Temperature interval

Figure 6.14 Shifting the composite curves in temperature allows complete heat recovery within temperature intervals.

It is important to note that shifting the curves vertically does not alter the horizontal overlap between the curves. It therefore does not alter the amount by which the cold composite curve extends beyond the start of the hot composite curve at the hot end of the problem and the amount by which the hot composite curve extends beyond the start of the cold composite curve at the cold end. The shift simply removes the problem of ensuring temperature feasibility within temperature intervals. 

Set up shifted temperature intervals from the stream supply and... 

In each shifted temperature interval, calculate a simple energy balance from... 

First, determine the shifted temperature intervals T from actual supply and target temperatures. Hot streams are shifted down in temperature by and cold streams up by AT J2, as detailed... 

Next, we carry out a heat balance within each shifted temperature interval according to Eq. (6.1). The result is given in Fig. 6.17. Some of the shifted intervals in Fig. 6.17 are seen to have a surplus of heat... 

Now, carry out a heat balance within each shifted temperature interval, as shown in Fig. 6.20. 

Figure 6.20 Temperature-interval heat balances for Example 6.1.

The shaded areas in Fig. 6.24, known as pockets, represent areas of additional process-to-process heat transfer. Remember that the profile of the grand composite curve represents residual heating and cooling demands after recovering heat within the shifted temperature intervals in the problem table algorithm. In these pockets in Fig. 6.24, a local surplus of heat in the process is used at temperature differences in excess of AT ,in to satisfy a local deficit. ... 

Nature of cut (temperature interval, "Q Mercaptan sulfur, % Total sulfur, % % mercaptan sulfur total sulfur... 

Temperature. The kelvin is the SI unit of thermodynamic temperature, and is generally used in scientific calculations. Wide use is made of the degree Celsius (°C) for both temperature and temperature interval. The temperature interval 1°C equals 1 K exacdy. Celsius temperature, t, is related to thermodynamic temperature, T, by the following equation ... 

If V9 and Vi are the volumes at U and ti, respectively, then V9 = t>i(l + CAf), C being the coefficient of cubical expansion and At the temperature interval. Where only a single temperature is stated, C represents the true coefficient of cubical expansion at that temperature. 

The family of short curves in Fig. 29-45 shows the power efficiency of conventional refrigeration systems. The curves for the latter are taken from the Engineering Data Book, Gas Processors Suppliers Association, Tulsa, Oklahoma. The data refer to the evaporator temperature as the point at which refrigeration is removed. If the refrigeration is used to cool a stream over a temperature interval, the efficiency is obviously somewhat less. The short curves in Fig. 29-45 are for several refrigeration-temperature intervals. A comparison of these curves with the expander curve shows that the refrigeration power requirement by expansion compares favorably with mechanical refrigeration below 360° R (—100° F). The expander efficiency is favored by lower temperature at which heat is to be removed. 

However, we have a problem in working out this integral unless we continuously monitor the movements of the car, we will not know just how much heat dQ will be put into the system in each temperature interval of T to T + dT over the range to Tj. The way out of the problem lies in seeing that, because Qextemai = 0 (see Fig. 5.2), there is no change in the entropy of the (system + environment) during the movement of the car. In other words, the increase of system entropy S2 - Si must be balanced by an equal deerease in the entropy of the environment. Since the environment is always at Tq we do not have to integrate, and can just write... 

For example, the rate constant of the collinear reaction H -f- H2 has been calculated in the temperature interval 200-1000 K. The quantum correction factor, i.e., the ratio of the actual rate constant to that given by CLTST, has been found to reach 50 at T = 200 K. However, in the reactions that we regard as low-temperature ones, this factor may be as large as ten orders of magnitude (see introduction). That is why the present state of affairs in QTST, which is well suited for flnding quantum contributions to gas-phase rate constants, does not presently allow one to use it as a numerical tool to study complex low-temperature conversions, at least without further approximations such as the WKB one. ... 

In applying the transition stability eoeffieient for sealing up, the designer requires systematie proeess steps in a pilot plant seale reaetor with a satisfaetory performanee stability over a temperature interval of interest at stable eomponent eoneentrations and other variables that may be used to eontrol the proeess. 

Next, we construct a table of exchangeable heat loads TEHL to determine the heat-exchange loads of the process streams in each temperature interval. The exchangeable load of the uth hot stream (losing sensible heat) which passes through the zth interval is defined as... 

Having determined the individual heating loads and cooling ctq)acities of all process streams for all temperature intervals, one can also obtain the collective loads (capacities) of the hot (cold) process streams. The collective load hot process streams within the zth interval is calculated by summing up the individual loads of the hot process streams that pass through that interval, i.e.. 

As has been mentioned earlier, within each temperature interval, it is ther modynamically as well as technically feasible to transfer beat from a hot process stream to a cold process stream. Moreover, it is feasible to pass heat from a hot process stream in an interval to any cold process stream in a lower interval. Hence, for the zth temperature interval, one can write the following heat-balance equation ... 

Figure 9.10 The temperature interval diagram for the pharmaceutical case study.

Figure 9.14 A heat balance around a temperature interval including utilities.

For the zth temperature interval, one can write the following heat-balance equation (see Fig. 9.14) ... 

The lifetime for GPC columns used under high temperatures is lower than at room temperature. If higher temperatures are necessary, the user should look for special offers of high temperature columns or check which temperature interval is permitted for the selected column type. For a maximum lifetime a few precautions are advantageous ... 

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