Specific energy per unit volume

It is important to be able to calculate how much energy is required to generate the same R in different flow fields, in particular in extension and in shear. The specific energy (per unit volume) required to generate the aerial strain R in a passive liquid mixture with viscosity, T), for time t, is given by the following expressions [Erwin, 1991] ... 

To calculate expansion energy, multiply the specific expansion work by the mass of fluid released or else, if energy per unit volume is used, multiply by the volume... 

At all points in a system, the static pressure is always equal to the original static pressure less any velocity head at a specific point in the system and less the friction head required to reach that point. Since both the velocity head and friction head represent energy and energy cannot be destroyed, the sum of the static head, the velocity head, and the friction head at any point in the system must add up to the original static head. This is known as Bernoulli s principal, which states For the horizontal flow of fluids through a tube, the sum of the pressure and the kinetic energy per unit volume of the fluid is constant. This principle governs the relationship of the static and dynamic factors in hydraulic systems. 

As early as 1916 Hildebrand pointed out that the order of solubility of a given solute in a series of solvents is determined by the internal pressures of the solvents. Later Scatchard (1931) introduced the concept of "cohesive energy density" into Hildebrand s theories, identifying this quantity with the cohesive energy per unit volume. Finally Hildebrand (1936) gave a comprehensive treatment of this concept and proposed the square root of the cohesive energy density as a parameter identifying the behaviour of specific solvents. In 1949 he proposed the term solubility parameter and the symbol S. 

The internal energy per unit volume of fiuid is pu, where u is the specific internal energy. Following the methodology in Section 25-2, the left side of the microscopic equation of change for internal energy, with units of energy per volume per time, is... 

C being the specific heat and T the absolute temperature. The corresponding thermal energy per unit volume is ... 

U is the specific internal energy, thus /2pv + pU is the total energy per unit volume as the sum of internal and kinetic energies. Further, q is the heat flux relative to the motion, x is the momentum flux tensor. The enthalpy can be introduced by the relation U = H — pV = H — pjp. 

The specific energy of a cell is expressed in terms of watt-hours (Wh) that can be delivered per unit weight (kg) or unit volume (L) of the cell. The specific energy per unit weight (Wh kg ) is the more frequently used parameter. Its theoretical value can be calculated as follows. 

Modern polymer electrolyte membrane fuel cell stacks are basically intended for high energy densities at the electrodes (up to 0.6 W/cm ). For this reason, and also because of the compact design, the maximum values of the stacks specific power per unit volume and weight are higher for them, than for all other batteries of conventional type. Often, polymer electrolyte membrane fuel cells are used as well for operation at lower energy densities. 

It has been known for a long time that a size effect exists in metal cutting, where the specific energy inCTeases with decrease in deformation size. Backer et al. [1] performed a series of experiments in which the shear energy per unit volume deformed (Ms) was determined as a function of specimen size for a ductile metal (SAE 1112 steel). The deformation processes involved were as follows, listed from top to bottom with increasing size of specimen deformed ... 

To apply the crossover procedure one needs the expression for the Helmholtz energy A. Specifically, we need to decompose the reduced Helmholtz energy per unit volume A = T /P ) (A/VT) into a critical part A A and Ap, and an analytic background in accordance with Eq. (29) ... 

The most important performance indicators for power supplies designed for portable equipment are the specific energy per unit mass (weight), Ym (in J/kg) and/or per unit volume, Yi> (in J/L). Often, miniplants with fuel cells are used in portable equipment as a replacement for lithium-ion batteries, which have specific performance indicators of 150 Wh/kg and 350 Wh/L. 

The first step in an application of the first law is to identify the system. This is conveniently done by drawing a line around the system, which is called the control volume. The quantities Q, W, and AE are then introduced into Eq. (11.5). The change in thermal energy AE) in thermal problems usually involves changes in temperature T) and pressure P). Tables of relative values of specific energy per unit mass (m) in kJ/Kg for different materials such as air, water, steam, refrigerant, etc. are available. These tables also give values of other properties at different combinations ofP and T, such as volume per unit mass. The Bernoulli equation [Eq. (5.15)] is a special application of the first law for applications where there are no losses, no heat transfer, and no work done. 

How can AH be estimated Well, for the formation of regular solutions (those in which the solute and the solvent do not form specific interactions), the change in internal energy per unit volume of solution is given by... 

Here a is the crystal-liquid specific surface free energy, is the molecular volume, and AGj. is the difference between the liquid and crystal phases of the standard Gibbs free energy per unit volume. For small departures from equilibrium this may be expressed as... 

The dependence of the methane conversion and methanol neld on the specific discharge energy per unit volume of feed gas, varied by changing the applied voltage amplitude and the gas flow rate, is shown in Fig. 9.13. 

A number of metrics can be assessed from stress-strain behavior (Dowling 2007). Properties that are often evaluated include the modulus (initial modulus, or secant modulus evaluated to some specific strain), the yield stress, the yield strain, the ultimate strength, and the strain at break, as have been discussed in O Chap. 19. The area under the curve is known as the modulus of toughness, as this area has physical units of energy per unit volume, which are equivalent to force per unit area, the units of stress and modulus. 

Energy density This refers to the nominal battery energy per unit volume or mass. Specific energy density is a characteristic of the battery chemistry and packaging. 

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