Second, time unit

Nuclide. Each nuclide is identified by element name and the mass number A, equal to the sum of the numbers of protons Z and neutrons N in the nucleus. The m following the mass number (for example, Zn) indicates a metastable isotope. An asterisk preceding the mass number indicates that the radionuclide occurs in nature. Half-life. The following abbreviations for time units are employed y = years, d = days, h = hours, min = minutes, s = seconds, ms = milliseconds, and ns = nanoseconds. 

Using cm as unit surface and seconds as unit time, n is the number of molecules falling on 1 cm /sec. The number n thus denotes the number of molecules striking each cm of the surface every second, and this number can be calculated using Maxwell s and the Boyle-Gay Lussac equations. The number n is directly related to the speed of the molecules within the system. It is important to realize that the velocity of the molecules is not dependent on the pressure of the gas, but the mean free path is inversely proportional to the pressure. Thus ... 

This interpretation of Fig. 38b leads to the conclusion that better insight into the variations can be obtained by separating the data into two time histories—the first covers time k = 1 to 53, and the second covers time k = 54 to 113 (all time units are in minutes). Incorporating this extended perspective, Fig. 39 provides score plots for two PC models where the score plots are now divided into these two main processing phases. Observe the... 

MATLAB always considers time to be in seconds, but this should not concern us as long as we keep our own time units consistent. 

However, this time when the temperature is increased a failure occurs. Therefore, the next time the temperature is changed it is decreased a/3 (afi = 0.75). The second time the pressure was increased an increase in yield occurred. Therefore, the next time the pressure is changed it will be increased a2 (a2 =2.25). By the time each variable has been changed 4 times (point Ps) every variable has had a success and a failure. Therefore a new set of directions is chosen. The first has the same direction as the vector through points R and P9. The second is perpendicular to that. A unit step is now made in each direction. The new points are easy to find geometrically using a draftsman s compass or a ruler and pencil. With more than two variables the use of a computer greatly facilitates matters. 

The type of operation considered in the zero effluent methodology means that the amount of time points used for an operation has to increase. This is due to the fact that there is a processing step and a cleaning step associated with each batch of product. Normally two time points are used to describe a task in a unit. The first time point is used when the task commences in a unit and the second when the task terminates in a unit. In the type of operation considered in the zero effluent models, three time points are used. At the first time point the raw material processing task commences. The raw material processing step ends at the second time point, where the final product is removed and the cleaning operation commences. At the third time point the cleaning operation comes to an end and wastewater is produced. 

Table 10.2 Test results. The values refer to the points of time at which the first-best solution was found, the total effort to terminate was nearly the same (5 10 nodes). Times are in seconds, initial quantities of S0 are in tons, objective values (mspan) are in time units and the overproduction (op) is measured in tons.

In clinical chemistry the activity of an enzyme should be expressed as units and must be related to the amount of material used as enzyme source. Many authors define the unit of enzyme activity as that amount of enzyme in a given volume or weight unit of material which causes a certain change of absorbance [A log (I0//)] at 340 or 366 mp per time unit under defined, but varying conditions, e.g., A A, = 1.000 or 0.001 per minute at 25°C. In European literature activities are often given as Biicher-Einheiten (B5) where the unit is defined as the amount in 1.00 ml medium causing the change of A, of 0.1 per 100 seconds at 366 mp and 25°C. 

To convert k from SI units to the time unit of choice, just multiply the value of k by the fraction of the time interval occurring during a single second. 

Based on this equation one can predict the temperature increase to be expected for a defined annulus thickness as shown in Fig. 3. With the above-described approach one can in addition construct a monolithic annulus of a desired radius but limited thickness. By preparing a series of annuluses where the outer diameter of the smaller monolith is equal to the inner diameter of a larger one, a large volume monolithic unit can be constructed by forming a so called tube in a tube system, as shown in Fig. 4. In this way, a monolithic unit of the required volume and uniform pore size distribution can be prepared. Furthermore, the voids between the annuluses can be filled with the reaction mixture and polymerization is allowed to proceed for a second time. Since the voids are very thin, no increase in temperature during the course of the reaction is expected. 

Checking to see that the units of all terms in all equations are consistent is perhaps another trivial and obvious step, but one that is often forgotten. It is essential to be particularly careful of the time units of parameters in dynamic models. Any units can be used (seconds, minutes, hours, etc.), but they cannot be mixed. We will use minutes in most of our examples, but it should be remembered that many parameters are commonly on other time bases and need to be converted appropriately, e.g., overall heat transfer coefficients in Btu/h °F ft or velocity in m/s. Dynamic simulation results are frequently in error because the engineer has forgotten a factor of 60 somewhere in the equations. 

The International System of Units (SI) built on seven base units the unit of mass is the kilogram, the unit of time is the second, the unit of length is the meter, the unit of electric current is the ampere, the unit of tempera-... 

Flux Rates We use the term flux to describe the movement of material. Flux rate is then the quantity of material moved por unit time. In the literature we find rates quoted in different time units, sometimes seconds, sometimes minutes, or hours, or days. In particular, flux rates are sometimes presented in pg/cm2-day and sometimes in fg/cm2-sec. We can simplify this a bit by normalizing these to cm2. Thus, Table 1.9 provides a correlation of the rates. 

Multiplying miles per hour times hours or feet per second times seconds results in the distance because the fractions reduce, cancelling out units, as shown here. 

You can write these values with either unit on top or bottom. It depends on what you are starting with and what you want to end up with. Miles per hour and feet per second both have a distance unit on top and a time unit on bottom. Therefore, you should set the start of the problem this way ... 

Additional improvement may be noted if the simulated current-time curve is rendered more exact through the judicious selection of DMA. This may be done by noting that unit relative concentration of A exists in the second volume element at the start of the second time iteration. Therefore, Z(2) as calculated in the simulation will be jLDMA. This may be set equal to L[QC(2) - Qc(l)], as obtained from Equation 20.35 and solved for DMA. Thus... 

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