Heat capacity dependence

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... 

Figure 4.2. Variation of heat capacity with temperature as calculated from the equations of Frenkel et al. [4]. The differences observed between isotopic species and the way heat capacity depends on molecular size and structure can be described thermodynamically, but they must be explained by the methods of quantum-statistical thermodynamics. The right-hand scale is for H2 and D2 the left-hand scale is for the other compounds.

The heat capacity is the amount of energy required to increase the temperature of a unit mass of material. It is commonly measured using a differential scanning calorimeter (DSC). The heat capacity depends on the resin type, additives such as fillers and blowing agents, degree of crystallinity, and temperature. A temperature scan for the resin will reveal the Tg for amorphous resins and the peak melting temperature and heat of fusion for semicrystalline resins. The heat capacities for LDPE and PS resins are shown in Fig. 4.15. 

Calorimetric measurements are time consuming and very expensive because of the amount of the IL taken to the experiment. The results usually show the same type of interaction as in other experiments as the activity coefficients at the infinite dilution or solubility measurements. Prom calorimetric measurements it can be observed that the molar heat capacities depend linearly on the temperature and increase proportionally to the alkyl chain length of the cation. 

For ideal gases with heat capacities dependent on temperature, the procedure requires the isentropic final temperature to be found by trial from... 

In heat installations with use of hydrides efficiency of their operation (efficiency, quantity of heat (or colds) and heat capacity) depends on amount of the hydrogen participating in reaction. The amount reserved an alloy of hydrogen is characterized by equilibrium R-S-Tdependence which today define empirically. Let s open the specified directions in more details. 

As a check, the low temperature experimental heat capacity values are smoothed by fitting the data with orthogonal polynomials over selected overlapping temperature intervals. This fitting procedure gave an S (298.15 K) identical to that reported by Osborne and Flotow (2 ). The ice calorimetric data of Satoh (7) are not extensive enough to reliably define the entire heat capacity dependence from 350 to 1086 K, however the three data prints at 373 K, 578 K, and 773 K are sufficient to define a reasonable temperature dependence. 

Molar Heat Capacity Depends on the Number of Atoms... 

Very early in the study of the nature of heat it was observed that if two bodies of equal mass but different temperatures are placed in thermal contact, their specific heat capacities depend inversely on the change in temperature each undergoes on reaching its final temperature. Write a mathematical equation in modern notation to express this fact. 

Heat capacities depend on temperature and pressure, or on temperature and volume. For practical use, the temperature dependence of Cp is given in tables in the form of empirical equations of the type... 

Calorimetry of non-reacting systems involves the measurement of heat capacity dependencies on temperature, which enables us to calculate the enthalpies of phase transformations. Based on the prevailing mode of the heat exchange between their individual parts, calorimeters for this purpose can be classified as low-, medium-, and high-temperature calorimeters. In the measurement of thermodynamic parameters of molten electrolytes, mostly the last two types of calorimeters are used. 

In the situation being considered here, the thermodynamic properties such as the heat capacity depend on the stress (just as for a gas the heat capacity depends on the pressure).. 

Specific heat describes the capacity of 1 g of a substance to absorb heat. A related term, heat capacity, depends on how much of the substance is under study. Experience tell us that if we add the same amount of heat (in joules) to two samples of the same substance, one being twice the mass of the other, it is clear that the smaller quantity will have a higher temperature. 

Furnace heating capacity depends on factors such as rate of heat liberation, rate of heat transfer to the load surface, and rate of heat conduction (diffusion) to the coldest point in the load. 

The specific heat capacity of graphite is taken as the constant value Cc = 8.5 J/ (mol K). All the other heat capacities depend on temperature. In order to determine them recourse is had to the information of Sect. 2.1.1.8. Use is made of the facts that the integral of Cp over temperature is the enthalpy and that the relationship... 

Fig. 3.1 (a) Constant pressure heat capacity dependence upon pressure and temperature, (b) Thermal conductivity dependence upon pressure and temperature, (c) Dynamic viscosity dependence upon pressure and temperature. 

The value of the heat capacity depends on the conditions in which the experiment is carried out. The most commonly used heat capacities are ... 

Despite the simplicity of these expressions for the heat capacity of a monatomic ideal gas, expressions for polyatomic molecules such as H2O can become quite complex. Of course HjO is not an ideal gas the question is what is the heat capacity (and other heat capacity-dependent properties) of a gas having molecules with the properties of the H2O molecule, but with no intermolecular forces This is a nontrivial problem in statistical mechanics. For H2O, the results of Wooley (1980) are used. These were fit to an equation by Cooper (1982) which, after some rearranging, was used by Wagner and Pru6 (2002) in their equation of state for H2O (see below). This equation is a summation of simple harmonic oscillator functions, and is... 

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