Cumulative Quantities

Unfortunately (for the sake of simplidtyX as conditions vary within a polymerization reactor, so do the instantaneous quantities. The polymer in the reactor is a mixture of material formed under varying conditions of temperature and concentrations, and therefore must be characterized by cumulative quantities, which are integrated averages of the instantaneous quantities of the material formed up until the reactor is sampled. The cumulative number-average chain 

A good analogy for visualizing the relation between x and x, is the well-stirred, adiabatic bathtub. x, corresponds to the temperature of the water leaving the tap and x to the temperature of the water in the tub. The amount of water that has left the tap corresponds to the amount of polymer formed. As long as the tub is not full, the analogy applies to a batch reactor. If the tub is allowed to fill and overflow, it applies to a continuous stirred-tank reactor as well. 

Had it been necessary to include chain transfer, we would have used (10.35) with [R H] related to M] with (10.37). Similar treatment of (10.65) gives 

It is instructive to compare the results of Example 12 with Eq. 9.6 for step-growth polymerization. There, x increases monotonically with conversion (p), and high conversions are necessary for high chain lengths. This is not true for free-radical addition, where chains formed early in the reaction have fully developed chain lengths. 

Keep in mind also that if samples are removed from the reactor and analyzed for number-average chain length, the quantity determined is x . The cumulative quantity is what characterizes the reactor contents. The only way to measure x would be to sample at a very low conversion, where x ss Xn . 

TABLE 9.1 Comparison of Step-Growth (Chapter 8) and Addition (Chapter 9) Poiymerizations 

Characteristic Step-Growth Polymerization Addition Polymerization 

Typical monomer Bifunctional monomers with two Monomers have a polymerizable 

Reactor contents p=. 5 50% of functional groups X = 0.5 large polymer chains and 

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The committee analyzed several implications relative to domestic resource use. For biomass production, it examined the amount of land that would be required to grow the crops used as feedstocks. For coal-based hydrogen production, it examined the amount of coal that would be used over time. For technologies involving sequestration, it examined the amount of C02 that would be sequestered on a year-by-year basis and the cumulative quantity sequestered. The committee did not try to quantify several other resource use impacts it did not examine the amount of land that would be required for wind farms, production facilities, or distribution infrastructure it did not examine the impacts on water use for steam reforming processes or for biomass production it did not attempt to examine any labor force issues nor did it examine the needs for metals or other materials for fuel cells, electrolyzers, or production facilities, or the number of pipelines, or other infrastructure. 

The PV manufacturing capacity to support the production of H2 to power 250 million FCVs over a thirty-year timeframe, which is approximately 25% of the projected world fleet of light-duty vehicles and light commercial trucks, is presented in Table 11. The H2 to power 250 million FCVs is 0.24 TW of energy, which replaces 0.52 TW of energy consumed by gasoline powered ICE vehicles. This level of H2 production from PV electrolysis plants will require the annual manufacture of 50-GWp of PV. The thirty-year cumulative quantity of installed PV is 1.735-TWp. 

Absolute Humidity—the ratio of mass of vapor (moisture) to mass present in the carrier gas stream. Example 0.02 pounds of water per pound of air. This number can be used to find the relative humidity on the psychrometric charts. It is also useful for cumulative quantities in a stream due to such items as products of combustion (when a gas fired heater is used), and evaporation and ambient quantities. This is necessary for calculating condenser or venting amounts. 

This behaviour is a consequence of the extremely high hydroxyl number of water (OH = 6233.3 mg KOH/g). At higher levels of water, there is a tendency for the hydroxyl number of monomers to increase - it is practically impossible to obtain polyethers with low hydroxyl numbers such as 25-36 mg KOH/g. For higher MW polyethers, the ratio of monomers starter is high and the cumulative quantity of water introduced into the reaction with monomers is high. 

The preferred method of disposal of radioactive krypton isotopes, after being separated from other volatile fission products, is by dumping at sea as the compressed gas, confined in steel cylinders. According to a report by Bryant and Jones the cumulative quantities of Kr and in the environment by the year 2000 are such that these nuclides will pose no significant health problem. 

Fig. 5.41. Continuous activation of adenylate cyclase by successive doublings of the constant cAMP stimuli, (a) The level of extracellular cAMP is increased from 1.193 X10 M up to 10 M by 25 successive doublings each level of stimulation is maintained for 90s, as in the experiments of Devreotes Steck (1979). The time evolution of intracellular cAMP (j3) is represented, as well as that of the cumulated quantity of cAMP synthesized, ft, and the level of stimulation (y). The corresponding scale for extracellular cAMP is indicated, for the value ATr = 10 M. The curves are obtained by integration of eqns (5.16) for the parameter values of fig. 5.38 (Martiel Goldbeter, 1987a). (b) Experimental results of Devreotes Steck (1979) to which the simulations relate. The curve represents the accumulated amount of cAMP synthesized by the cells vertical bars indicate the level of extracellular cAMP. The heavy bar indicates the total duration ( 8 min) of the response to a single, instantaneous 0-10 M step.

Oidiaal number of steam soak (steam cycle) Number of wells treated again Quantity of steam consum for all of the wells treated, tons Specific consumption of steam per well, toas Quantity of water (sleanr condensate) produced, tons Quantity of additional oil produced, tons Cumulative quantity of additio oil produced, tons Steam /oil factor, tonsi tons Relative additional froducdon of oil per ileam soak, %... 

Fig. 1. The mean dry weight per unit ground area in relation to the cumulative quantity of visible radiation intercepted by a Z. mays crop in N.E. Essex, England. The broken line is the expected relationship in the absence of any depression in conversion "efficiency".

The cumulative quantity of RU from the reprocessing of European and Japanese spent fuel by 2000 was around 25,000 Mg. This RU, which is owned by the utilities or reprocessors, is an alternative fuel source to new natural uranium for use in LWR and CANDU reactors. Each country and utility will determine its strategy for RU based on local factors. Theoretically, this 25,000 Mg would provide sufficient fuel for 500 CANDU 6 reactor-years of operation because the initial core load of uranium for a CANDU 6 reactor is 85 Mg, and... 

A cumulable quantity like volume, number, or scattering intensity of a dilute particle system. 

Type of quantity A cumulable quantity, like volume, number, or (ideally) scattering intensity of the particle system, which is used to quantify the frequency (weights) of... 

Figure 5.2 Cumulative quantity of oxygen permeating retort trays made from a co-extrusion with and without calcium chloride drying agent and retorted under different conditions (redrawn from Tsai and Wachtel, 1990, with permission).

At the moment of stabilization of the jet, the pressure in the vessel has decreased from its initial value Pq and is now equal to P. It is possible to deduce the maximum volume of the flammable zone by applying the model of the stationary jet corresponding to the pressure P. This is assuming that the total cumulative quantity of gas discharged into the atmosphere in the time during which the pressure in the vessel has gone from Pq to P is at last equal to the quantity of gas contained in the flammable zone. 

The plastics accumulating in seas have been storing up and breaking down since the post-World War II rise in plastic consumer goods (Ryan et al. 2009). Plastics in the seas are now present in considerable densities, a record of accumulation that is due in many ways to the increasing quantities of plastics, since as Richard Thompson and colleagues (Thompson et al. 2009b 2154) write the production of plastic has increased substantially over the last 60 years, from around [half a] million tons in 1950 to over 260 million tons today . Plastics also collect and sediment over time in cumulative quantities. All plastics ever manufactured since the rise of the Plastic Age are still likely to be present in the enviromnent and oceans in some form, as they will not have completely broken down yet (Lebwohl 2010 Andrady 2003). 

Each term is estimated by the method of trapezoids. Let us call , /) the number of moles involved (consumed or produced) in the reaction since the beginning of the experiment by definition no reaction has been observed before the first sample at time /. The cumulated quantity /7,(/) involved between the observations at time t, and i (beginning of the experiment) is easily calculated by the sum of the increments ... 

An example of calculation of the cumulated quantities is given in the paragraph 6.4 together with the calculation of the atom and energy balances. 

Another way to judge the correctness of the balance is to compute the balance for the elements. For each entity the net consumption rate in the reactor must be equal to the net production rate. For 5 different species containing the element k the balance for that element can be expressed by rates ( ) or by cumulated quantities () as follows [32,33], on rates ... 

When calculated on cumulated quantities, balances and statistical test are recursively calculated for each observation. Thus on obtains the profile of h versus time, which indicates subsets of data for which the hypothesis might be rejected. The first observations usually do not satisfy the statistical test because even low level of noise have a large effect on the h value. A significant result necessitates at least 10 observations. 

Figure 11 Cumulated quantity of glucose (+), oxygen ( ), CO2 ( ) biomass (O) and ethanol (A). The cumulated quantity decreases for substrates, and conversely increases for products. See the change in the slope of the cumulated amount of ethanol. Since the test function is always significantly lower than the threshold value, there is no indication that the data are erroneous [24],...

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