Use of heat capacities

Values of A°(T) were obtained by using simulant elements which have the same number of bonding electrons as each intermetallic phase. Second law values of AH (298) were also obtained by use of heat capacities of the same simulant and constituent... 

If either T or 7) happen to be equal to 298.15 K then the Cp m values required will be those tabulated in thermochemical databases. Frame 11 discusses further the use of heat capacity. 

The fact that internal energy and enthalpy are state properties means that any conv enient process path from a reference state to a process state may be chosen, even if the actual process proceeds by a different path. As a rule, you would choose a path that allows ou to make use of heat capacities, phase transition temperatures, and latent heats tabulated in an avtulable reference (like this text). 

It will be observed that Table XXV contains values for the free energy function of graphite this has not been obtained from equation (33.43), which is applicable to gases only. The method for the calculation of — (F — HD/T for solids is based on the use of heat capacities. For a pure solid, since So is zero, by the third law of thermodynamics, equation (23.1) becomes... 

Use of the Wagner equations requires relatively extensive and internally consistent data they may produce unphysical slopes of the vapor-pressure curve if fitted to inconsistent data. Neither the Wagner nor the Antoine equation should be extrapolated far below the temperature range in which it was fitted. Vapor-pressure data at low temperatures (where the vapor pressures are small) are scarce. Often, better estimates of the vapor pressure at low temperatures may be obtained from extrapolation techniques that make use of heat-capacity data, as discussed in The Properties of Gases and Liquids [15]. 

Polyakov VB, Kharlashina NN (1995) The use of heat capacity data to calculate carbon dioxide fractionation between graphite, diamond, and caibon dioxide A new approach. Geochim Cosmochim Acta 59 2561-2572... 

Use of heat capacities. The change in enthalpy at constant pressure due to a change in temperature from To to Tj is given by... 

The remaining question is how we got from G3MP2 (OK) = —117.672791 to G3MP2 Enthalpy = —117.667683. This is not a textbook of classical thermodynamics (see Klotz and Rosenberg, 2000) or statistical themiodynamics (see McQuarrie, 1997 or Maczek, 1998), so we shall use a few equations from these fields opportunistically, without explanation. The definition of heat capacity of an ideal gas... 

The thermal conductivity of soHd iodine between 24.4 and 42.9°C has been found to remain practically constant at 0.004581 J/(cm-s-K) (33). Using the heat capacity data, the standard entropy of soHd iodine at 25°C has been evaluated as 116.81 J/ (mol-K), and that of the gaseous iodine at 25°C as 62.25 J/(mol-K), which compares satisfactorily with the 61.81 value calculated by statistical mechanics (34,35). 

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. 

The heat capacity of a subshince is defined as the quantity of heat required to raise tlie temperature of tliat substance by 1° the specific heat capacity is the heat capacity on a unit mass basis. The term specific heat is frequently used in place of specific heat capacity. This is not strictly correct because traditionally, specific heal luis been defined as tlie ratio of the heat capacity of a substance to the heat capacity of water. However, since the specific heat of water is approxinuitely 1 cal/g-°C or 1 Btiiyib-°F, the term specific heal luis come to imply heat capacity per unit mass. For gases, tlie addition of heat to cause tlie 1° tempcniture rise m iy be accomplished either at constant pressure or at constant volume. Since the mnounts of heat necessary are different for tlie two cases, subscripts are used to identify which heat capacity is being used - Cp for constant pressure or Cv for constant volume. Tliis distinction does not have to be made for liquids and solids since tliere is little difference between tlie two. Values of heat capacity arc available in the literature. ... 

The second term on the right side of the expression for AH accounts for any phase changes that may occur between 25°C and for the final products it should be deleted if not applicable. Using molal heat capacity data C (T) for all the species present, the following equality is solved for by trial and error. 

Method 2. Use mean heat capacity data from Table 2-45 with reference conditions of P = 0 and T = 25°C for the combustion gases. Then the equation for T, becomes... 

Special correlations have also been developed for liquid metals, used in recent years in the nuclear industry with the aim of reducing the volume of fluid in the heat transfer circuits. Such fluids have high thermal conductivities, though in terms of heat capacity per unit volume, liquid sodium, for example, which finds relatively widespread application, has a value of Cpp of only 1275 k.l/ni1 K. 

As explained in Section 6.5, the heat capacity of a substance is the constant of proportionality between the heat supplied to a substance and the temperature rise that results (q = CAT). However, the rise in temperature and therefore the heat capacity depend on the conditions under which the heating takes place because, at constant pressure, some of the heat is used to do expansion work rather than to raise the temperature of the system. We need to refine our definition of heat capacity. 

We can see how the values of heat capacities depend on molecular properties by using the relations in Section 6.7. We start with a simple system, a monatomic ideal gas such as argon. We saw in Section 6.7 that the molar internal energy of a monatomic ideal gas at a temperature T is RT and that the change in molar internal energy when the temperature is changed by AT is A(Jm = jRAT. It follows from Eq. 12a that the molar heat capacity at constant volume is... 

Use the heat capacity of a substance to calculate the heat required to raise its temperature by a given amount (Example 6.3). 

It is always important in thermochemical studies to be aware of the temperature at which the thermochemical properties are determined, and to combine only those properties at the same temperature. Temperature corrections can be made by using integrated heat capacities over the temperature ranges in question. However, it is often assumed that the temperature corrections for ionization energies and electron affinities are small (<1 kJ/mol) and therefore can be neglected. 

The maximum compression ratio (ratio of outlet to inlet pressure) for compressors depends on the design of the machine, the properties of the lubricating oil used in the machine, the ratio of heat capacities of the gas(Cp/Cy = y), other properties of the gas (e.g. tendency to polymerize when heated), and the inlet temperature. The most common types of compressor used for gas compression in the process industries are ... 

The importance of temperature-controlled scanning calorimetry for measurements of heat capacity and of scanning transitiometry for simultaneous caloric and pVT analysis has been demonstrated for polymorphic systems [9]. This approach was used to study an enantiotropic system characterized by multiphase (and hindered) transitions, the role of heat capacity as a means to understand homogeneous nucleation, and the creation of (p, T) phase diagrams. The methodology was shown to possess distinct advantages over the more commonly used combination of characterization techniques. 

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