Isochore compressibility

Compression in a Roots pump is performed by way of external compression and is termed as isochoric compression. Experience shows that the following equation holds approximately ... 

Fig. 2.27 Compression curve for a daw pump without internai compression ( isochoric compression )...

Young s and bulk moduli in Pa, mass density in kg.m isochore compressibility in Pa , dimensionless isentropic exponents, y = C /C -... 

Finally, we consider the isothennal compressibility = hi V/dp)y = d hi p/5p) j, along tlie coexistence curve. A consideration of Figure A2.5.6 shows that the compressibility is finite and positive at every point in the one-phase region except at tlie critical point. Differentiation of equation (A2.5.2) yields the compressibility along the critical isochore ... 

In an isothermal process, heat must be added during an expansion and removed during a compression to keep the temperature constant. We will describe this more fully as we now calculate the heat added or removed in isobaric, isochoric, and isothermal processes. 

Assume isentropic for compression process 1-2, isentropic for compression process 2-3, isochoric for heating process 3-4, isentropic for expansion process 4-5, and isochoric for cooling process 5-6. 

To solve this problem, we build the cycle as shown in Fig. 3.14. Then, (1) assume isobaric for the precooling process 7-8, isentropic for the compression process 8-9, isentropic for the compression process 9-10, isobaric for the heating process 10-11, isentropic for the expansion process 11-12, and isochoric for the cooling process 12-13 (2) input pq= 14.7 psia. 

Air is compressed from 14.7 psia and 500°R isothermally to 821.8 psia, heated isochorically to 2500° R, and then expanded isentropically to 14.7 psia in a Wicks cycle. Determine the heat added, heat removed, work added, work produced, net work, and cycle efficiency. 

Assume a process for each of the four devices (1) compression and expansion devices as isothermal, and (2) cooling and heating devices as isochoric. 

Figure 11.5 compares the fluid entropy vectors, whose lengths range from about 0.25 (ideal gas) to about 0.75 (ether). As expected, the entropy vectors exhibit an approximate inverted or complementary (conjugate) relationship to the corresponding T vectors of Fig. 11.3. The length of each S vector reflects resistance to attempted temperature change (under isobaric conditions), i.e., the capacity to absorb heat with little temperature response. The lack of strict inversion order with respect to the T lengths of Table 11.3 reflects subtle heat-capacity variations between isochoric and isobaric conditions, as quantified in the heat-capacity or compressibility ratio...

The adiabatic compression of saturated vapours was considered by Bruhat, who also calculated the angle between the liquid and vapour phase isochores in the entropy-temperature diagram. Amagat investigated the discontinuity in specific heats where an isothermal cuts the saturation curve. Hausen, from a complicated formula for the specific heat of steam involving two Einstein terms ( 2.IX N), calculated the heat content and entropy of steam. Leduc found the value of n for dry steam in Rankine s equation for adiabatic... 

In eqs Al-1—Al-3, k is the Boltzmann constant, T is the absolute temperature, Np is the number of particles of species / in the volume v, is the chemical potential per molecule of species a, Va is the partial molar volume per molecule of species a, kf is the isothermal compressibility, and Ca is the bulk molecular concentration of component a (ca = Na/v). The derivative (dfiJdNp)T,v y f is taken rmder isothermal—isochoric conditions and with Ny = constant for any y B o/3 represents the cofactor... 

A vector field v satisfying V v = 0 is called solenoidal. A volume-preserving motion is called isochoric, i.e., a motion for which the density in the neighborhood of any particle remains constant as the particle moves. The flow of an incompressible fluid is necessarily isochoric, but there may also be isochoric flows of compressible fluids [104] (p. 212). 

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