**Introduction to Thermal Systems...echanics, and Heat...**

Livro: Introducao à Engenharia de Sistemas Térmicos (Inglês)

(Parte **1** de 6)

USING ENERGY AND THE FIRST LAW OF THERMODYNAMICS3

Introduction…

Energy is a fundamental concept of thermodlynamics and one of the most significant aspects of engineering analysis. In this chapter we discuss energy anddevelop equations for applying the principle of conservation of energy. The current presentation is limited to closed systems. In Chap. 5 the discussion is extended to control volumes.

Energy is a familiar notion,and you already know a great deal about it. In the present chapter several important aspects of the energy concept are developed. Some of these we have encountered in Chap. 1. A basic idea is that energy can bestoredwithin systems in various forms. Energy also can be convertedfrom one form to another and transferredbetween systems. For closed systems,energy can be transferred by workand heat transfer.The total amount of energy is conserved in all transformations and transfers.

The objectiveof this chapter is to organize these ideas about energy into forms suitable for engineering analysis. The presentation begins with a review of energy concepts from mechanics. The thermodynamic concept of energy is then introduced as an extension of the concept of energy in mechanics.

Reviewing Mechanical Concepts of Energy

Building on the contributions of Galileo and others,Newton formulated a general description of the motions of objects under the influence of applied forces. Newton’s laws of motion, which provide the basis for classical mechanics,led to the concepts of work,kinetic energy, and potential energy,and these led eventually to a broadened concept of energy. In the present section,we review mechanical concepts of energy.

3.1.1Kinetic and Potential Energy

Consider a body of mass mthat moves from a position where the magnitude of its ve- locity is V1and its elevation is z1to another where its velocity is V2and elevation is z2, each relative to a specified coordinate frame such as the surface of the earth. The quan- tity 1⁄2mV2is the kinetic energy,KE,of the body. The changein kinetic energy, ,of the body is

Kinetic energy can be assigned a value knowing only the mass of the body and the magnitude of its instantaneous velocity relative to a specified coordinate frame,without regard

3.1 chapter objective kinetic energy for how this velocity was attained. Hence,kinetic energy is a propertyof the body. Since kinetic energy is associated with the body as a whole,it is an extensiveproperty.

The quantity mgzis the gravitational potential energy,PE. The changein gravitational potential energy, PE, is

Potential energy is associated with the force of gravity (Sec. 2.3) and is therefore an attribute of a system consisting of the body and the earth together. However,evaluating the force of gravity as mgenables the gravitational potential energy to be determined for a specified value of gknowing only the mass of the body and its elevation. With this view,potential energy is regarded as an extensive propertyof the body.

To assign a value to the kinetic energy or the potential energy of a system,it is necessary to assume a datum and specify a value for the quantity at the datum. Values of kinetic and potential energy are then determined relative to this arbitrary choice of datum and reference value. However,since only changesin kinetic and potential energy between two states are required,these arbitrary reference specifications cancel.

Units.In SI,the energy unit is the newton-meter,Nm,called the joule,J. In this book it is convenient to use the kilojoule,kJ. Other commonly used units for energy are the footpound force,and the British thermal unit,Btu.

When a system undergoes a process where there are changes in kinetic and potential energy,special care is required to obtain a consistent set of units.

For Example…to illustrate the proper use of units in the calculation of such terms,consider a system having a mass of 1 kg whose velocity increases from 15 m/s to 30 m/s while its elevation decreases by 10 m at a location where g 9.7 m/s2. Then

For a system having a mass of 1 lb whose velocity increases from 50 ft/s to 100 ft/s while its elevation decreases by 40 ft at a location where g 32.0 ft/s2,we have

In mechanics,when a body moving along a path is acted on by a resultant force that may vary in magnitude from position to position along the path,the work of the force is written as the scalar product (dot product) of the force vector Fand the displacement vector of the

0.05 Btu

778 ft#lbf

0.15 Btu

2 1 lb2ca100 b2d1 lbf

0.10 kJ

1 kg2 a9.7 m

2 1 kg2ca30 ms b2 a15 ms b2d1 N ft # lbf, # gravitational potential energy body along the path ds. That is (3.3)

When the resultant force causes the elevation to be increased,the body to be accelerated,or both,the work done by the force can be considered a transferof energy tothe body,where it is storedas gravitational potential energy and/or kinetic energy. The notion thatenergy is conserved underlies this interpretation.

3.1.3 Closure

The presentation thus far has centered on systems for which applied forces affect only their overall velocity and position. However,systems of engineering interest normally interact with their surroundings in more complicated ways,with changes in other properties as well. To analyze such systems,the concepts of kinetic and potential energy alone do not suffice,nor does the rudimentary conservation of energy principle introduced above. In thermodynamics the concept of energyis broadened to account for other observed changes,and the principle of conservation of energyis extended to include other ways in which systems interact with their surroundings. The basis for such generalizations is experimental evidence. These extensions of the concept of energy are developed in the remainder of the chapter,beginning in the next section with a fuller discussion of work.

Broadening Our Understanding of Work

The work done by,or on,a system evaluated in terms of forces and displacements is given by Eq. 3.3. This relationship is important in thermodynamics,and is used later in the present section. It is also used in Sec. 3.3 to evaluate the work done in the compression or expansion of a gas (or liquid). However,thermodynamics also deals with phenomena not included within the scope of mechanics,so it is necessary to adopt a broader interpretation of work,as follows.

A particular interaction is categorized as a work interaction if it satisfies the following criterion,which can be considered thethermodynamic definition of work:Work is done by a system on its surroundings if the sole effect on everything external to the system could have been the raising of a weight.Notice that the raising of a weight is,in effect,a force acting through a distance,so the concept of work in thermodynamics is an extension of the concept of work in mechanics. However,the test of whether a work interaction has taken place is not that the elevation of a weight has actually taken place,or that a force has actually acted through a distance,but that the sole effect could have beenan increase in the elevation of a weight.

For Example…consider Fig. 3.1showing two systems labeled A and B. In system A,a gas is stirred by a paddle wheel:the paddle wheel does work on the gas. In principle,the work could be evaluated in terms of the forces and motions at the boundary between the paddle wheel and the gas. Such an evaluation of work is consistent with Eq. 3.3,where work is the product of force and displacement. By contrast,consider system B,which includes only the battery. At the boundary of system B,forces and motions are not evident. Rather,there is an electric current idriven by an electrical potential difference existing across the terminals a and b. That this type of interaction at the boundary can be classified as work follows from the thermodynamic definition of work given previously:We can imagine the current is supplied to a hypotheticalelectric motor that lifts a weight in the surroundings.

Work is a means for transferring energy. Accordingly,the term work does not refer to what is being transferred between systems or to what is stored within systems. Energy is transferred and stored when work is done.

conservation of energy thermodynamic definition of work

3.2.1Sign Convention and Notation

Engineering thermodynamics is frequently concerned with devices such as internal combustion engines and turbines whose purpose is to do work. Hence,it is often convenient to consider such work as positive. That is,

W 0:work done bythe system W 0:work done onthe system

This sign conventionis used throughout the book. In certain instances,however,it is convenient to regard the work done onthe system to be positive. To reduce the possibility of misunderstanding in any such case,the direction of energy transfer is shown by an arrow on a sketch of the system,and work is regarded as positive in the direction of the arrow.

Returning briefly to Eq. 3.3,to evaluate the integral it is necessary to know how the force varies with the displacement. This brings out an important idea about work:The value of W dependson the details of the interactions taking place between the system and surroundings during a process and not just the initial and final states of the system. It follows that work is not a propertyof the system or the surroundings. In addition,the limits on the integral of Eq. 3.3mean “from state 1 to state 2”and cannot be interpreted as the valuesof work at these states. The notion of work at a state has no meaning,so the value of this integral should never be indicated as W2 W1. The differential of work, W,is said to be inexactbecause,in general,the following integral cannot be evaluated without specifying the details of the process

On the other hand,the differential of a property is said to be exactbecause the change in a property between two particular states depends in no way on the details of the process linking the two states. For example,the change in volume between two states can be determined by integrating the differential dV,without regard for the details of the process,as follows

where V1is the volume atstate 1 and V2is the volume atstate 2. The differential of every property is exact. Exact differentials are written,as above,using the symbol d.To stress the difference between exact and inexact differentials,the differential of work is writtenas W. The symbol is also used to identify other inexact differentials encountered later.

sign convention for work work is not a property

Gas PaddlewheelSystem A

System B

Battery ab i

Figure 3.1Two examples of work.

3.2.2 Power

Many thermodynamic analyses are concerned with the time rate at which energy transfer occurs. The rate of energy transfer by work is called powerand is denoted by When a work interaction involves an observable force,the rate of energy transfer by work is equal to the product of the force and the velocity at the point of application of the force

A dot appearing over a symbol,as in is used to indicate a time rate. In principle,Eq. 3.4 can be integrated from time t1to time t2to get the total work done during the time interval

The same sign convention applies for as for W.Since power is a time rate of doing work, it can be expressed in terms of any units for energy and time. In SI,the unit for power is J/s, called the watt. In this book the kilowatt,kW,is generally used. Other commonly used units for power are Btu/h,and horsepower,hp.

For Example…to illustrate the use of Eq. 3.4,let us evaluate the power required for a bicyclist traveling at 20 miles per hour to overcome the drag force imposed by the surrounding air. This aerodynamic dragforce,discussed in Sec. 14.9,is given by where CDis a constant called the drag coefficient,A is the frontal area of the bicycle and rider,and is the air density. By Eq. 3.4the required power is or

Using typical values:CD 0.8,A 3.9 ft2,and 0.075 lb/ft3together with V 20 mi/h 29.3 ft/s,and also converting units to horsepower,the power required is

Power Transmitted by a Shaft.A rotating shaft is a commonly encountered machine element. Consider a shaft rotating with angular velocity and exerting a torque ton its surround- ings. Let the torque be expressed in terms of a tangential force Ftand radius R:t FtR. The velocity at the point of application of the force is V R ,where is in radians per unit time. Using these relations with Eq. 3.4,we obtain an expression for the powertransmitted from the shaft to the surroundings

A related case involving a gas stirred by a paddle wheel is considered in the discussion of Fig. 3.1.

Electric Power.Shown in Fig. 3.1is a system consisting of a battery connected to an external circuit through which an electric current,i,is flowing. The current is driven by the electrical potential difference eexisting across the terminals labeled a and b. That this type of interaction can be classed as work is considered in the discussion of Fig. 3.1.

0.183 hp ft3b a29.3 fts ft # lbf/s,

Motor Wshaft power

The rate of energy transfer by work,or the power,is (3.6)

The minus sign is required to be in accord with our previously stated sign convention for power. When the power is evaluated in terms of the watt,and the unit of current is the ampere (an SI base unit),the unit of electric potential is the volt,defined as 1 watt per ampere.

Modeling Expansion or Compression Work

Let us evaluate the work done by the closed system shown in Fig. 3.2consisting of a gas (or liquid) contained in a piston-cylinder assembly as the gas expands. During the process the gas pressure exerts a normal force on the piston. Let pdenote the pressure acting at the interface between the gas and the piston. The force exerted by the gas on the piston is simply the product pA,where A is the area of the piston face. The work done by the system as the piston is displaced a distance dxis

The product A dxin Eq. 3.7equals the change in volume of the system,dV.Thus,the work expression can be written as

Since dVis positive when volume increases,the work at the moving boundary is positive when the gas expands. For a compression, dV is negative, and so is work found from Eq. 3.8. These signs are in agreement with the previously stated sign convention for work.

For a change in volume from V1to V2,the work is obtained by integrating Eq. 3.8

Although Eq. 3.9is derived for the case of a gas (or liquid) in a piston-cylinder assembly,it is applicable to systems of anyshape provided the pressure is uniform with position over the moving boundary.

Actual Expansion or Compression Processes

To perform the integral of Eq. 3.9requires a relationship between the gas pressure at the moving boundaryand the system volume,but this relationship may be difficult,or even impossible,to obtain for actual compressions and expansions. In the cylinder of an automobile engine,for example,combustion and other nonequilibrium effects give rise to nonuniformities throughout the cylinder. Accordingly,if a pressure transducer were mounted on the cylinder head,the recorded output might provide only an approximation for the pressure at the

(Parte **1** de 6)