Heat Capacities of Gases in the Ideal Gas State

For ideal gases, Cp is independent of pressure for real gases at modest pressures it is almost independent of 

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Table C.l Heat Capacities of Gases in the Ideal-Gas State Table C.2 Heat Capacities of Solids Table C.3 Heat Capacities of Liquids...

Table B3 Heat capacities of gases in the ideal-gas state C),/R = a + hT + cT + dT T K) from 298 to ...

The specific heat capacity of an ideal gas is defined as the heat per amount of substance in the ideal gas state necessary to obtain a certain temperature change. It must be distinguished between the specific isobaric heat capacity c p (at constant pressure) and the specific isochoric heat capacity c[f (at constant volume). For ideal gases, both quantities are related [52] via... 

Hea.t Ca.pa.cities. The heat capacities of real gases are functions of temperature and pressure, and this functionaHty must be known to calculate other thermodynamic properties such as internal energy and enthalpy. The heat capacity in the ideal-gas state is different for each gas. Constant pressure heat capacities, (U, for the ideal-gas state are independent of pressure and depend only on temperature. An accurate temperature correlation is often an empirical equation of the form ... 

Property values in the standard state are denoted by the degree symbol (°). For example, C°P is the standard-state heat capacity. Since the standard state for gases is the ideal-gas state, C% for gases is identical with Cj , and the data of Table 4.1 apply to the standard state for gases. All conditions for a standard state are fixed except temperature, which is always the temperature of the system. Standard-state properties are therefore functions of temperature only. 

As shown in Chap. 6, for gases it is die ideal-gas heat capacity, rather than the actual heat capacity, that is used in the evaluation of such diennodynamic properties as the enthalpy. The reason is that thermodynamic-property evaluation is most conveniently accomplished in two steps first, calculation of values for a hypodietical ideal-gas state wherein ideal-gas heat capacities are used second, correction of die ideal-gas-state values to the real- s values. A real gas becomes ideal in the limit as P —> 0 if it were to remain ideal when compressed to finite pressures, its state would remain diat of an ideal gas. Gases in their ideal-gas states have properties that reflect their individuality just as do real gases. Ideal-gas heat capacities (designated by C p and Cy ) are therefore different for different gases although functions of temperature,they are independentof pressure. 

Gas mixtures of constant composition may be treated in exactly the same way as pure gases. An ideal gas, by definition, is a gas whose molecules liave no influence on one another. Tills means that each gas in a mixture exists independent of the others its properties are unaffected by the presence of different molecules. Thus one calculates the ideal-gas heat capacity of a gas mixture as the mole-fraction-weightedsum of the heat capacities of the individual species. Consider 1 mol of gas mixture consisting of species A, B, and C, and let yA,jB, and yc represent the mole fractions of these species. The molar heat capacity of the mixture in the ideal-gas state is ... 

A rigid insulated tank is divided into two parts, one that contains 50 mol of ethylene at 400 K, 1 bar, and the other contains 150 mol nitrogen at 300 K, 2 bar. The partition that divides the tank is removed and the contents are allowed to reach equilibrium. Determine the final pressure and temperature in the tank and determine the entropy generation. You may assume the pure gases and the final mixture to be in the ideal-gas state. The ideal-gas heat capacities of ethylene and nitrogen are 43 J/mol K and 29 J/mol K, respectively, and may be assumed independent of temperature. 

The Molar Heat Capacities of Gases the Ideal Gas (Zero-Pressure) State in ... 

Values of heat capacity for gases are almost always reported for the ideal gas state. Thus, when doing calculations using these data, you must choose a hypothetical path where the change in temperature occurs when the gas behaves ideally. 

We define the standard state of a real gas so that Eq. (51) is general (i.e., so that it also applies to ideal gases). For ideal gases, the standard state is at 1.0 bar pressure. For real gases, we also use a 1.0-bar ideal gas as the standard state. We find the standard state by the two-step process shown in Fig. 6. First we extrapolate the real gas to very low pressure, where / —> P and the gas becomes ideal (Step I). We then convert the ideal gas to 1.0 bar (step II). The convenience of an ideal gas standard state is that it allows temperature conversions to be made with ideal gas heat capacities (which are pressure independent). Conversion to the real gas state is then made at the temperature of interest. 

The specific heat capacity of an ideal gas is the basic quantity for the enthalpy calculation, as it is independent from molecular interactions. It is also possible to define a real gas heat capacity, but for process calculations it is more convenient to account for the real gas effects with the enthalpy description of the equation of state used (see Section 6.2). In process calculations, the specific heat capacity of ideal gases mainly determines the duty of gas heat exchangers, and it has an influence on the heat transfer coefficient as well. 

At a total pressure of 1 bar, the equilibrium concentrations of N2O4 in the gas phase were reported to be 0.6349 (30 C), 0.4088 (50 X), 0.2113 (70 X), and 0.09321 (90 C). Calculate the difference between the heat capacity of the mixture and a mixture of ideal gases between 20 ""C and 100 C. Assume that only the chemical reaction contributes to the non-ideal behavior. Calculate the equilibrium of water formation from the elements in their most stable state for a stoichiometric feed of oxygen and hydrogen at P = 0.01 Pa and T = 2000 K using the data from Appendix A and assuming ideal gas phase behavior ... 

Example 4.1 illustrates this kind of calculation and compares the result with that obtained by taking the steam to behave as an ideal gas. For nonideal gases with known PVT equations of state and low pressure heat capacities, the method of calculation is the same as for compressors which is described in that section of the book. 

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