Specific heat ideal gas

Table A-1 Molar mass, gas constant, and ideal-gas specific heats of some substances 842...

Edmister (1948) published a generalized plot showing the isothermal pressure correction for real gases as a function of the reduced pressure and temperature. His chart, converted to SI units, is shown as Eigure 3.2. Edmister s chart was based on hydrocarbons but can be used for other materials to give an indication of the likely error if the ideal gas specific heat values are used without corrections. 

The approach is predictive, and the only input data required are the critical parameters, molecular weight, Pitzer s acentric factor and, for thermal conductivity, the ideal gas specific heat. 

This ideal reaction produces the net enthalpy of combustion AH , (T,net) for the burning of one mole of CiHjSk. Measurements of this property are almost always made at 25°C (298.15 K). To convert from 25°C to another temperature requires the ideal gas specific heats (heat capacities) per mole,... 

With few exceptions, thermodynamic property tabulations are calculated from P-V-T meaz.urements and from zero-pressure specific heat values derived from spectroscopic measurements. It should be noted that the zero-pressure (ideal gas) specific heat values, Cp, for the cryogenic fluids are generally known with an uncertainty of less than 3 parts in 10,000 whereas the random deviations of the P-V-T data are of the order of 2 to 5 parts in 1000. The phase boundaries involve a further complication and, consequently, must be defined by additional experimental data. As a minimum requirement, measurements of the vapor pressure are sufficient for the calculation of thermodynamic property differences due to a phase change. This is indicated by the Clapeyron equation, which may be expressed... 

In the first part of this paper general thermodynamic relations are presented for the calculation of thermodynamic properties from functions representing P-F-T and specific heat, velocity of sound, or Joule-Thomson data. In the latter part of the paper the equations for thermodynamic properties are developed in terms of zero-pressure (i.e., ideal gas) specific heats and are applied to a particular equation of state. 

If the relationship between the pressure P, the molar volume v, the absolute temperature T and, additionally, the ideal gas specific heat capacity Cp of a pure substance are known, all thermodynamic properties of this substance can be calculated. The typical PvT behavior is shown in Figure 2.1 in a three-dimensional diagram. All thermodynamically stable states are represented by the surface. Depending on the values of the state variables P, v, T the substance exists as a solid (S), liquid (L), or a vapor phase (V) or as a combination of two or three phases. They can be characterized as follows. 

An ancillary equation is used to evaluate the ideal gas specific heat, C j. The reference entropy of the ideal gas at r" " and p" " is taken from a suitable source for the fluid under investigation. The enthalpy of any state may be calculated from... 

In addition to estimating individual properties, LOADER-2 checks whenever possible that the thermodynamic consistency between properties is maintained. For example, the liquid heat capacity will be compatible with the enthalpy of vaporization and liquid enthalpy. The ideal-gas thermal conductivity will be compatible with the ideal-gas specific heat capacity. By fitting well-behaved representative equations to each property, the program produces a self-contained set of thermophysical property data, which can be used with the main PPDS system. 

The dependence of gas specific heats on temperature was discussed in Chapter 3, Section 3.5. For a gas in the ideal state the specific heat capacity at constant pressure is given by ... 

The recuperated Brayton cycle approaches Carnot efficiency in the ideal limit. As compressor and turbine work are reduced, the average temperatures for heat addition and rejection approach the cycle limit temperature. The limit is reached as compressor and turbine work (and cycle pressure ratio) approach zero and fluid mass flow per unit power output approaches infinity. It can be expected from this that practical recuperated Brayton cycles would operate at relatively low pressure ratios, but be very sensitive to pressure drop. With tire assumption of constant gas specific heat over the cycle temperature range, a good assumption for helium, the cycle efficiency of a recuperated Brayton cycle may be expressed ... 

Deviations from the ideal gas law may be incorporated by multiplying in Equation (5.180) or (5.182) by the compressibility factor, Z, for the gas. The expansion factor Y depends upon the pressure drop X, the dimensions (clearance) in the valve, the gas-specific heat ratio k, and the Reynolds number (the effect of which is often negligible). The expansion factor for a given valve can be represented, to about 2%, by the expression (Hutchison, 1971)... 

Ideally, the specific heat of conduction electrons (or holes) in a metal is a linear function of temperature C = yT, where y, known as the Sommerfeld constant, is in the range 0.001 to 0.01 J/(molK ) for normal materials. In HF compounds, y reaches values up to 10 times larger (see tables 9, 10 and 11). In the basic theory of the specific heat of itinerant electrons (free Fermi gas), y is proportional to the effective mass m of the charge carriers, and so the name heavy fermions has come to be attached to these high-y materials (see Stewart 1984). The linear relation between C and T is strictly fulfilled only in the limit of a free degenerate electron gas. In real materials, weak non-linearities show up that can be encompassed by, for example, allowing y to be temperature dependent, y T). The Sommerfeld constant of interest is then the extrapolation of y for... 

Estimate the ideal gas specific isobaric heat capacity of ethyl acetate (CH3-COO-CH2-CH3) at T = 298.15 K using the joback method. The molar mass of ethyl acetate is M = 88.11 g/mol. 

The thermal properties of an ideal gas, enthalpy, entropy and specific heat, can be estimated using the method published by Rihani and Doraiswamy in 1965 ... 

The specific heat of gases at constant pressure is calculated using the principle of corresponding states. The for a mixture in the gaseous state is equal to the sum of the C g of the ideal gas and a pressure correction term ... 

Hgp = specific enthalpy of the ideal gas Cpgp = specific heat of the ideal gas... 

Agp = conductivity of the ideal gas pgp specific heat of the ideal gas = critical pressure M = molecular weight... 

In an ideal fluid, the stresses are isotropic. There is no strength, so there are no shear stresses the normal stress and lateral stresses are equal and are identical to the pressure. On the other hand, a solid with strength can support shear stresses. However, when the applied stress greatly exceeds the yield stress of a solid, its behavior can be approximated by that of a fluid because the fractional deviations from stress isotropy are small. Under these conditions, the solid is considered to be hydrodynamic. In the absence of rate-dependent behavior such as viscous relaxation or heat conduction, the equation of state of an isotropic fluid or hydrodynamic solid can be expressed in terms of specific internal energy as a function of pressure and specific volume E(P, V). A familiar equation of state is that for an ideal gas... 

This is the state equation of an ideal gas, where p is pressure, v is specific volume, p is density, R is the gas constant, and T is absolute temperature. In an airflow there is a transfer of heat from one layer to another. This change of... 

Figure 15.5 shows the ideal open cycle for the gas turbine that is based on the Brayton Cycle. By assuming that the chemical energy released on combustion is equivalent to a transfer of heat at constant pressure to a working fluid of constant specific heat, this simplified approach allows the actual process to be compared with the ideal, and is represented in Figure 15.5 by a broken line. The processes for compression 1-2 and expansion 3-4 are irreversible adiabatic and differ, as shown from the ideal isentropic processes between the same pressures P and P2 -... 

The work done by an ideal gas of constant specific heat in passing from one isotherm to another is the same for all adiabatic paths, is independent of the initial or final pressures or volumes, and is proportional to the difference of temperature between the isotherms. 

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