigg V f V i bracketrightbigg . The ideal gas law and the internal energy EoS remain operative and hence the tools that we shall use for our analyses of isothermic transitions of an ideal gas system are W = nRT ln bracketleftbigg V f V i bracketrightbigg , Q = W , and PV = nRT. Adiabatic Processes Adiabatic processes occur with no heat flow. The application of this constraint to an ideal gas system has several implications. FIRST LAW In the absence of heat flow, changes in the internal energy of the system are identical in magnitude and opposite in sign to the work done by the system: Δ U = − W. Any work done by the gas is accompanied by a concomitant reduction in the system’s internal energy; work input to the system is transformed into internal energy. 45–295 45–296 Properties of Materials TRAJECTORY The phase space trajectory of an ideal gas undergoing an adiabatic transi-tion [ quasi-statically ] satisfies PV γ = constant , where γ is a parameter dependent on properties of the gas, and the constant factor is system-and context-dependent. For monatomic gasses [ e.g., He, Ne, etc . ], γ ≃ 5 / 3. For air at room temperature, γ ≃ 7 / 5. ASIDE: The exponential factor governing the shape of the adiabatic phase trajectory, γ , is the ratio of the molar specific heats of the gas at constant pressure, f C P , and at constant volume, f C V , γ ≡ f C P f C V = C P C V .
eBook - PDF- J Kestin(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
Fig. 2 a. Reversible adiabatic (isentrope). A, and isothermal, I, for a perfect gas in the Γ, V-plane. In order to obtain a clear idea of the reversible nature of a process we imagine the gas to be confined in a cylindrical vessel of cross-sectional area A . The vessel is, in turn, enclosed by walls which prevent any exchange of heat, and the gas is contained at the top by a weightless piston. The piston is maintained in equilibrium by a weight P = p A which balances the gas pressure. We imagine P to be subdivided into many small weights δΡ which will be removed one by one. This causes the piston to rise each time, its pressure p decreasing. Each weight δΡ is placed outside the vessel at the same level at which it has been removed so that no work is gained or lost in the process. The gas pressure will fall from its initial value p (e. g. 2 kp/cm 2 ) 22 THERMODYNAMICS. GENERAL CONSIDERATIONS 5. to a final value p x (say 1 kp/cm 2 ), and the volume will increase from an initial value V (e. g. 1 liter) to a final value V x (in our example 2 1/y liter). The center of gravity of each bP has been raised compared with its original level. This work against the forces of gravity stems from the work performed by the gas on the piston. It has not been lost, being found stored in the raised dP's. If we now replace these weights one by one on the piston, the gas will be re-compressed and heated and will revert to its initial state. The process is reversible on condition that it has been carried out in infinitely small steps and sufficiently slowly, 1 i. e. with a sufficiently fine subdivision of P into elements of δΡ each. B. THE IRREVERSIBLE ADIABATIC PROCESS If the piston (together with the weight P) is raised suddenly the gas will first flow into a vacuum performing no external work. The resulting turbulent motion gradually subsides, the gas coming to rest.
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