Reversibility, isothermal flow

Response time constant 403 Rkster. S. 6-13,655 Return bends, heat exchanger 505 Reversed flow 668 Reversibility, isothermal flow 143 Reversible adiabatic, isentropic flow 148... 

We can represent states of the system (with constant values specified for all the variables except 9 and at) by a set of isotherms as shown in Figure 2.1 la. Two isotherms, 9 and 92 are shown, with 92 < 9t. State I, which is defined by 9 and A], can be connected to states T and 1" by a series of reversible isothermal processes (horizontal lines in the figure). We remember that heat is absorbed or evolved along a reversible isothermal path, and we will assume that this flow of heat is a continuous function of at along the isotherms, with the absorption or liberation depending upon the direction in which at is varied. That is, suppose... 

Pressure drop on the tube-side of a shell and tube exchanger is made up of the friction loss in the tubes and losses due to sudden contractions and expansions and flow reversals experienced by the tube-side fluid. The friction loss may be estimated by the methods outlined in Section 3.4.3 from which the basic equation for isothermal flow is given by equation 3.18 which can be written as ... 

One mole of an ideal gas is compressed isothermally but irreversibly at 400 K from 3 bar to 7 bar in a piston/cylinder device. The work required is 35 percent greater than the work of reversible, isothermal compression. The heat transferred from the gas during compression flows to a heat reservoir at 300 K. Calculate the entropy changes of the gas, the heat reservoir, and A5Iolal. 

In a binary mixture, diffusion coefficients are equal to each other for dissimilar molecules, and Fick s law can determine the molecular mass flows in an isotropic medium at isothermal and isobaric conditions. In a multicomponent diffusion, however, various interactions among the molecules may arise. Some of these interactions are (i) diffusion flows may vanish despite the nonvanishing driving force, which is known as the mass transfer barrier, (ii) diffusion of a component in a direction opposite to that indicated by its driving force leads to a phenomenon called the reverse mass flow, and (iii) diffusion of a component in the absence of its driving force, which is called the osmotic mass flow. 

The principle of FFF can be explained best with the aid of Fig. 7.1. A lateral field acting across a narrow channel, composed usually of two planparallel walls, interacts with molecules or particles of a solute and compresses them to one of the channel walls in the direction of x-axis perpendicular to this wall. Hence a concentration gradient is established in the direction of the x-axis. This concentration gradient induces a diffusion flow in the reverse direction. After a certain time a steady state has been reached and the distribution of the solute across the channel can be characterized by a mean layer thickness /. At a laminar isothermal flow of a Newtonian fluid along a narrow channel, usually a parabolic velocity profile is formed inside the channel. It means that the molecules or the particles of the solute are transported in the direction of the longitudinal axis of the channel at varying... 

The curve is elevated relative to zero by a constant amount (0.125) and has a contribution of 2o), double the modulation frequency (+, second harmonic). Both these contributions are not included in the experimental reversing heat flow which contains only the contribution to the first harmonic ( , see Sect. 4.4.3). Accepting the present analysis, it is possible to determine y and x from the reversing heat capacity by matching the last term of the equation in Figs. 6.118 and 4.131, and then use the paramters describing the match to compute (A), the actual response of the TMDSC to the quasi-isothermal temperature modulation. 

It should be noted that the corrected heat flow phase is very small in most cases, so that the difference in value between C and Cp is negligible. For isothermal experiments, the reversing heat flow equals zero because of a zero underlying heating rate and consequently the non-reversing heat flow equals the total heat flow. 

The total heat flow obtained in quasi-isothermal MTDSC experiments agrees very well with the heat flow evolution obtained in a conventional DSC experiment, performed under the same conditions without of the modulation (Figure 2.2a). Neither changing the modulation amplitude nor the period had an effect on the reaction exotherm seen in the non-reversing heat flow. This illustrates the negligible effect of the perturbation on the cure reaction. 

Figure 2.2. Quasi-isothermal cure of an epoxy-anhydride at 100°C (a) comparison of the non-reversing heat flow obtained in MTDSC to the heat flow obtained in conventional DSC (arrow), (b) heat capacity and (c) corrected heat flow phase.

Figure 2.3. Quasi-isothermal cure of an unsaturated polyester at 30°C (a) non-reversing heat flow and complex viseosity (logarithmie seale) (b) heat capacity and heat flow phase the symbol (o) denotes the point at maximum auto-aeeeleration in the non-reversing heat flow...

Figure 2.5. Quasi-isothermal cure of a melamine-formaldehyde (MF) resin (pH 9.5 F/M = 1.7) at 119°C in closed high-pressure steel (HPS) and open A1 pans (a) non-reversing heat flow and heat capacity (b) heat flow phase.

Figure 2.7. Non-isothermal cure of an epoxy-anhydride at 0.2 (1), 0.4 (2), and 0.7°C min (3) and for the fully-cured material (4) non-reversing heat flow and heat capacity.

Figure 2.17. Quasi-isothermal cure at 80°C of an epoxy(/ = 2)-amine(/ = 2) (unmodified u) and epoxy(/ = 2)-amine(/ = 2)/20% PES (modified m) (a) non-reversing heat flow (b) change in heat capacity and heat flow phase.

The ejq)erimental MTDSC observations on anhydride-cured and amine-cured epoxies, described in the previous section, will now be modelled to illustrate the benefits of the technique to obtain a quantitative law of cure kinetics for such thermosetting systems. Because cure kinetics are often complicated by diffusion limitations and/or mobility restrictions, the effect of diffusion has to be incorporated into the overall reaction rate law. For this purpose, both heat capacity and non-reversing heat flow signals for quasi-isothermal and non-isothermal cure experiments are used. 

Figure 4.79. Reversing heat flow rate and Lissajous figure of the quasi-isothermal analysis at...

Modulated temperature DSC has also been used to study plasticization of poly(ethylene terephthalate) by water. PET is somewhat hygroscopic and absorbs moisture, so the glass transition temperature will decrease. Quasi-isothermal analysis was used and the glass transition temperature was found to increase with time as the water evaporated (Toda et al. 1997d). A similar analysis was performed to investigate the effects of water on Nylon 6. A hermetically sealed pan was used and the plasticized glass transition separated into the reversing heat flow (TA Instruments 1994). 

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