Calculating the Conversion Factor

Trivial calculations show that the efficiency could be increased if the machine could operate in the nonequilibrium mode. Speaking of the nonequilibrium mode, we mean that either loading or unloading of the device occurs at the machine cycle states preceding the establishment of thermal equilibrium. Optimal condition for machine operation should be realized in the following ways  

In the first case, when the input of energy occurs immediately after loading the system, but unloading is realized only after relaxation of the stretched helix to the state of equilibrium, trivial calculations lead to the following term for the conversion factor  

can be attained with (p- 0, corresponding to a heavy load (fext oo), while 0 in the limit (p- oo. The physical meaning of this result is quite clear the replacement of a very light body (Fgxt 0 (p co) by moving a 

For a heavy load model with the parameters in the intervals eft = 10-100 A, M = 10 -10 in proton units and m 10 -10, formula (3) gives the 

As we noted in the preceding section, in spite of the microscopic dimensions of molecular machines, each macromolecular device is large enough to be considered as a statistical system. Thus, the behavior of any individual molecular machine can be described in terms of statistical thermodynamics. On the other hand, there are certain mechanical features in the behavior of molecular machines. The reader can find a lot of theoretical and experimental data concerning various aspects of the structure and functioning of biopolymers in plenty of excellent monographs, and in original and review- 

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Calculate the conversion factor for changing liter atmosphere to (a) erg, (b) joule, and (c) calorie. Calculate the conversion factor for changing atmosphere to pascal and atmosphere to bar. 

Calculate the conversion factor for changing calorie to (a) cubic meter atmosphere and (b) volt faraday. 

Atomic units (a.u.) are obviously convenient when finding electrical properties by ab initio calculations. The conversion factor to SI units (Coulombs, meters, and joules) is... 

Suppose a 10.00-kg mass drops through a height difference of 3.00 m, and the resulting work is used to turn a paddle in 200.0 g water, initially at 15.00°C. The final water temperature is found to be 15.35°C. Assuming that the work done is used entirely to increase the water temperature, calculate the conversion factor between joules and calories. 

Show that Jbar is a volume term, and calculate the conversion factor from Jbar to cm. See Appendix A. 

Calculating the conversion factor, 1 — [M(]/[Mo], and multiplying it by the maximum length, 312, one then obtains the polymer length 23. For the time points taken from Table 10.3, the results of these calculations are shown in Table 10.4 The length obtained is larger than that using the other two methods shown in Table 10.3. 

Calculating the conversion factor 6, Gray has used the formula 0 = W/(Q + A ), where W is the work done by the system, AE is the energy cost of information, and Q is the net energy input. However, any device working cyclically has to pay the cost of information due to energy inputted, Q, Therefore, the term AE should be involved in the Q value and, thus, the conversion factor must be calculated as 0 = IF/Q. 

Unear Umts. The following procedure is used for converting linear units to the proper number of significant places the maximum and minimum limits in inches are calculated. The corresponding two values are converted exacdy into millimeters by multiplying each by the conversion factor 1 in. = 25.4 mm. The results are rounded in accordance with Table 4. 

Table 0.1 shows such atomic units . The accepted values of the SI constants are themselves subject to minor experimental improvements, so authors generally report (he results of molecular modelling calculations as (e.g.) R = 50aa and give the conversion factor to SI somewhere in their paper, usually as a footnote. 

Fig. 13. Calculated 2H solid echo spectra for log-Gaussian distributions of correlation times of different widths. Note the differences of the line shapes for fully relaxed and partially relaxed spectra. The centre of the distribution of correlation times is given as a normalized exchange rate a0 = 1/3tc. For deuterons in aliphatic C—H bonds the conversion factor is approximately 4.10s sec-1...

If an inhalation study in animals, list the conversion factors used in determining human equivalent dose Calculations 200 ppm X 7/24 hr X 1/30 UF = 1.94 ppm. 

The model is designed to calculate the 241 Am intake that would produce the maximum allowed occupational radiation dose to all major organs, including the bone surfaces, bone marrow, and liver, but the conversion factors for other tissues and organs are published in the same tables. 

It should be noted that a dimensional analysis of this problem results in one more dimensionless group than for the Newtonian fluid, because there is one more fluid rheological property (e.g., m and n for the power law fluid, versus fi for the Newtonian fluid). However, the parameter n is itself dimensionless and thus constitutes the additional dimensionless group, even though it is integrated into the Reynolds number as it has been defined. Note also that because n is an empirical parameter and can take on any value, the units in expressions for power law fluids can be complex. Thus, the calculations are simplified if a scientific system of dimensional units is used (e.g., SI or cgs), which avoids the necessity of introducing the conversion factor gc. In fact, the evaluation of most dimensionless groups is usually simplified by the use of such units. 

The conversion factor varies much less when the mean dose to all epithelial cells is evaluated (Figure 2). This is especially marked for RaC decays which contribute most of the dose. In this case, very similar doses are calculated if the complex depth distributions of Table I are represented by a single epithelial thickness of 50 pm in the bronchi, i.e. generations 1-10, and 15 pm in bronchioles. 

Notice that we do not have to consider each step separately. We can simply use values produced in the course of the calculation as conversion factors. 

For chemical reactions and phase transformations, the energy absorbed or liberated is measured as heat. The principal unit for reporting heat is the calorie, which is defined as the energy needed to raise the temperature of 1 gram of water at l4.5° C by a single degree. The term kilocalorie refers to 1,000 calories. Another unit of energy is the joule (rhymes with school), which is equal to 0.239 calories. Conversely, a calorie is 4.184 joules. The translation of calories to joules, or kilocalories to kilojoules, is so common in chemical calculations that you should memorize the conversion factors. 

The conversion factors you need to do the calculations require a balanced equation, so do the balancing first. 

This works out because the ampere (the standard unit of current, abbreviated A) is defined as 1 coulomb per second. Because this equation gives you the amount of charge that has passed through the circuit during its operating time, all that remains is to calculate the number of moles of electrons that make up that amount of charge. For this, you use the conversion factor 1 mol e = 96,500 C. 

The SI system is based on mutually consistent units assigned to the nine physical quantities listed in Table B. 1. In addition to the SI units for these nine quantities, the table also lists cgs or other commonly encountered units, as well as the conversion factors between the two. In this table the headings at the top of the table indicate how the conversion factors are to be used in going from SI to cgs/common units, whereas the bottom headings indicate the use of these factors for calculations in the reverse direction. 

The calculation may be simplified if the values for and it are included in the conversion factor, 1.389 x I05 kJ mol 1 pm (the reader should confirm this value), which allows direct calculation of the lattice energy using ionic charges and distances in picometers. 

Basis of units listed below is 22.4140 liters at 0°C and 1 atm for the volume of 1 g mole. All other values were calculated from conversion factors. 

The third-order nonlinear properties are specified in different ways by different authors and several systems of units are used. The conversions between different systems are not always obvious, as the numerical values of the conversion factors may depend on the definitions of particular properties. Table I lists some of the more important conversion factors and units. It should be noted that conversion of n2 values to /3) values can be performed using Eq. (4) in SI units. A frequently utilized conversion is that between n2 values in SI units (cm2 W1) and in cgs units (esu), namely n2 = (C]y3))/n2, where Q is approximately 0.039.7 Calculation of y values can be performed using Eq. (3). Reference 7 provides a discussion of the pitfalls that arise when applying conversion procedures between nonlinear properties defined in different ways. 

The results by interpretation 4 were based on the calibration curve of Figure 2. For NMWD sample the low molecular weight peak at the count number larger than 37 was ignored, assuming that the peak resulted from an impurity. For all four interpretations the conversion factor, 17.5 was used to calculate the molecular weights from the chain lengths. 

Then we apply the conversion factor to calculate the moles of Fe atoms produced in the reaction ... 

The balanced chemical equation for a reaction is used to set up the conversion factor from one substance to another and that conversion factor, the mole ratio for the reaction, is applied to the moles given to calculate the moles required. 

Figure 10 Global map of aerosol UV-flux attenuation factor rj= 1-F,er/Fd(air = l-exp -(k/b)AI, estimated from the aerosol index map. The conversion factor k/b= 0.25, was obtained from the clear sky radiative transfer calculations, assuming single layer (dust or smoke) between 2and 4 km and solar zenith angle 30°. The map shows that aersosol absorption can produce very large reduction in UV flux ( 50%) in certain parts of the world (from plate 2 of Krotkov et al. 1998).

To calculate the amount of MTBE that could theoretically be produced from 26.3 g of isobutylene, we first have to find the number of moles of reactant, using molar mass as the conversion factor ... 

For work in the laboratory, it s necessary to weigh reactants rather than just know numbers of moles. Thus, it s necessary to convert between numbers of moles and numbers of grams by using molar mass as the conversion factor. The molar mass of any substance is the amount in grams numerically equal to the substance s molecular or formula mass. Carrying out chemical calculations using these relationships is called stoichiometry. 

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