Varying directly

Charles law, also known as Gay-Lussac s law, states that the volume of a given mass of gas varies directly as the absolute temperature if the pressure remains constant, that is. 

This important equation shows that the stationary-state free-radical concentration increases with and varies directly with and inversely with. The concentration of free radicals determines the rate at which polymer forms and the eventual molecular weight of the polymer, since each radical is a growth site. We shall examine these aspects of Eq. (6.23) in the next section. We conclude this section with a numerical example which concerns the stationary-state radical concentration for a typical system. 

Based on dryer cost alone, indirect-heat dryers are more expensive to build and install than direct-heat dryers designed for the same duty. As environmental concerns and resulting restrictions on process emissions increase, however, indirect-heat dryers are more attractive because they employ purge gas only to remove vapor and not to transport heat as well. Dust and vapor recovery systems for indirect-heat dryers are smaller and less cosdy to supply heat for drying, gas throughput in direct-heat dryers is 3—10 kg/kg of water evaporated indirect-heat dryers require only 1—1.5 kg/kg of vapor removed. System costs vary directly with size, so whereas more money may be spent for the dryer, much more is saved in recovery costs. Wet scmbbers ate employed for dust recovery on indirect-heat dryers because dryer exit gas usually is close to saturation. Where dry systems are employed, all external surfaces must be insulated and traced to prevent vapor condensation inside. 

Ideal Gas Behavior, In 1787 it was demonstrated that the volume of a gas varies directly with temperature if the pressure remains constant. Other investigations determined complementary correlating relations from which the perfect or ideal gas law was drawn (1 3). Expressed mathematically, the ideal gas law is... 

Table 7 also indicates that the rate enhancements for a 3- and 5-methyl group vary significantly among 1,2-azoles. The difference between the increments in log units for a 3-and 5-methyl group, which should vary directly with bond fixation in the ground state, is larger for isoxazole (1.4) than for pyrazole (0.7) and for isothiazole (0.2). This indicates that the aromaticity increases in the same order and contributes the first quantitative evidence that the 1,2-azoles follow the same aromaticity order as furan < pyrrole < thiophene. 

When speed varies, (1) capacity varies directly as the speed ratio, (2) pressure varies as the square of the speed ratio, and (3) horsepower varies as the cube of the speed ratio. 

When the density of air or gas varies, horsepower and pressure vary directly as the density, speed and capacity being constant. 

First of all, one needs to choose the local coordinate frame of a molecule and position it in space. Figure 2a shows the global coordinate frame xyz and the local frame x y z bound with the molecule. The origin of the local frame coincides with the first atom. Its three Cartesian coordinates are included in the whole set and are varied directly by integrators and minimizers, like any other independent variable. The angular orientation of the local frame is determined by a quaternion. The principles of application of quaternions in mechanics are beyond this book they are explained in detail in well-known standard texts... 

Slightly lower horsepower since the fan is in cold air. (Horsepower varies directly as the absolute temperature.)... 

Capacity varies directly with impeller diameter and speed. 

Total frequencies of environmental illness are difficult to measure. When causes can be identified, however, scientists observe that frequencies of occurrence of a particular illness vary directly with the severity and extent of exposure. Particularly frequent in the workplace are skin lesions from many different causes and pulmonary diseases related to the inhalation of various dusts, such as coal dust (black lung), cotton dust (brown lung), asbestos fibers (asbestosis), and silica dust (silicosis). Environmental agents can also cause biological effects without overt clinical illness (for example, chromosome damage from irradiation). 

Therefore, the elear filtrate flowrate varies directly with the square root of the drum speed. 

For speed and pressure constant, BHP varies directly with viscosity. 

Power requirements vary directly tvith the impeller height-to-diameier ratio. 

The free air capacity of a valve varies directly as the square root of the absolute standard temperature, expressed as 460°F + 60°F, divided by the square root of the valve absolute inlet temperature in Rankine. 

Heat flows from higher-temperature to lower-temperature objects without any help. It follows that the rate of flow will vary directly with temperature differences, and inversely with any resistances to this flow. A temperature difference is necessary for heat to flow ... 

There are great advantages to an absolute temperature scale that has its zero point at — 273°C. Whereas the zero of temperature in the Centigrade scale is based upon an arbitrary temperature, selected because it is easily measured, the zero point of the absolute scale has inherent significance in the kinetic theory. If we express temperatures on an absolute temperature scale, we find that the volume of a fixed amount of gas (at constant pressure) varies directly with temperature Also, the pressure of a fixed amount of (at constant volume) varies directly with temperature. And, according to the kinetic theory, the kinetic energy of the molecules varies directly with the absolute temperature. For these reasons, in dealing with gas relations, we shall usually express temperature on an absolute temperature scale. 

Similarly, the rate of evaporation of materials depends on the vapor pressure, p, of the volatile constituent, which in turn varies directly as its molar concentration and the temperature ... 

We have seen in these three examples a reaction that is second-order but not bi-molecular, another whose rate varies directly with a species not involved in the stoichiometric process, and a third whose rate is independent of the concentration of one reactant. Not one of these findings could have been predicted from the stoichiometric equation, which can guide one a priori neither to the rate law nor to the mechanism. 

Internal shells are thus seen to screen completely, and the screening effects of penetrated shells are additive. Moreover, it is seen that for properties proportional to different powers of n and Z the total screening defect varies directly with rjt. 

Figure 7 shows the limiting maximum molecular weight of products from a reactor of fixed size varies directly with the frequency factor of the initiator at a fixed activation energy, while the limiting conversion varies inversely with the frequency factor. In addition, the length of the chain-transfer controlled zone is increased inversely with the frequency factor. 

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