Liquids heat capacity for

Compute saturated-liquid heat capacity. For n-octane,... 

Example Estimate the liquid heat capacity for 2-methyl-2-propanol at... 

For the calculation of a vapor enthalpy, the liquid heat capacity for each component is integrated from the reference temperature to a transition temperature trans which can be chosen arbitrarily. A good choice is the normal boiling point. 

Liquid Heat Capacity The two commonly used liqmd heat capacities are either at constant pressure or at saturated conditions. There is negligible difference between them for most compounds up to a reduced temperature (temperature/critical temperature) of 0.7. Liquid heat capacity increases with increasing temperature, although a minimum occurs near the triple point for many compounds. 

There are a number of reliable estimating techniques for obtaining pure-component hq uid heat capacity as a function of tem )erature, including Ruzicka and Dolmalsld, Tarakad and Danner, " and Lee and Kesler. These methods are somewhat compheated. The relatively single atomic group contribution approach of Chueh and Swanson for liquid heat capacity at 29.3.15 K is presented here ... 

A = rate constant (pre-exponential factor from Arrhenius equation k = A exp (-E /RT), sec (i.e., for a first order reaction) B = reduced activation energy, K C = liquid heat capacity of the product (J/kg K)... 

The heat capacity for liquid Pu02 has been estimated (21) as 96 J mol-l K- assuming no electronic contribution. If an electronic contribution is found by experiment to be present, the liquid heat capacity would be increased. 

For a thermometer to react rapidly to changes in the surrounding temperature, the magnitude of the time constant should be small. This involves a high surface area to liquid mass ratio, a high heat transfer coefficient and a low specific heat capacity for the bulb liquid. With a large time constant, the instrument will respond slowly and may result in a dynamic measurement error. 

Table 8.3. Group contributions for liquid heat capacities at 20°C, kJ/kmol°C (Chueh and Swanson, 1973a, b)...

Equation 9-24 provides a conservative estimate of the required vent area. By considering the case of 20% absolute overpressure, assuming a typical liquid heat capacity of 2510 J/kg K for most organic materials, and assuming a saturated water relationship, we can obtain the following equation13 ... 

Heat Capacity for 20 g. at Constant Pressure (Clusius et al., 12 Dahmlos and Jung, 4) Solid Liquid... 

Thermal Properties of Metallic Solids. In the preceding sections, we saw that thermal conductivities of gases, and to some extent liquids, could be related to viscosity and heat capacity. For a solid material such as an elemental metal, the link between thermal conductivity and viscosity loses its validity, since we do not normally think in terms of solid viscosities. The connection with heat capacity is still there, however. In fact, a theoretical description of thermal conductivity in solids is derived directly from the kinetic gas theory used to develop expressions in Section 4.2.1.2. 

Liquid Heat Capacity — The value is the heat (in Btu) required to raise the temperature of one pound of the liquid one degree Fahrenheit at constant pressure. For example, it requires almost 1 Btu to raise the temperature of 1 pound of water from 68°F to 69°F. The value is useful in calculating the increase in temperature of a liquid when it is heated, as in a fire. The value increases slightly with an increase in temperature. 

Condensation theory is based on thermodynamic equilibrium. More than a century s worth of experiments have yielded thermodynamic data (entropy and enthalpy of formation, plus heat capacity) for elements and compounds. Equations of state describing the stabilities of different compounds under various conditions can be calculated from these data, as briefly described in Box 7.1. Because liquids are not normally stable at the low pressures appropriate for space, the compounds in condensation calculations are generally solid minerals, but liquids can exist at higher pressures (achievable if areas of the nebula with enhanced dust concentrations relative to gas were vaporized). 

Hence, for temperatures very close to the boiling point, we integrate Eq. 4-7 by assuming that Avap//,(T) = AvapH,(Tb) = constant (see Section 4.2). However, in most cases, one would like to estimate the vapor pressure at temperatures (e.g., 25°C) that are well below the boiling point of the compound. Therefore, one has to account for the temperature dependence of Avap// below the boiling point. A first approximation is to assume a linear temperature dependence of Avap/7, over the temperature range considered, that is, to assume a constant heat capacity of vaporization, A Cpi (the difference between the vapor and liquid heat capacities). Thus, if the heat capacity of vaporization, AvapCpi(Tb), at the boiling point is known, Avap/7,(7) can be expressed by (e.g., Atkins, 1998) ... 

In the second edition of this volume, special attention has been paid lo improving the accuracy of the estimation techniques used for liquid heat capacity, vapor and liquid viscosity. and vapor thermal conductivity. Improved methods of extending data on liquid density and thermal conductivity have been used m this edition New experimental data has also been included. Particular attention has been paid to include new data on aqueous solution and pressure effects on physical properties... 

The liquid hear capacities have been determined only up (o room temperature.Constant for ihc Lyman-Danner equations are available lor methyl ucetale and ethyl acetate The me ho. I of Yuan and Sleil was used to determine the liquid heat capacities of hutyl acetate und vinyl nee tate., -lw... 

The liquid heat capacities have been determined at 20 C for acetic anhydride and propionic anhydride J The heat ca polities of ethyl formate and acetic anhydride urc presented using (lie constants to (lie equation presented by Lyman and Danner.37,3 The method uf Yuan and Sieil 0- has been used to determine the heat capacity of Isopropyl acetate. The data for propionic anhydride were extended by the equation heat capacity iime density equals a constant... 

Hough and co-workers 4 have determined the liquid heat capacity of cthykocdruminc from 30X to 70 C Tlic heat capacities of clhylaminc und diethyl amine were calculated by the method of Lyman and Danner u Hie data for iticih ylamme were determined by the method n Yuan and StieJ.r,(0 Data for clhvlcnedumimc were eMended by the equation heat capacity times density equals a constant... 

Liquid heat capacities have been measured tor DMA from 2G C to m°C,m for DMF from 0aC to I50T.1 lor aniline from (PC to 280 C, M13 and for pyridine at room temperature,w The heat capacities of pyridine have been estimated by the method of Yuan and Sticl. MU Other data were extended over u 0-2WPC range by the equation relating heat capacity to density. The error averaged 1 S ... 

The liquid heal capacities have been measured from -I7.VC 10 22o C for styrene. M 3liquid heat capacity uCeyclooctadicne was calculated. and the data for eye lope me nc and cyclohexene were extended by the methofl or Yuan and suel/" 1 ... 

Liquid heat capacity data arc available from the melting point to the boiling point for all four compounds.2 aj3W... 

The method of Lyman and Danner was used to calculate the liquid heat capacities with the aid of a computer,1J Thut method requires the radius of gyration and an association factor for the compound. If the moment of inertia along each axis of the molecule is known, these parameters can be calculated.m... 

Constant volume heat capacities for liquid oiganic compounds were estimated with a four parameter fit (219). A 1.3% average absolute error for 31 selected species was reported. A group contribution method for heat capacities of pure solids and liquids based on elemental composition has also been provided (159). 

In equation 33, the superscript I refers to the use of method I, a T) is the activity of component i in the stoichiometric liquid (si) at the temperature of interest, AHj is the molar enthalpy of fusion of the compound ij, and ACp[ij] is the difference between the molar heat capacities of the stoichiometric liquid and the compound ij. This representation requires values of the Gibbs energy of mixing and heat capacity for the stoichiometric liquid mixture as a function of temperature in a range for which the mixture is not stable and thus generally not observable. When equation 33 is combined with equations 23 and 24 in the limit of the AC binary system, it is termed the fusion equation for the liquidus (107-111). 

Note that regular methanol (or monoethylene glycol) injection is used only with gas-dominated systems. In oil-dominated systems the higher liquid heat capacity allows the system to retain reservoir heat, so that insulation maintains sufficient temperatures to prevent hydrate formation. Thermodynamic inhibitor is normally only injected for planned shutdowns in oil-dominated systems. 

The large effective heat capacity of the liquid-solid slurry absorbent enables relatively small slurry flows to absorb the carbon dioxide heat of condensation with only modest absorber temperature rise. This contrasts with other acid gas removal processes in which solvent flows to the carbon dioxide absorber are considerably larger than flows determined by vapor-liquid equilibrium constraints. Large flows are required to provide sensible heat capacity for the large absorber heat effects. Small slurry absorbent flows permit smaller tower diameters because allowable vapor velocities generally increase with reduced liquid loading (8). 

Estimation methods applicable for liquid heat capacities fall into four general categories theoretical, group contribution, corresponding states, and Watson s thermodynamic cycle. An assumption is made that various groups in a molecule contribute with a value to the total molar heat capacity, which is independent of other groups present. 

Chueh and Swanson (15) have proposed values for different molecular groups to estimate molar liquid heat capacity, Op, at room temperature (T = 293 K). This method is accurate and more general. Errors for the Chueh-Swanson method rarely exceed 2 to 3% ... 

Equation 12-18 gives a conservative estimate of the vent area, and the simple design method represents overpressure (AP) between 1 ()%-30%. For a 20% absolute overpressure, a liquid heat capacity of 2,510 J/kg K for most organics, and considering that a saturated water relationship exists, the vent size area per 1,000 kg of reactants is ... 

By definition, write CP = Cp+CP , where CP is the residual heat capacity for the liquid phase. Also by definition, CP 1 = (dHR,1/dT)P. By assumption (modest pressure levels) ClPg CP. 

---