Molar heat capacities

You ll encounter heat capacity in different forms, each of which is useful in different scenarios. Any system has a heat capacity. But how can you best compare heat capacities between chemical systems You use molar heat capacity or specific heat capacity (or just specific heaf). Molar heat capacity is simply the heat capacity of 1 mol of a substance. Specific heat capacity is simply the heat capacity of 1 g of a substance. How do you know whether you re dealing with heat capacity, molar heat capacity, or specific heat capacity Look at the units. 

Heat capacity (molar), entropy (molar) joule per mole kelvin J/(mol K) ... 

By approximation other quantities are additive as well, such as the molar volume, molar heat capacity, molar heat of combustion and formation, molar refraction, etc. 

Heat capacity, molar Heat capacity at constant pressure Heat capacity at constant volume Helmholtz energy Internal energy Isothermal compressibility Joule-Thomson coefficient Pressure, osmotic Pressure coefficient Specific heat capacity Surface tension Temperature Celsius... 

The molar heat capacity (molar thermal capacity), which is the energy required to increase the temperature of 1 mol by 1°C, is 75.4 J mol-1 °C-1 for water. The energy to heat water from 0°C to 25°C therefore is... 

The bare proton has an exceedingly small diameter compared with other cations, and hence has a high polarising ability, and readily forms a bond with an atom possessing a lone pair of electrons. In aqueous solution the proton exists as the H30+ ion. The existence of the H30+ ion in the gas phase has been shown by mass spectrometry [4], and its existence in crystalline nitric acid has been shown by NMR [5], Its existence in aqueous acid solution may be inferred from a comparison of the thermodynamic properties of HC1 and LiCl [6]. The heat of hydration of HC1 is 136 kcal mole"1 greater than that of LiCl, showing that a strong chemical bond is formed between the proton and the solvent, whereas the molar heat capacity, molar volume and activity coefficients are similar,... 

When the experimental or measured value of Cp for a particular liquid is not available, a fair approximation for Cp near room temperature can be obtained by Kopp s Rule, which states that the heat capacity of a liquid is approximately equal to the sum of the atomic heat capacities of its individual atoms. For the purpose of Kopp s Rule, these individual atomic heat capacities (molar basis) are given in Table 8.5. 

Math.-physik. Klasse, Biol. physiol. chem. Abt. 1949, No. 1, 11 pp. Heat capacity, molar volume and A// sublimation H2O, D2O. 

Fundamental properties, such as the van der Waals volume, cohesive energy, heat capacity, molar refraction and molar dielectric polarization, are directly related to some very basic physical factors. Specifically, materials are constructed from assemblies of atoms with certain sizes and electronic structures. These atoms are subject to the laws of quantum mechanics. They interact with each other via electrical forces arising from their electronic structures. The sizes, electronic stmctures and interactions of atoms determine their spatial arrangement. Finally, the interatomic interactions and the resulting spatial arrangements determine the quantity and the modes of absorption of thermal energy. 

Certain physical properties of materials, such as the cohesive energy, molar volume, molecular weight per repeat unit, molar heat capacity, molar enthalpy and molar entropy, are extensive properties. An extensive property depends upon the size of the system. Its value increases in direct proportion to the amount of material present. For example, the molar volume... 

Molar heat capacity, molar entropy joule per (mole kelvin) J/(molK) m kg/ (s K mol)... 

Boiling point Melting point Molar heat capacity Molar heat of vaporization Molar heat of fusion Viscosity... 

Figure A2.5.2. Schematic representation of the behaviour of several thennodynamic fiinctions as a fiinction of temperature T at constant pressure for the one-component substance shown in figure A2.5.1. (The constant-pressure path is shown as a dotted line in figure A2.5.1.) (a) The molar Gibbs free energy Ci, (b) the molar enthalpy n, and (c) the molar heat capacity at constant pressure The fimctions shown are dimensionless...

Figure A2.5.4 shows for this two-component system the same thennodynamic fimctions as in figure A2.5.2, the molar Gibbs free energy (i= + V2P2> the molar enthalpy wand the molar heat capacity C. , again all at...

An exponent a governs the limiting slope of the molar heat capacity, variously y, ( or along a line tln-ongh the critical point,... 

Figure A2.5.26. Molar heat capacity C y of a van der Waals fluid as a fimction of temperature from mean-field theory (dotted line) from crossover theory (frill curve). Reproduced from [29] Kostrowicka Wyczalkowska A, Anisimov M A and Sengers J V 1999 Global crossover equation of state of a van der Waals fluid Fluid Phase Equilibria 158-160 532, figure 4, by pennission of Elsevier Science.

The heat capacity of thiazole was determined by adiabatic calorimetry from 5 to 340 K by Goursot and Westrum (295,296). A glass-type transition occurs between 145 and 175°K. Melting occurs at 239.53°K (-33-62°C) with an enthalpy increment of 2292 cal mole and an entropy increment of 9-57 cal mole °K . Table 1-44 summarizes the variations as a function of temperature of the most important thermodynamic properties of thiazole molar heat capacity Cp, standard entropy S°, and Gibbs function - G°-H" )IT. 

The explanation of the hydrogen atom spectmm and the photoelectric effect, together with other anomalous observations such as the behaviour of the molar heat capacity Q of a solid at temperatures close to 0 K and the frequency distribution of black body radiation, originated with Planck. In 1900 he proposed that the microscopic oscillators, of which a black body is made up, have an oscillation frequency v related to the energy E of the emitted radiation by... 

Fig. 12. Correlatioa of AT. The three lines represeat the best fit of a mathematical expressioa obtaiaed by multidimensional nonlinear regressioa techniques for 99, 95, and 90% recovery the poiats are for 99% recovery. = mean molar heat capacity of Hquid mixture, average over tower AY = VA2 slope of equiHbrium line for solute, to be taken at Hquid feed temperature mg = slope of equilibrium line for solvent.

The properties of calcium chloride and its hydrates are summarized in Table 1. Accurate data are now available for the heats of fusion of the hexahydrate, the incongment fusion of the tetrahydrate, and the molar heat capacities of the hexahydrate, tetrahydrate, and dihydrate (1). These data are important when considering the calcium chloride hydrates as thermal storage media. A reevaluation and extension of the phase relationships of the calcium chloride hydrates, has led to new values for the heats of infinite dilution for the dihydrate, monohydrate, 0.33-hydrate, and pure calcium chloride (1). 

An overview of some basic mathematical techniques for data correlation is to be found herein together with background on several types of physical property correlating techniques and a road map for the use of selected methods. Methods are presented for the correlation of observed experimental data to physical properties such as critical properties, normal boiling point, molar volume, vapor pressure, heats of vaporization and fusion, heat capacity, surface tension, viscosity, thermal conductivity, acentric factor, flammability limits, enthalpy of formation, Gibbs energy, entropy, activity coefficients, Henry s constant, octanol—water partition coefficients, diffusion coefficients, virial coefficients, chemical reactivity, and toxicological parameters. 

Cp = molar heat capacity at 273.15 K, J/kmol K M = molecular weight N = number of atoms in the molecule... 

The ideal-gas-state heat capacity Cf is a function of T but not of T. For a mixture, the heat capacity is simply the molar average X, Xi Cf. Empirical equations giving the temperature dependence of Cf are available for many pure gases, often taking the form... 

B = Bottoms molar rate or subscript for bottoms c = Heat capacity (gas phase), Btu/lb °F CAF = Vapor capacity factor... 

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