Ideal stage temperature

In each stage calculation it will necessary to estimate the stage temperatures to determine the K values and liquid and vapour enthalpies. The temperature range from top to bottom of the column will be approximately 120 — 60 = 60°C. An approximate calculation (Example 11.7) has shown that around fourteen ideal stages will be needed so the temperature change from stage to stage can be expected to be around 4 to 5°C. 

Benzene (B) and chlorobenzene (C) are being separated in a distillation column. Vapor and liquid streams, each containing both species, are fed to one of the trays of the column, and liquid and vapor streams are taken off the tray. The tray functions as an ideal stage (see Problem 6.63) the effluent streams are in equilibrium at temperature T and pressure P, with compositions related by Raoult s law. Equation 6.4-1. 

In the following formulation of the Newton-Raphson equations, the independent variables are taken to be the N-stage temperatures 7 and the N-ratios of the total-flow rates Lj/Vj. When the gas and liquid phases form ideal solutions, the procedure described is an exact application of the Newton-Raphson method. 

In final computer calculations, neither constant molal overflow nor temperature-independent iiTfactors are assumed, and plate efficiencies are also introduced, but in preliminary estimates the simplifying assumptions are common. When the activity coefficients are assumed to be temperature independent, group methods are used in which the number of ideal stages in a cascade is the dependent variable. The calculation gives this number without solving for either the plate temperature or the compositions of the interstreams between plates. If a values are temperature dependent, these simple methods are not used and plate-by-plate calculations are necessary. The temperature and liquid composition for plate n 1 are calculated by trial from those already known for plate n, and the calculation proceeds from plate to plate up or down the column. 

Example 203. A countercurrent extraction plant is used to extract acetone A) from its mixture with water by means of methyl isobutyl ketone (MIK) at a temperature of 25°C. The feed consists of 40 percent acetone and 60 percent water. Pure solvent equal in mass to the feed is used as the extracting liquid. How many ideal stages are required to extract 99 percent of the acetone fed What is the extract composition after removal of the solvent ... 

A liquid mixture containing 50 mol% n-heptane (A), 50 mol% n-octane (B), at 303 K, is to be continuously flash-vaporized at a pressure of 1 atm to vaporize 60 mol% of the feed. What will be the composition of the vapor and liquid and the temperature in the separator if it behaves as an ideal stage Calculate the amount of heat to be added per mole of feed. n-Heptane and n-octane form ideal solutions. 

Let us consider now the number of additional ideal stages required in the rectifying section (NR) to achieve the desired distillate concentration xD - 0.001. This portion of the column behaves like a water absorber with very dilute solutions of water in methanol. From the construction in Figure 6.18, the vapor entering the absorber contains 2.3 mol% water (97.7 mol% methanol), while the vapor leaving it contains only 0.1 mol% water. The liquid entering it has a concentration x = xD = 0.001. To calculate the absorption factor for the absorber, we must estimate the slope of the equilibrium curve in the limit as xg tends to zero (mab)- In that portion of the column, the temperature is very close to the normal boiling point of pure methanol then Tab = 337.7 K. From the modified form of Raoult s law,... 

Depending on the Flory parameter x, there is a particular special temperature T = 6 at X = 1/2, which corresponds to an exact cancellation between steric repulsion and van der Waals attraction between monomers, and thus the chains are nearly ideal. This temperature is known as the collapse temperature or theta temperature [15]. Equation (15.10) for the free energy of mixing is an expression that finds wide use in physical chemistry. A quantitative understanding of hydrophobie eollapse is required to understand the initial stage of protein folding, as proteins are often a finite chain consisting of a 50-300 amino acid residue linear chain, which in many aspects resembles a heteropolymer. 

Equation (13-50) is used to calculate, from the previous stage, the (f/d) ratio on each stage in the rectifying section. The assumed temperature and phase-rate-profile assumptions conveniently fix all the A values for ideal solutions. The calculations are started by writing the equation for stage N ... 

The solid-liquid transition temperatures of ionic liquids can (ideally) be below ambient and as low as -100 °C. The most efficient method for measuring the transition temperatures is differential scanning calorimetry (DSC). Other methods that have been used include cold-stage polarizing microscopy, NMR, and X-ray scattering. 

A three-stage compressor is required to compress air from 140 kN/m2 and 283 K to 4000 kN/m2. Calculate fee ideal intermediate pressures, the work required per kilogram of gas, and fee isothermal efficiency of fee process. Assume the compression to be adiabatic and the interstage cooling to cool the air to the initial temperature. Show qualitatively, by means of temperature-entropy diagrams, fee effect of unequal work distribution and imperfect intercooling, on the performance of the compressor. 

Calculate the ideal intermediate pressures and the work required per kilogram of gas. Assume compression to be isentropic and the gas to behave as an ideal gas. Indicate on a temperature-entropy diagram the effect of imperfect imercooling on the work done at each stage. 

STRATEGY We expect a positive entropy change because the thermal disorder in a system increases as the temperature is raised. We use Eq. 2, with the heat capacity at constant volume, Cv = nCV m. Find the amount (in moles) of gas molecules by using the ideal gas law, PV = nRT, and the initial conditions remember to express temperature in kelvins. Because the data are liters and kilopascals, use R expressed in those units. As always, avoid rounding errors by delaying the numerical calculation to the last possible stage. 

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