Specific volume and temperature

P = F(r,T). (10), and since this fixes the external conditions (viz., the one that the pressure on the system must have a given value) in order that the system may be in equilibrium, with chosen values of the independent variables specific volume and temperature, it may be called the equation of equilibrium of the fluid. 

This means that an equation of state exists relating pressure, molar or specific volume, and temperature for any pure homogeneous fluid in equilibrium states. The simplest equation of state is for an ideal gas, PV = RT, a relation which has approximate validity for the low-pressure gas region of Fig. 3.2 and which is discussed in detail in Sec. 3.3. 

Figure 23.12 Relation between specific volume and temperature (no pressure applied).

P, V and T are the actual pressure, specific volume and temperature while the values with asterisks are characteristic for a given material. Moreover, the free volume is defined as = v — v. The Hartmann equation has been demonstrated to work well for both polymer solids and melts. Figure 12.4 shows that the combination of equations (12.1)-(12.3) provides the capability of prediction of the shift factor aj values both below and above the glass transition temperature. 

FIGURE 2 Specific volume and temperature history of the lOOlF/DDS epoxy resin during curing under a pressure of 5 MPa. 

It was shown that, for filled and unfilled PMMA, the straight lines describing the dependence of Vg on Tg and Vp onTp (where Vp and Tp are specific volume and temperature of the secondary transition) have an intercept at the point with coordinates v and. The last values are limiting values of the specific volume of a melt and temperature, at which, due to the high hydrostatic pressure, the segmental mobility is fully suppressed and free volrune becomes zero. Using v = v for Eq 4.27, one can find sA-... 

Reduced conditions are corrected, or normalised, conditions of temperature T, pressureand specific volume and are expressed mathematically as... 

Humid volumes are given by the curves entitled Volume mVkg diy air. The volumes are plotted as func tions of absolute humidity and temperature. The difference between dry-air specific volume and humid-air volume at a given temperature is the volume of water vapor. 

Dehumidification and heating Decreased moisture content increase in specific volume and dry- and wet-bulb temperature decreased specific enthalpy and % saturation Chemical dcliumidification... 

An artificial neural network based approach for modeling physical properties of nine different siloxanes as a function of temperature and molecular configuration will be presented. Specifically, the specific volumes and the viscosities of nine siloxanes were investigated. The predictions of the proposed model agreed well with the experimental data [41]. 

The heat evolved per unit isothermal increase of pressure is equal to the continued product of the absolute temperature, the specific volume, and the coefficient of expansion o. 

Figure 3 Curves of specific volumes vs. temperature for poly(vinyl acetate) measured on cooling. Equilibrium values measured 0.02 h and 100 h after cooling, as indicated. Tg and Tg are glass transitions respectively at fast and slow cooling rate. Reproduced from Ref. [2] with permission of John Wiley Sons, Inc.

Below T0 the material is in the glassy state. Compared with the crystal the glass shows a larger specific volume and heat content, but both quantities have a smaller temperature coefficient than in the melt (< ). The transition from melt to glass is often called a transition of the second order (2, 3) since it is not accompanied by finite changes of volume and enthalpy, but only by changes of their temperature coefficients. 

The observation that T0 for PVN has disappeared, as shown by examining both the damping constant and the dilatometric curve, unequivocally shows that PVN has lost its identity and that the whole copolymer behaves as an entity. The specific volume for temperatures in the amorphous region (above 60°C.) show that volume additivity for the two components is not followed, but that a contraction of about 2% has taken place. Examining the molecular models shows that one can readily entwine PEO and PVN chains. Optimum spacing is obtained with 3 ethylene oxide 1 naphthalene moiety—the complex composition Thus here, as with polyblends, the importance of conformation coupled with favorable but probably weak interactions is evident. 

CARNOT CYCLE. An ideal cycle or four reversible changes in the physical condition of a substance, useful in thermodynamic theory. Starting with specified values of die variable temperature, specific volume, and pressure, the substance undergoes, in succession, an isothermal (constant temperature) expansion, an adiabatic expansion (see also Adiabatic Process), and an isothermal compression to such a point that a further adiabatic compression will return the substance to its original condition. These changes are represented on the volume-pressure diagram respectively by ub. he. ctl. and da in Fig. I. Or the cycle may he reversed ad c h a. 

Because the volume of one mole of gas at any specific pressure and temperature contains the same number of molecules even though there may be several different gases in the mixlure. the percent by volume of any given gas is equal to the percent pressure exerted by that gas and is also equal to the mole percent of that gas. Mole percent equals volume percent equals pressure percent. 

Fig. 8. The dependence of partial specific volume on temperature. Reproduced from Holcomb and Van Holde 0851).

Chemists use the equation to determine the pressure, volume, amount, or temperature for a specific gas. For example, say you know the volume and temperature of the air in a car tire. To... 

Effects of structural changes on properties, such as specific heat, specific volume, and/or dynamic mechanical and electrical properties, are observed at various temperatures. A number of transitions were observed by various investigators their interpretation and the modes of identification are listed in Table 3.2. 

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