Mixtures, Law of

If we desire to measure the quantity of heat Q, which is absorbed or liberated in any process, we arrange matters so that the process takes place in the interior of a known mass m, of a liquid of known specific heat c. is the initial, the final temperature of the calorimeter fluid. Q is therefore positive when the temperature of the liquid rises and heat is evolved by the system e.g. combustion). 

In making a determination it is necessary to consider a number of sources of error, and to correct for them. Thus we must make corrections for the change in temperature of the walls of the calorimeter vessel, of the thermometer itself, of the stirrer with which the hquid is agitated to secure efficient mixing, etc. 

The reader must consult handbooks on laboratory practice for further details of the experimental methods, as space does not permit of their being described here.  

The determination of the specific heat of a body by means of the calorimeter which has just been described is carried out in the following manner, grams of the body under investigation are heated to the temperature g, and are then immersed in the calorimeter, which is initially at the temperature t. The temperature is then allowed to come to its final equihbrium value t. As the heat which is given out by the body is equal to the heat which the calorimeter absorbs from it, we have 

At the same time, however, as the transfer of heat inside the calorimeter is going on, an interchange of heat with the sur-. roundings is taking place. 

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A method for the estimation of composite material performance from the characteristics of fillers and the matrices and from the configuration of filler is generally called the law of mixture. In the most basic form of the law of mixture, the characteristics of a composite material are represented as a function of characteristics of constituent components and their volume fractions, as shown in Fig. 3. For a composite material (characteris-ticsiA f) that consists of component A (characteristics Xa, volume fraction ) and component B (characteristics Xf, volume fraction b), the basic formulae of the law of mixture are as follows ... 

Figure 3 Relation between the properties of composites and various laws of mixture.

This function is intermediate between the parallel model and the series model and referred to as the logarithmic law of mixture shown in curve 3. The law of mixture is valid for a composite system when there is no interaction in the interface. However, it is natural to consider that interaction will occur in the interface due to contact between A and B. Then considering the creation of interfacial phase C, different from A and B, the following equation can be presented ... 

This is referred to as quadratic law of mixture shown in curve 4. The parameter K involves an interaction between components A and B and provides an expression for the interfacial effect. 

The law of mixtures for particulates, expressed by relation (20), yields the effective or average value of the elastic modulus of the mesophase, which may enter into any kind of law of mixtures, interconnecting the moduli of the phases and the composite. 

For fiber composites, on the other hand, a simple law of mixtures is valid, which is expressed by ... 

In order now to evaluate the exponent rp we make recourse to the law of mixtures, given by relation (21), which expresses the elastic modulus of the composite in terms of the moduli and the radii (or volume fractions) of the constituent phases. This relation yields the average elastic modulus for the mesophase Ef. Then, it is valid for the mesophase layer that ... 

The law of mixtures is classically applied by replacing the strength of the fibres by their contribution to the strength of the composite, and by taking account of the a and coefficients ... 

Some of them, such as density and water absorption, obey a law of mixtures. 

Because the law of mixtures applies to the solubility parameter, it is possible to easily calculate the solubility parameter of blended liquids forming mixtures that can serve as solvents. For example, an equal molar mixture of -pentane (5 = 7.1 H) and -octane (5 = 7.6 H) will have a solubility parameter value of 7.35 H (simply (7.1 + 7.6)/2). 

The transverse modulus (Mt) and many other properties of a long fiber resin composite may be estimated from the law of mixtures. The longitudinal modulus (Ml) may be estimated from the Kelly-Tyson equation (8.5), where the longitudinal modulus is proportional to the sum of the fiber modulus (Mp) and the resin matrix modulus (Mm)- Each modulus is based on a fractional volume (c). The constant k is equal to 1 for parallel continuous filaments and decreases for more randomly arranged shorter filaments. 

In general, the Tg of a random polymer may be estimated from the law of mixtures. For example, the Tt of a copolymer containing equimolar quantities of styrene and 2,4-dimethylstyrene is 381 K, while the Tg values of polystyrene and poly-2,4-dimethylstyrene are 356 and 404 K, respectively. The Tg of random copolymers may be estimated from... 

According to P. Pascal,0 fluorine is diamagnetic the specific magnetic susceptibility is —3447 X10 j and the atomic susceptibilitv calculated from the additive law of mixtures for organic compounds is —63X10-1. Ionic fluorine is univalent and negative. The decomposition voltage required to separate this element from its compounds is 1 75 volts.7 The ionic velocity (transport number) 8 of fluorine ions at 18° is 46 6, and 52-5 at 25° with a temp, coeff. of 0 0238. 

Relatively little theoretical and experimental work has been done on discontinuous fiber composites, and most of this work has been confined to metal-metal composites (4, 5, 8). For the metal-metal systems the law of mixtures is applicable for composite modulus as follows ... 

A thermal conductivity of the gas-solid particle mixture is determined (cf., 14) by the correlation of Gelperin and Einstein (23). We use a law of mixtures to define a radiation diffusion coefficient and, for the present, we consider only the limits of (1) opaque gas and opaque particles and (2) transparent gas and opaque particles. 

Empirical, uncontrolled skin thickness, low foam density Law of mixtures, thick skins, high foam density Tentative, few data from many test procedures Very tentative, rule-of-thumb Very tentative, rule-of-thumb... 

The law of mixtures applies to the solubility parameter, and thus it is possible to mix two or more solvents to form a mixture with a certain... 

The specific heat of mixtures of liquids can rarely be calculated additively from the specific heats of the components. There is generally a considerable deviation from the law of mixtures, and the calculated value is always larger than one would expect. Mixtures of hquids which are closely related chemically, such as ethyl and methyl alcohol, chloroform and carbon disulphide, behave normally mixtures of water with alcohol, or of alcohol with other organic hquids, show large deviations. It is noteworthy that heat is evolved on mixing these hquids, an indication that chemical combination also is taking place. This is probably the reason for the alteration in the heat capacity, since the specific heat of liquid chemical compounds cannot be calculated additively from the specific heats of the components. The regularities shown by sohd bodies do not hold even approximately for hquids. 

The specific heat of aqueous solutions is always considerably smaller than would be demanded by the law of mixtures. The decrease of the capacity for heat, consequent on solution, is often so great that the heat capacity of the solution is actually smaller than that of the water which it contains. The formation of aqueous solutions is accompanied by absorp-tion of heat, in contra-distinction to the behaviour of the mixtures of hquids which we have just mentioned. There would appear, therefore, to be some connection between the change in the capacity for heat and the heat which is evolved or absorbed on mixing, so far, at least, as the sign is concerned. The heat capacity of many solutions is approximately equal to that of the water which they contain. As far as the specific heat and specific volume of aqueous solutions is concerned, we might compare them to pure water under a high pressure. ... 

Figure 3 shows shrinkage behavior of powder mixtures calculated by Eqs. (1) (7) with the heating rate of 100°C/min. The sintering balance of MC2 is better than that of MCI. The shrinkage does not follow the law of mixture, that is, the minimum shrinkage is obtained at the low volume fraction of ceramic [1,2]. This is considered to be because of the increase in the average radius of pores due to mixture. This phenomenon was expressed as the reduction in relative density in Eq. (6) in the present work. 

Both positive and negative ions for percentages of NH3 more than 0.3% have their mobilities reduced by further addition of NH3 and more rapidly than the common law of mixtures would lead one to expect. The law of decrease is, however, not the same as that found for NH3-air mixtures, whose accuracy may be doubtful in view of the possibility of over-correc-... 

The geometrical approach by Jonsson and Hogmark (1984) separates coating and substrate contributions to the measured composite hardness by applying a simple area law of mixtures as... 

Figure 7.54 Jonsson-Hogmark area law of mixture model (see text).

In the case of a substrate with additives, the initial deposition of energy follows the law of mixtures — the total energy absorbed by each component of the mixture is proportional to the relative amounts of orbital electrons of each component in unit volume, or in practical terms, it is very nearly proportional to the fraction of the component by weight [Klots, 1968 Spinks and Woods, 1990]. However, it is not unusual to see disproportionately large radiolytic changes in the smaller component of a mixture. This is usually a result of the participation of the smaller component in energy and charge transfer reactions, as discussed below. 

When reinforcing fibres are added, and orientated parallel to an applied uniaxial tensile stress, the modulus of the reinforced composite material, E in the fibre direction is given by a simple law of mixtures ... 

The strength and modulus of the reinforced material falls rapidly from those predicted by the law of mixtures for unidirectional laminates, as the angle between the fibre direction and the stress is increased from zero towards 90°. We assumed above that the fibres are all parallel to the applied uniaxial stress, but if they are lying normal to the stress, the equation below applies and gives a much lower value for the composite modulus ... 

Lee and Gurland [8] attempted to express the relationship that exists between the hardness of WC-Co, its microstructure and its composition by using a simple law of mixtures of the type... 

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