Cubical Expansion of Liquids

The coefficients of thermal expansion.—The coefl. of cubical expansion of liquid chlorine follows from the determinations of sp. gr. at various temp. According to A. Lange s data,17 the coeff. of expansion of liquid chlorine, a, is... 

If Vo is the volume at 0 , then at the e3q>ansion formula is V, = Vo(l + oti + + yt ). The table gives values of a, p, and y, and of C, the true coefficient of cubical expansion at 20 for some liquids and solutions. The temperature range of the observation is At. Values for the coefficient of cubical expansion of liquids can be derived from the tables of specific volumes of the saturated liquid given as a function of temperature later in this section. 

Discharge rates may be increased by circulating air at room temperature (20-25 C) around the cylinders with a fan. Jfeyi r placfi. dicjcofl. er ip a bath of hot water or apply diregt heat (high coefficient of cubic expansion of liquid chlorine and rise in pressure with temperature i.e. at 0 C - 3.5 bar, 20"C - 6.7 bar, 40"C - 11 bar). 

Between 0 and 80 C the cubical expansion of liquid water is given by ... 

H. Billet, the coeff. of cubical expansion of solid iodine is 0 0002350, and according to J. Dewar 0 0002510 between —38 85° and 17° the coeff. of thermal expansion for liquid iodine is 0-000856 according to H. Billet. 

F/=real volume of liquid at F/ =apparent volume of liquid at t°C. as measured by the graduation on the vessel, a =apparent coefficient of cubical expansion of the liquid, a=true coefficient of cubical expansion of the liquid ( l.VIII C), g=coefficient of cubical expansion of the glass of the vessel (taken as three times the coefficient of linear expansion). Then ... 

Expansion of liquids on heating. The definition of the co-efiicient of expansion of a hquid is identical with that of the coefficient of cubical expansion of a solid substance. There are two important methods of measuring the coefiicient of... 

The volume of liquid chlorine increases considerably with increasing temperature. For example, in a cylinder with 75 kg, roughly corresponding to a volume of 52 litres, the volume will increase 2.1 litres when the temperature rises from 0°C to 20 "C, i.e. the volume expands 4% over 20°C, a coefficient of cubic expansion of 0.002 per °C. 

Linke et al. (1983) and Franz (1984, 1986) developed a different version of the lattice-gas concept. These models emphasize the experimental observation (Secs. 3.4 and 4.4) that thermal expansion of liquids is mainly achieved by a reduction of the average near-neighbor coordination number. A given structure such as the artificial, but mathematically convenient Cayley Tree or Bethe lattices can, when partially populated, be viewed as a crystalline alloy of atoms and vacancies. Tight-binding methods then permit calculation of the electronic structure, in particular the density of electronic states. Franz made use of quantum percolation theory to model the DC conductivity. A more recent model (Tara-zona et al., 1996) employs a body-centered-cubic lattice which, when fully occupied, provides a reasonable approximation to the local structure of liquid metals near the melting point. 

Conversion of Specific Gravity at 25°/25°C to Density at any Temperature from 0° to 40°C. Liquids change volume with change in temperature, but the amount of this change, /3 (coefficient of cubical expansion), varies widely with different liquids, and to some extent for the same liquid at different temperatures. 

B = cubical expansion coefficient per °F of liquid at expected temperature (see tabulation in text)... 

Coefficients of Cubical Expansion for Various Liquids and Aqueous Solutions, in Lange s Handbook of Chemistry, 12th ed., ed. John A. Dean (New York, McGraw-Hill 1979), Table 10-42. 

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