The Specific Heat

Example 9.1 A process involves the use of benzene as a liquid under pressure. The temperature can be varied over a range. Compare the fire and explosion hazards of operating with a liquid process inventory of 1000 kmol at 100 and 150°C based on the theoretical combustion energy resulting from catastrophic failure of the equipment. The normal boiling point of benzene is 80°C, the latent heat of vaporization is 31,000 kJ kmol the specific heat capacity is 150 kJkmoh °C , and the heat of combustion is 3.2 x 10 kJkmok. ... 

British thermal unit (Btu) The most commonly used industrial heal unit the amount of heat required to raise 1 lb of water through UF under specified conditions. Since the specific heat of water varies, particularly with temperature, the actual value of Btu is dependent on the conditions chosen as stan-... 

Dulong and Pedt s law The product of the atomic weight and the specific heat of a metal is constant of value approximately 6-2. Although not true for all metals at ordinary temperatures, these metals and several non-metals approximate to the law at high temperatures. 

The specific heat for a liquid at constant pressure, written as and expressed in kJ/(kg-K), can be calculated for mixtures in two ways ... 

The specific heat of gases at constant pressure is calculated using the principle of corresponding states. The for a mixture in the gaseous state is equal to the sum of the C g of the ideal gas and a pressure correction term ... 

The specific heat along the critical isochore hence has the same smgularity as (5 P /5T )p for a lattice gas. 

This shows very clearly that the specific heat has a jump discontinuity at J= T ... 

There is jump discontinuity in the specific heat as the temperature passes from below to above the critical temperature. 

The specific heat at zero field follows easily,... 

The most direct effect of defects on tire properties of a material usually derive from altered ionic conductivity and diffusion properties. So-called superionic conductors materials which have an ionic conductivity comparable to that of molten salts. This h conductivity is due to the presence of defects, which can be introduced thermally or the presence of impurities. Diffusion affects important processes such as corrosion z catalysis. The specific heat capacity is also affected near the melting temperature the h capacity of a defective material is higher than for the equivalent ideal crystal. This refle the fact that the creation of defects is enthalpically unfavourable but is more than comp sated for by the increase in entropy, so leading to an overall decrease in the free energy... 

Physical Properties. Physical properties of anhydrous hydrogen fluoride are summarized in Table 1. Figure 1 shows the vapor pressure and latent heat of vaporization. The specific gravity of the Hquid decreases almost linearly from 1.1 at —40°C to 0.84 at 80°C (4). The specific heat of anhydrous HF is shown in Figure 2 and the heat of solution in Figure 3. 

SpeciTc Heat. The specific heat of a cellular polymer is simply the sum of the specific heats of each of its components. The contribution of the gas is small and can be neglected in many cases. 

The value of the specific heat at constant pressure and constant volume is 1.404 at 0°C. 

The specific heat of aqueous solutions of hydrogen chloride decreases with acid concentration (Fig. 4). The electrical conductivity of aqueous hydrogen chloride increases with temperature. Equivalent conductivity of these solutions ate summarized in Table 8. Other physicochemical data related to... 

To convert from kPa to mm Hg, multiply by 7.5. Values for the specific heat of aqueous borax (73) solutions as a function of weight percent decahydrate are... 

The thermal conductivity, W/ (m-K), along the a axis teaches a maximum of 285 at — lOO C and falls rapidly with declining temperature. It is 251 at 20°C. Along the c axis it remains ca 837 to very low temperatures. The specific heat varies markedly with temperature (Fig. 5). The steep rise in above 3500 K probably results from reversible formation of vacancies or other thermal defects (4). 

Decreasing the specific heat of combustion increases the amount of the coke that must be burned the coke component that increases is essentially the cat-to-od coke, which is increased by increasing the catalyst circulation rate. Cat-to-oil coke can be expressed as (20) ... 

Thus decreasing the specific heat of combustion results in an increase in catalyst circulation rate. Because of this relationship to coke yield (eq. 9), the increase in the catalyst circulation rate results in a decrease in regenerator temperature. 

The theoretical energy requirement for the burning of Portiand cement clinker can be calculated from the heat requirements and energy recovery from the various stages of the process. Knowledge of the specific heats of the various phases, and the heats of decomposition, transformation, and reaction then permits calculation of the net theoretical energy requirement of 1760 kj (420 kcal) for 1 kg of clinker from 1.55 kg of dry CaCO and kaolin (see Clays) (8). 

The specific heat of coal can be deterrnined by direct measurement or from the ratio of the thermal conductivity and thermal diffusivity. The latter method gives values decreasing from 1.25J/(g-K)(0.3cal/(g-K)) at 20°C to 0.4J/(g-K)(0.1 cal/(g-K)) at 800°C. The specific heat is affected by the oxidation of the coal (46). 

Cg = humid heat for humidity H in units of kj / (kg-K) and = latent heat of vaporization at / in kj /kg. The slope of the constant-enthalpy adiabatic cooling line is —C j which is the relationship between temperature and humidity of gas passing through a totally adiabatic direct-heat dryer. The humid heat of a gas—vapor mixture per unit weight of dry gas includes the specific heat of the vapor... 

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