Adiabatic constant

The adiabatic (constant enthalpy) line AC is almost parallel to the line of constant wet bulb. Had the latter been used, the final error would have been about 0.2 K, and it is sometimes convenient and quicker to calculate on the basis of constant wet bulb. (This... 

Table 1-1 Fanno Line—Adiabatic, Constant Area Flow (k = 1.400) ...

The Hayashi track (Hayashi 1961, 1966) is the locus of fully convective stars in the HR diagram, dependent on the mass, luminosity and chemical composition. However, it is mainly the surface properties - luminosity and radius or luminosity and effective temperature - that govern the entire stellar structure by fixing the adiabatic constant. A sketch derivation of its properties is the following. 

For an adiabatic constant pressure system the first law reduces to... 

However, these potentials do not yet express the second law in the form most convenient for chemical applications. Open laboratory vessels exposed to the temperature and pressure of the surroundings are subject neither to constraints of isolation (as required for entropy maximization) nor to adiabatic constant-volume conditions (as required for energy minimization). Hence, we seek alternative thermodynamic potentials that express the criteria for equilibrium under more general conditions. 

Consider now an irreversible process in a closed system wherein no heat transfer occurs. Such a process is represented on the P V diagram of Fig. 5.6, which shows an irreversible, adiabatic expansion of 1 mol of fluid from an initial equilibrium state at point A to a final equilibrium state at pointB. Now suppose the fluid is restored to its initial state by a reversible process consisting of two steps first, the reversible, adiabatic (constant-entropy) compression of tile fluid to tile initial pressure, and second, a reversible, constant-pressure step that restores tile initial volume. If tlie initial process results in an entropy change of tlie fluid, tlien tliere must be heat transfer during tlie reversible, constant-P second step such tliat ... 

System = contents of the turbine. This is a steady-state, adiabatic, constant volume system. 

System nitrogen contained in both tanks (closed, adiabatic, constant volume)... 

For a reversible adiabatic (constant-entropy) change in a perfect gas dll = dw = — pd V... 

To illustrate the use of this equilibrium criterion, consider the very simple, initially nonuniform system shown in Fig. 7.1-1. There a single-phase, single-component fluid in an adiabatic, constant-volume container has been divided into two subsystems by an imaginary-boundary. Each of these subsystems is assumed to contain the same chemical species of uniform thermodynamic properties. However, these subsystems are open to the flow of heat and mass across the imaginary internal boundary, and their temperature and-pressure need not be the same. For the composite system consisting of the two subsystems, the total mass (though, in fact, we will use number of moles), internal energy, volume, and entropy, all of which are extensive variables, are the sums of these respective quantities for the two subsystems, that is. 

Two identical metal blocks of mass M with initial temperatures T j and T ,, respectively, are in contact with each other in a well-insulated (adiabatic), constant-volume enclosure. Find the... 

A thermally insulated (adiabatic) constant-volume bomb has been very carefully prepared so that half its volume, is filled with water vapor and half with subcooled liquid water, both at — 10°C and 0.2876 kPa (the saturation pressure of the subcooled liquid). Find the temperature, pressure, and fraction of water in each phase after equilibrium has been established in... 

Probably the most important characteristic of military and commercial explosives and solid rocket propellants is performance as related to end use and safety. Performance can be described by a variety of conventional properties such as thermal stability, shock sensitivity, friction sensitivity, explosive power, burning, or detonation rate, and so on. Thermal analysis methods, according to Maycock (51), show great promise for providing information on both these conventional properties and other parameters of explosive and propellant systems. The thermal properties have been determined mainly by TG and DTA techniques and isothermal or adiabatic constant-volume decomposition. Physical processes in pseudostable ma-... 

We introduce this topic with a simple example [24]. Consider an adiabatic, constant-volume CSTR with, the following elementary reaction taking place in the liquid phase... 

Consider the following reaction in an adiabatic, constant-pressure PFR... 

Here we deduce bounds on the directions of irreversible transfers across the interface in Figure 7.4. We consider six processes workfree constant-mass heat transfer, adiabatic constant-mass work, isobaric constant-mass heat transfer, isothermal constant-mass work, isothermal-isobaric diffusion, and adiabatic-workfree diffusion. 

Adiabatic constant-mass work. Now let the interface be impermeable, thermally nonconducting, and movable. We initiate an adiabatic process by again adjusting the reservoirs so the phases have different temperatures and pressures. Under these conditions, the closed-system form (7.2.10) of the combined laws reduces to... 

Consider expansion of a against p, so > 0. Then, we must have P > PP to make the Uis of (7.2.18) positive. Similarly, when phase a is compressed, then < q and (7.2.18) requires P < PP. That is, for both expansions and compressions of phase a, the pressure difference (P - PP) drives an adiabatic, constant-mass change of volume, and the work associated with such volume changes "flows" from regions of high pressure to regions of low pressure. Similar statements apply for other work modes. 

This shows that heat transfer must occur during our proposed process—the process is isothermal, not adiabatic. (For an adiabatic, constant-mass process, the energy balance (7.2.6) requires (-8W - 5WP) = 0, regardless of reversibility.)... 

We emphasize that states in mechanical equilibrium have both the driving force (P -PP) and the volume change (dU ) equal to zero. Moreover, neither isothermal nor adiabatic constant-mass changes in volume can occur without a mechanical driving force that is, we cannot have 0 with P - pP = 0. 

The calculation of theoretical flame temperature is based on the assumption that combustion process is an adiabatic constant volume process. Since the temperature of the combustion in drying is, in general, not very high, dissociations are not taken into consideration in the calculation of flame temperature of the burner model. 

Here, y is the adiabatic constant (the ratio of the specific heats) and J is the electric current density flowing through the plasma. 

Figure 1.5. A diagrammatic representation of an adiabatic (constant heat) calorimeter. The calorimeter consists of an insulated container filled with water in which the reaction chamber containing the sample and an excess of oxygen gas is immersed. In an exothermic reaction, the heat generated is transferred to the water and measured. Knowing the quantity of heat, the change in temperature, and the heat-absorbing characteristics of the system, the amount of heat evolved in the reaction may be calculated. ...

Consider reaction 1.1 (with first-order kinetics) conducted in a nonisothermal PFR. The mass balance for the PFR given by Equation 1.58 must now be supplemented by the energy balance. Restricting our attention to adiabatic constant-pressure operation, the energy balance may be written as... 

The adiabatic and isothermic bulk elasticity modules for water only slightly differ. The adiabatic modulus for water is 2.2-lO Pa. The bulk elasticity modulus for gas can be obtained from the equation of state. For ideal gas the isothermic modulus is approximately equivalent to Pa, and the adiabatic modulus is equivalent to yPA, where Pa is the pressure inside the cell, y = 1.4 the adiabatic constant. The isothermic modulus can be used in the case of infinitely slow processes. In the case of pressure oscillations at sound frequencies the adiabatic modulus should be used. Gas is much more compressible than liquids. The bulk elasticity modulus for gas is four orders of magnitude smaller than for water. Therefore, even small amounts of gas much smaller than the volume of the solution (Voas Va), can mimic small values of the effective cell elasticity modulus Eq. (6), i.e. a strong decrease of the cell resistance to pressure variations. It is extremely important to avoid the presence of any small amounts of gas in the solution because it can lead to uncontrolled changes of the effective cell elasticity modulus. 

A = (after - before), this is an order-specific convention definition in all of thermodynamics AT = 0 means isothermal, same temperature, constant temperature Aq = Q means adiabatic, constant heat, no heat flow AP = 0 means isobaric, constant pressure, no change in pressure... 

Theoretical adiabatic, constant-volume combustion pressure for... 

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