Specific-heat ratios

Available data on the thermodynamic and transport properties of carbon dioxide have been reviewed and tables compiled giving specific volume, enthalpy, and entropy values for carbon dioxide at temperatures from 255 K to 1088 K and at pressures from atmospheric to 27,600 kPa (4,000 psia). Diagrams of compressibiHty factor, specific heat at constant pressure, specific heat at constant volume, specific heat ratio, velocity of sound in carbon dioxide, viscosity, and thermal conductivity have also been prepared (5). 

To find the X facdor Xg for a gas of any k value refer to Fig. 6-34. This figure gives values of Xg/X for gases having specific-heat ratios between 1.0 and 1.4. The factor Xg is then the product of Xg X from Fig. 10-66 and the value X from Table 10-13 for desired compression ratio. 

Compression Adiabatic compression results in high temperatures determined by the compression and specific heat ratios, as shown in Eq. (26-46) ... 

Various types of rapid, adiabatic compressions have caused explosions. With propane at an initial temperature of 25°C, To = 432°K (I59°C) for compression and specific heat ratios of 25 and I.I3, respectively. Assume that now air enters a compressor to bring propane into the flammable range at 5 percent by volume. The mixture then will be mostly air with k = 1.47. The same compression ratio of 25 will elevate the final temperature T2 to 834°K (56I°C), i.e., above the published autoignition temperature of 450°C for propane and perhaps high enough to cause an explosion. 

Step 5. Solve for mixture specific heat ratio k , using Equation 2.21 9.59... 

Specific heat Cp can be calculated using specific gas constant R and specific heat ratio k. 

It has played a dual role, one in Equation 2.18 on specific heat ratio and the other as an isentropic exponent in Equation 2.53. In the previous calculation of the speed of sound. Equation 2.32, the k assumes the singular specific heat ratio value, such as at compressor suction conditions. When a non-perfect gas is being compressed from point 1 to point 2, as in the head Equation 2.66, k at 2 will not necessarily be the same as k at 1. Fortunately, in many practical conditions, the k doesn t change very... 

Inlet nozzle size 18 inches Inlet flow 10,000 CFM Inlet pressure 25 psia Inlet temperature 80°F Molecular weight 29 Specific heat ratio 1.35... 

Inlet flow 11,000 CFM Inlet pressure 31 psia Inlet temperature 40°F Molecular weight 31 Specific heat ratio 1.30... 

Gas Specific Heat Ratio K = Cp/C, Critical Flow Pressure Ratio, P,/P,... 

K = Specific heat ratio, at inlet conditions given for some substances in Table 1. Note Published values of K at 15 °C and one atmosphere may be used. If K is unknown, a conservative value of K = 1.001 may be used, in which case the factor C = 315. Note that a correction for non-ideal gases may be necessary. 

C = ASME Unfired Pressure Vessel Code constant for a vapor as described above, C is a function of the specific heat ratio, K. The equation given earlier for determining C is expressed in tabular form in Table 2. 

For gases with specific heat ratios of approximately 1.4, the critical pressure ratio is approximately 0.5. For hydrocarbon service, this means that if the back-pressure on the relief valve is greater than 50% of the set pressure, then the capacity of the valve will be reduced. In other words, if the pressure in the relief piping at the valve outlet is greater than half (he set pressure, then a larger relief valve will be required to handle the same amount of fluid. 

To overcome this problem, they proposed a working-fluid heat-addition model. This model implies that the gas dynamics are not computed on the basis of real values for heat of combustion and specific heat ratio of the combustion products, but on the basis of effective values. Effective values for the heat addition and product specific heat ratios were determined for six different stoichiometric fuel-air mixtures. Using this numerical model, Luckritz (1977) and Strehlow et al. (1979) systematically registered the properties of blast generated by spherical, constant-velocity deflagrations over a large range of flame speeds. 

Pa = absolute downstream pressure (N/m ) y = gas specific heat ratio (Cp/Cv, dimensionless)... 

The compressor manufacturer can control items a-c, e, f, and h however, the control of clearance volume at high compression ratios for gases/vapors with low specific heat ratios is of great concern. Compression efficiency is controlled by the clearance volume, valves, and valve pocket design. A decrease in compression efficiency leads to increased power requirements. ... 

Gases and Vapors Hydrocarbons Reference Symbols i Chemical Formula Mol. Wt. 1r> 1/7 I a Mol. Wt. Critical Conditions Boiling Point (F) 14,7 Psia Specific Volume Cu ft/lb 14.7 Psia 81 60F (Z Facior Accounted For) Latent Heat of Vaporization (Btu/lb 14.7 Psia) Specific heat Constant Pressure (Cp 60F) Specific heat Constant Volume Specific heat ratio K = Cp/Cv... 

Q is the rate of heat release per unit volume Y designates the specific heat ratio Cg is the speed of sound in the ambient medium surrounding the flame. 

It is not possible to obtain exactly identical flow conditions for the configurations explored. The level of velocity fluctuation at the burner outlet also differs in the various cases. This level was adjusted to get an acceptable signal-to-noise ratio. In the results presented here, the specific heat ratio was taken as equal to y= 1.4, the sound speed Cq = 343 m/s corresponds to a room temperature T = 293 K. The air density is taken equal to = 1.205 kg/m. Laminar burning velocities are... 

Bhattacharya and Gedanken [11] have reported a template-free sonochemical route to synthesize hexagonal-shaped ZnO nanocrystals (6.3 1.2 nm) with a combined micro and mesoporous structure (Fig. 8.1) under Ar gas atmosphere. The higher porosity with Ar gas has been attributed to the higher average specific heat ratio of the Ar which leads to higher bubble collapse temperatures. With an intense bubble collapse temperature, more disorder is created in the product due to the incompleteness of the surface structure that led to greater porosity. Importance of gas atmosphere has been noted when the same process was carried out in the presence of air which results in the formation of ZnO without any porosity. 

A gas well contains hydrocarbon gases with an average molecular weight of 24, which can be assumed to be an ideal gas with a specific heat ratio of 1.3. The pressure and temperature at the top of the well are 250 psig and 70°F, respectively. The gas is being produced at a slow rate, so conditions in the well can be considered to be isentropic. 

The specific heat ratio k is approximately 1.4 for diatomic gases (02, N2, etc.) and 1.3 for triatomic and higher gases (NH3, H20, C02, etc.). The corresponding expression for isothermal conditions follows from Eq. (8-17) ... 

In reality, most compressor conditions are neither purely isothermal nor purely isentropic but somewhere in between. This can be accounted for in calculating the compression work by using the isentropic equation [Eq. (8-21)], but replacing the specific heat ratio k by a polytropic constant, y, where 1 < y < k. The value of y is a function of the compressor design as well as the properties of the gas. 

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