Heat capacities, ratio

R distillation column reflux ratio (-) or heat capacity ratio of 1-2 shell-and-tube heat exchanger (-)... 

Figure 1. Approximate heat-capacity ratios of hydrocarbon gases.

LMTD = log mean temperature difference, °F M = mass flow rate, Ib/hr Ntu = number of heat transfer units, dimensionless N = number tubes/row in direction of air flow n = number tubes/row, per ft of exchanger width, 1 /ft Q = total exchanger heat load (duty), Btu/hr R = = heat capacity ratio, dimensionless... 

Table 13.8 Heat capacity ratio for various gases.

The polytropic coefficient can be estimated from the heat capacity ratio and an estimate of the polytropic efficiency from the relationship (see Appendix B) ... 

The values of the heat capacity ratio y can be obtained from physical property data at average conditions. 

Equation B.27 relates the isen tropic compression efficiency, heat capacity ratio y and polytropic coefficient n to the inlet and outlet pressures and can be rearranged to give ... 

An interesting feature of Equation 4-49 is that for ideal gases the choked pressure is a function only of the heat capacity ratio y. Thus ... 

Table 4-3 Heat Capacity Ratios y for Selected Gases1...

Gas Chemical formula or symbol Approximate molecular weight (M) Heat capacity ratio 7 = CpICy... 

Values for the heat capacity ratio y for a variety of gases are provided in Table 4-3. 

The gas expansion factor Yg in Equation 4-68 depends only on the heat capacity ratio of the gas y and the frictional elements in the flow path 2 K. An equation for the gas expansion factor for choked flow is obtained by equating Equation 4-68 to Equation 4-66 and solving for Yg. The result is... 

The calculation to determine the expansion factor can be completed once y and the frictional loss terms 2 Kf are specified. This computation can be done once and for all with the results shown in Figures 4-13 and 4-14. As shown in Figure 4-13, the pressure ratio ( f - P2)/Pi is a weak function of the heat capacity ratio y. The expansion factor Yg has little dependence on y, with the value of Yg varying by less than 1 % from the value at y = 1.4 over the range from y = 1.2 to y = 1.67. Figure 4-14 shows the expansion factor for y = 1.4. 

Figure 4-13 Sonic pressure drop for adiabatic pipe flow for various heat capacity ratios. From AICHE/CCPS, Guidelines for Consequence Analysis of Chemical Releases (New York American Institute of Chemical Engineers, 1999).

P is the absolute upstream pressure, y is the heat capacity ratio for the gas, gc is the gravitational constant,... 

Ps is the final peak pressure during the vent, and y is the heat capacity ratio. 

The reactor system in a pilot plant contains stock tanks that are 24 in in diameter and 36 in high. A relief system must be designed to protect the vessel in the event of fire exposure. The vessel contains a flammable polymer material. What rupture disc diameter is required to relieve the vessel properly Assume a discharge pressure of 10 psig. The molecular weight of the liquid is 162.2, its boiling point is 673°R, the heat of vaporization is 92.4 Btu/lb, and the heat capacity ratio of the vapor is 1.30. 

A relief device must be installed on a vessel to protect against an operational upset. The relief must discharge 53,500 lb/hr of hydrocarbon vapor. The relief temperature is 167°F, and the set pressure is 75 psig. Assume an overpressure of 10% and a backpressure of 0 psig. The hydrocarbon vapor has a molecular weight of 65, a compressibility of 0.84, and a heat capacity ratio of 1.09. Determine the diameter of the relief. 

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