Engineering Thermodynamics. Chapter 3. Energy Transport by Heat, Work and Mass

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1 Chapter 3 Energy Transport y Heat, ork and Mass 3. Energy of a System Energy can e viewed as the aility to cause change. Energy can exist in numerous forms such as thermal, mechanical, kinetic, potential, electric, magnetic, chemical, and nuclear, and their sum constitutes the total energy E of a system. The total energy of a system on a unit mass asis is denoted y e and is expressed as E e ( kj / kg ) (3.) m In thermodynamic analysis, energy can e group in to two forms: Macroscopic Microscopic Microscopic forms of energy are those related to the molecular structure of a system and the degree of the molecular activity, and they are independent of outside reference frames. The sum of all the microscopic forms of energy is called the internal energy of a system and is denoted y U. Example:- Latent energy Chemical energy Nuclear energy Sensile energy Internal energy A system associated with the kinetic energies of the molecules is called the sensile energy. The internal energy associated with the phase of a system is called the latent energy. The internal energy associated with the atomic onds in a molecule is called chemical energy. Compiled y Yidnekachew M. Page of 3

2 The tremendous amount of energy associated with the strong onds within the nucleus of the atom itself is called nuclear energy. The total energy of a system, can e contained or stored in a system, and thus can e viewed as the static forms of energy. The forms of energy not stored in a system can e viewed as the dynamic forms of energy. The only two forms of energy interactions associated with a closed system are heat transfer and work. Macroscopic forms of energy are those a system possesses as a whole with respect to some outside reference frame, such as kinetic and potential energies. The energy that a system possesses as a result of its motion relative to some reference frame is called kinetic energy (KE) and is expressed as KE m ( kj ) (3.) Per unit mass ke ( kj / kg ) (3.3) The energy that a system possesses as a result of its elevation in a gravitational field is called potential energy (PE) and is expressed as Per unit mass PE pe mgz ( kj ) (3.4) gz ( kj ) (3.5) The magnetic, electric, and surface tension effects are significant in some specialized cases only and are usually ignored. In the asence of such effects, the total energy of a system consists of the kinetic, potential, and internal energies and is expressed as E U KE PE E U m mgz ( kj ) (3.6) Per unit mass Compiled y Yidnekachew M. Page of 3

3 euke pe eu gz ( kj / kg ) (3.7) Most closed systems remain stationary during a process and thus experience no change in their kinetic and potential energies. Closed systems whose velocity and elevation of the center of gravity remain constant during a process are frequently referred to as stationary systems. The change in the total energy E of a stationary system is identical to the change in its internal energy U. 3. Energy transport y heat and work Energy can cross the oundary of a closed system in two distinct forms: heat and work. Figure 3. Energy can cross the oundaries of a closed system in the form of heat and work. Energy transport y heat Heat is defined as the form of energy that is transferred etween two systems (or a system and its surroundings) y virtue of a temperature difference. Compiled y Yidnekachew M. Page 3 of 3

4 Figure 3. Heat transfer from hot surface to cold surface That is, an energy interaction is heat only if it takes place ecause of a temperature difference. Then it follows that there cannot e any heat transfer etween two systems that are at the same temperature. A process during which there is no heat transfer is called an adiaatic process. The word adiaatic comes from the Greek word adiaatos, which means not to e passed. There are two ways a process can e adiaatic: Either the system is well insulated so that only a negligile amount of heat can pass through the oundary, or oth the system and the surroundings are at the same temperature and therefore there is no driving force (temperature difference) for heat transfer. Figure 3.3 During an adiaatic process, a system exchanges no heat with its surroundings. As a form of energy, heat has energy units, kj eing the most common one. The amount of heat transferred during the process etween two states (states and ) is denoted y Q, or just Q. Heat transfer per unit mass of a system is denoted q and is determined from Q q ( kj / kg ) (3.8) m Sometimes it is desirale to know the rate of heat transfer (the amount of heat transferred per unit time) instead of the total heat transferred over some time interval. Compiled y Yidnekachew M. Page 4 of 3

5 Figure 3.4 The relationships among q, Q, and Q. The heat transfer rate is denoted, where the overdot stands for the time derivative, or per unit time. The heat transfer rate has the unit kj/s, which is equivalent to k. hen varies with time, the amount of heat transfer during a process is determined y integrating over the time interval of the process: t Q Qdt ( kj ) (3.9) t hen remains constant during a process, this relation reduces to here: t t t Q Q t ( kj ) (3.0) Heat is transferred y three mechanisms: conduction, convection, and radiation. Conduction is the transfer of energy from the more energetic particles of a sustance to the adjacent less energetic ones as a result of interaction etween particles. Convection is the transfer of energy etween a solid surface and the adjacent fluid that is in motion, and it involves the comined effects of conduction and fluid motion. Radiation is the transfer of energy due to the emission of electromagnetic waves (or photons). Energy Transport y ork ork, like heat, is an energy interaction etween a system and its surroundings. As mentioned earlier, energy can cross the oundary of a closed system in the form of heat or work. Therefore, If the energy crossing the oundary of a closed system is not heat, it must e work. ork is the energy transfer associated with force acting through a distance. Example:- Compiled y Yidnekachew M. Page 5 of 3

6 A rising piston A rotating shaft ork is also a form of energy transferred like heat and, therefore, has energy units such as kj. The work done during a process etween states and is denoted y, or simply. The work done per unit mass of a system is denoted y w and is expressed as w ( kj / kg ) (3.) m The work done per unit time is called power and is denoted y. The unit of power is kj/s, or k. Heat and work are energy transfer mechanisms etween a system and its surroundings, and there are many similarities etween them: Both are recognized at the oundaries of a system as they cross the oundaries. That is, oth heat and work are oundary phenomena. Systems possess energy, ut not heat or work. Both are associated with a process, not a state. Unlike properties, heat or work has no meaning at a state. Both are path functions (i.e., their magnitudes depend on the path followed during a process as well as the end states). Sign convention for energy transported y heat and work Heat and work are directional quantities, and thus the complete description of a heat or work interaction requires the specification of oth the magnitude and direction. One way of doing that is to adopt a sign convention. The generally accepted formal sign convention for heat and work interactions is as follows: heat transfer to a system and work done y a system are positive; heat transfer from a system and work done on a system are negative. Another way is to use the suscripts in and out to indicate direction Compiled y Yidnekachew M. Page 6 of 3

7 Figure 3.5 Specifying the directions of heat and work. Qin > 0 Heat transfer to a system (positive) Qout < 0 Heat transfer from a system (negative) Figure 3.6 Process from stage to Figure 3.7 Process from stage to > 0 work done y the system (positive) Figure 3.6 < 0 work done on the system (negative) Figure 3.7 Path functions have inexact differentials designated y the symol. Therefore, a differential amount of heat or work is represented y Q or, respectively, instead of dq or d. Properties, however, are point functions (i.e., they depend on the state only, and not on how a system reaches that state), and they have exact differentials designated y the symol d. A small change in volume, for example, is represented y dv, and the total volume change during a process etween states and is dv v v v (3.) Compiled y Yidnekachew M. Page 7 of 3

8 Figure 3.8 Properties are point functions; ut heat and work are path functions The total work done during process, however, is ( not ) (3.3) That is, the total work is otained y following the process path and adding the differential amounts of work () done along the way. The integral of is not - (i.e., the work at state minus work at state ), which is meaningless since work is not a property and systems do not possess work at a state. 3.3 Boundary work The work associated with a moving oundary is called oundary work. The expansion and compression work is often called moving oundary work or simply oundary work. Example:- piston cylinder device. Figure 3.9 The work associated with a moving oundary is called oundary work. Compiled y Yidnekachew M. Page 8 of 3

9 In this section, we analyze the moving oundary work for a quasiequilirium process, a process during which the system remains nearly in equilirium at all times. A quasi-equilirium process, Boundary work is done y the steam on the piston is calculated from figure 3.0. Figure 3.0 The area under the process curve on a P- diagram represents the oundary work. (3.4) F Fds Ads Pd (3.5) A Pd (3.6) This integral can e evaluated only if we know the functional relationship etween P and v during the process. P= f () is simply the equation of the process path on a P- diagram. The differential area da is equal to Pd. The total area A under the process curve is otained y adding these differential areas: (3.7) Area A da Pd A comparison of this equation with the aove ( process curve on a P-v diagram is equal, in magnitude, to the work done during a quasi- Compiled y Yidnekachew M. Page 9 of 3 Pd ), reveals that the area under the

10 equilirium expansion or compression process of a closed system. (On the P-v diagram, it represents the oundary work done per unit mass.) Some typical process Pd (3.8) Boundary work at constant volume process Figure 3. Schematic and P- diagram for constant pressure process If the volume is held constant, =0 and the oundary work equation ecomes Pd 0 (3.9) Boundary work at constant pressure Figure 3. Schematic and P-v diagram for constant pressure Compiled y Yidnekachew M. Page 0 of 3

11 If the pressure is held constant the oundary work equation ecomes. ( ) (3.0) Pd P d P Boundary work at constant temperature (Isothermal) Figure 3.3 Schematic and P- diagram for a polytropic process. If the temperature of an ideal gas system held constant, then the equation of state provides the pressure volume relation. mrt P (3.) The oundary work is: Pd But mrt P (3.) mrt d (3.3) Let mrt C P dv (3.4) C Cln (3.5) Compiled y Yidnekachew M. Page of 3

12 Sustitute the value of C mrtln P ln (3.5) P ln ln (3.6) Polytropic Process During actual expansion and compression processes of gases, pressure and volume are often related y P n = C. where n and C are constants Pd ut P n = C n n n P P C d C n n (3.7) Since n n C P P For an ideal gas (P = mrt), this equation can also e written as mr( T T) n n (3.8) For the special case of n = the system is isothermal process and the oundary work ecomes n ln P (3.9) Pd C d Spring ork hen the length of the spring changes y a differential amount dx under the influence of a force F, the work done is Figure 3.4 Elongation of a spring under the influence of a force. Compiled y Yidnekachew M. Page of 3

13 Fdx (3.30) spring But F kx spring k ( x x ) (3.3) 3.4 Energy transferred y Mass Mass flow into and out of a system changes the energy content of the system. hen mass enters a control volume, the energy of the control volume increase ecause the entering mass carries some energy with it. Likewise when some mass leaves the control volume, the energy contained within the control volume decreases ecause some leaving mass takeout some energy within it. Figure 3.4 The energy content of a control volume can e changed y mass flow Compiled y Yidnekachew M. Page 3 of 3

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