Energy balances work term

Work. Work (W) is a term that has wide usage in everyday life (such as I am going to work ), but has a specialized meaning in connection with energy balances. Work is a form of energy that represents a transfer between the system and surroundings. Work cannot be stored. For a mechanical force... 

It is convenient to write an energy balance in terms of this loss, F, which is the sum of all frictional losses per unit mass. For the case of steady-state flow, when a unit mass of fluid passes from inlet to outlet, the batch work done by the fluid, W, is expressed as... 

The viscous or frictional loss term in the mechanical energy balance for most cases is obtained experimentally. For many common fittings found in piping systems, such as expansions, contrac tions, elbows and valves, data are available to estimate the losses. Substitution into the energy balance then allows calculation of pressure drop. A common error is to assume that pressure drop and frictional losses are equivalent. Equation (6-16) shows that in addition to fric tional losses, other factors such as shaft work and velocity or elevation change influence pressure drop. 

Finally, the energy available from the above reaction might be used to operate a fuel cell such as those involved in the space program. In that case, as much as 818 kj/mol of useful electrical work could be obtained relatively litde heat is evolved. Summarizing this discussion in terms of an energy balance (per mole of methane reacting) ... 

Electrical, and the mechanical forms of energy, are included in the work term in an energy balance. Electrical energy will only be significant in energy balances on electrochemical processes. 

The work term in an energy balance is unlikely to be significant unless a gas is expanded or compressed as part of the process. To compute the pressure work term ... 

There are a variety of limiting forms of equation 8.0.3 that are appropriate for use with different types of reactors and different modes of operation. For stirred tanks the reactor contents are uniform in temperature and composition throughout, and it is possible to write the energy balance over the entire reactor. In the case of a batch reactor, only the first two terms need be retained. For continuous flow systems operating at steady state, the accumulation term disappears. For adiabatic operation in the absence of shaft work effects the energy transfer term is omitted. For the case of semibatch operation it may be necessary to retain all four terms. For tubular flow reactors neither the composition nor the temperature need be independent of position, and the energy balance must be written on a differential element of reactor volume. The resultant differential equation must then be solved in conjunction with the differential equation describing the material balance on the differential element. 

For reactions involving heat effects, the total and component material balance equations must be coupled with a reactor energy balance equation. Neglecting work done by the system on the surroundings, the energy balance is expressed by where each term has units of kj/s. For steady-state operation the accumulation... 

Equation 1.13 is simply an energy balance written for convenience in terms of length, ie heads. The various forms of the energy balance, equations 1.10 to 1.13, are often called Bernoulli s equation but some people reserve this name for the case where the right hand side is zero, ie when there is no friction and no pump, and call the forms of the equation including the work terms the extended or engineering Bernoulli equation. 

It is found convenient to base compressible flow calculations on an energy balance per unit mass of fluid and to work in terms of the fluid s specific volume V rather than the density p. The specific volume is the volume per unit mass of fluid and is simply the reciprocal of the density ... 

In this work, the goal is to design a control function in such a manner that neither the reaction heat nor kinetic nor mass transfer terms are required for stabilizing temperature. The scheme provides an estimated value of the heat generation from energy balance. Alkylation isobutane/propylene using sulfuric... 

This is the equation of energy balance, which states that the internal energy of a fluid changes because of the flow of energy into it, because of the pressure-volume work done on the surroundings by the fluid element, and because of loss of energy by viscous dissipation.6 The energy-balance equation may be written in an alternate form in terms of the temperature ... 

When elevation head and work transfer are neglected, the mechanical energy balance equation (6.13) with the friction term of Eq. (6.18) become... 

Next, Cornelissen extended the LCA study to include the effect of depletion of natural resources making use of ELCA, the exergetic life cycle assessment. In this analysis a full mass and energy balance was made, that is, a first law analysis. Exergy values for all mass and energy streams were included in accordance with the Tables 6.1, 6.2, 6.3, 7.1, 7.2, 7.3 and 7.4 in Chapters 6 and 7. This analysis clearly showed where work was available in inputs and outputs and where it was lost. He could show that the cup scored less favorable than the mug in terms of depletion of natural resources (817 MJ vs. 442 MJ). 

Since the process is one of steady flow for which the shaft work and kinetic- and potential-energy terms in the energy balance [Eq. (2.10)] are zero or negligible, AH - Q. Thus, Q - -5,368.64 kJ, and this amount of heat is transferred to the boiler for every 100 mol dry flue gases formed. This represents... 

The differences between the two forms of energy, heat and work, provide some insight into the second law. In an energy balance, both work and heat are included as simple additive terms, implying that one unit of heat, a joule, is equivalent to the same unit of work. Although this is true with respect to an energy balance, experience teaches that there is a difference in quality between heat and work. This experience is summarized by the following facts. 

In the energy balance the accumulation term is zero because the internal energy of an ideal gas depends only on the temperature, and the temperature is constant. The energy transport terms involve heat and work... 

Solid Energy Balance. The solid-phase energy balance is composed of terms related to thermal communication with the walls of neighboring unit cells, with the two gas-phase compartments of unit cell (k, ), and of the electrical work produced. For clarity, we have elected to show these terms in detail. 

The second term in the mechanical-energy balance. Equation 5.1, is the change in potential energy and requires no comment. The third term is "pressme work" and its evaluation depends on whether the fluid is compressible or incompressible. Because the increase in pressure across the fan is small, we treat the flow as essentially incompressible. Thus, the fluid density may be removed from the integral sign and the mechanical energy balance becomes... 

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