Energy rate change with time

The rate is defined as an intensive variable, and the definition is independent of any particular reactant or product species. Because the reaction rate changes with time, we can use the time derivative to express the instantaneous rate of reaction since it is influenced by the composition and temperature (i.e., the energy of the material). Thus,... 

Although racemization appeared to obey first-order kinetics during the early stages of the reaction, the apparent rate changed with time. The rate constants we used for calculation of thermo- namic and linear free-energy parameters were derived from the initial, linear rates. 

Whereas heat capacity is a measure of energy, thermal diffusivity is a measure of the rate at which energy is transmitted through a given plastic. It relates directly to processability. In contrast, metals have values hundreds of times larger than those of plastics. Thermal diffusivity determines plastics rate of change with time. Although this function depends on thermal conductivity, specific heat at constant pressure, and density, all of which vary with temperature, thermal diffusivity is relatively constant. 

The rate constants are determined by fitting the PO concentrations that change with time, as shown in Fig. 1. With the rate constants at different reaction temperatures, the activation energies and the pre-exponential factors are determined by plotting In k against 1 / T. 

The basic principle used to calculate the temperature in a compartment fire is the conservation of mass and energy. Since the energy release rate and the compartment temperature change with time, the application of the conservation laws will lead to a series of differential equations. 

The Monod equation differs from the Michaelis-Menten equation in that it includes as a factor biomass concentration [X], which can change with time. A microbe as it catalyzes a redox reaction harvests some of the energy liberated, which it uses to grow and reproduce, increasing [X], At the same time, some microbes in the population decay or are lost to predation. The time rate of change in biomass... 

The observed decays for E = 0 (and at higher energies) give the rates at which the BPS is changing with time due to proton transfer. The fact that the initial tautomerization is on the femtosecond time scale, when the total vibrational energy is zero, indicates that the proton transfer motion is direct and does not involve the entire vibrational phase space of the pair. The implication is that the motion can be described as localized in the coordinate of N—H N. Furthermore, the two decay components indicate the presence of the intermediate structure, which reflects the two-step motion in the transfer. 

Here Wn is the average energy of the two fine structure levels. The real numerical coefficients a and b, where a2+b2=1, depend on the polarizations used in the excitation scheme, but are constant in time. Thus the relative amounts of d5/2 and d3/2 states do not change with time but simply decay together at the radiative decay rate T. However, the relative amounts of m character oscillate at the fine structure frequency, and this oscillation is manifested in any property which depends upon m, such as the fluorescence polarized in a particular direction, or the field ionization signal due to a particular value of m. This fact becomes more apparent... 

The first term on the left is the rate of change with time of the total intern energy within the control volume, d(mt/)cv/df. Associated with each flowing stream are three forms of energy internal, kinetic on account of its velocity... 

Equilibrium — A system has reached equilibrium when the properties of the system (such as volume, pressure, color, composition, etc.) no longer change with time. For a chemical equilibrium (involving one or more reversible chemical reactions), the forward and reverse directions of each reaction proceed at equal rates and the system has reached a state of minimum -> Gibbs energy. See also -> reversibility. 

Variables in a system that remain constant with time are in a steady-state process, while those that change with time are in an unsteady-state process or in a transient process. At steady state, a system exchanges energy or matter at a constant rate. 

We are also interested in the effects of small applied fields imagine the electron wave packet described above, but now allow a weak, slowly varying potential K(r) to be present. The packet will work against this potential at the rate v dF/dr This energy can only come from the band energy of the electron, througli a change, with time, of the central wave number kg of the packet ... 

Mass and energy balances on the reactor provide the basis for relating the production rate and composition of the products to the chemical-reaction rate. If the operation is not steady, changes with time are also involved. In a single-reaction system one reactant is usually critical because of cost... 

The rate at which the total energy changes with time is determined by the principle of energy conservation for the material volume element, according to which... 

The actual rates of change of property with time in the accelerated tests are not sensibly contrasted to those from natural ageing from simple observation of the curves. This is simply because it is the rate at which the rates of change with time change with temperature (activation energy) that will largely determine predictions made to lower temperatures. 

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