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The First Law of Thermodynamics

Objectives How to use the first law of thermodynamics to analyze basic energy systems.

The first law of thermodynamics is one of the most important laws in science and engineering. The first law of thermodynamics, often referred to as the law of conservation of energy, enables engineers to analyze transformations that occur between the various forms of energy. Stated another way, the first law of thermodynamics allows engineers to study how one form of energy is converted to other forms. The most concise definition of the first law of thermodynamics is energy is conserved. Another way to state this law is energy cannot be created or destroyed, only change forms. The first law of thermodynamics, hereafter referred to as simply “the first law,” cannot be proved mathematically. Like Newton's laws of motion, the first law is taken as an axiom, a sound physical principle based on countless measurements. No energy transformation, either natural or manmade, is known to have violated the first law.

The first law is a very intuitive concept. Consider the system shown in Figure 19. The system may represent any substance or region in space chosen for thermodynamic analysis. The boundary of the system is the surface that separates the system from the surroundings. We may construct a mathematical representation of the first law by applying a simple physical argument. If an amount of energy, E_in, is supplied tothe system, that energy can leave the system, change the energy of the system, or both. The energy that leaves the system is E_out, and the energy change of the system is E. Thus, the energy that enters the system equals the energy that leaves the system plus the energy change of the system. The first law may therefore be expressed mathematically as

 

We see that the first law is nothing more than a simple accounting principle that maintains the system's “energy ledger” in balance. In fact, the first law is often referred to as an energy balance because that is precisely what it is. In most engineering thermodynamics texts, Equation 6-28 is typically written in the form

 

. The first law of thermodynamics.

As shown in Figure 19, E_in and E_out are energy quantities that are transferred across the system boundary, whereas E is the change in energy of the system itself. Because E_in and E_out are transferred forms of energy, these terms can only represent energy in the forms of heat, work, and mass flow. Heat is the transport of energy across the boundary of a system by virtue of a temperature difference. For heat transfer to occur, there must be a temperature difference between the system and the surroundings. Work may be mechanical in nature, such as the movement of the system boundary or the turning of a shaft inside the system, or electrical in nature, such as the transfer of electrical energy by a wire that penetrates the system boundary. When mass crosses a system boundary, energy crosses the boundary also because mass carries energy with it. Thus, the left side of Equation 6-29 becomes

 

where Q denotes heat, W denotes work and E_mass denotes energy transfer by mass flow. The in and out subscripts refer to energy transferred in and out of the system, respectively. These energy quantities should always be clearly indicated on a diagram as arrows pointing into or out of the system. The energy change of the system, E, is the sum of the potential, kinetic, and internal energy changes. Hence, the right side of Equation 6-29 is

 

where PE, KE, and U represent the potential, kinetic, and internal energy, respectively. Most thermodynamic systems of practical interest are stationary with respect to external reference frames, so PE= KE=0, leaving E= U. Furthermore, many thermodynamic systems are closed, which means that mass cannot enter or leave the system. For closed systems, the only forms of energy transfer possible are work and heat. The analysis of closed systems is considerably simpler than the analysis of systems that permit mass transfer. In this book, we consider closed systems only. Thus, the first law of thermodynamics for closed systems is

 

The heat and work transferred across the system boundary causes a change in the internal energy of the system. This change alters the thermodynamic state or condition of the system. A change in the thermodynamic state of a system is called a process. The internal energy change, U, is simply the difference between the internal energies at the end of the process and the beginning of the process. Thus, U=U₂U₁, where the subscripts 1 and 2 denote the beginning and end of the process, respectively.

The first law may be expressed in rate form by dividing each term in Equation 6-29 by a time interval, t, over which the process occurs. By dividing the energy terms by time, the quantities on the left side of the equation become quantities of power, and the quantity E becomes a change in energy that occurs during the specified time interval. Equation 6-29 is then rewritten as

 

where and denote the rate at which energy enters and leaves the system, respectively. The units for and are J/s, which is defined as the watt (W). The use of the first law given by Equation 6-33 is preferred over Equation 6-29 if the problem is stated in terms of energy rates rather than absolute energy quantities.

In the following examples, the first law is used to analyze some basic closed thermodynamic systems. We use the general analysis procedure of: (1) problem statement, (2) diagram, (3) assumptions, (4) governing equations, (5) calculations, (6) solution check, and (7) discussion.

EXAMPLE

Problem Statement A closed tank contains a warm liquid whose initial internal energy is 1500 kJ. A paddle wheel connected to a rotating shaft imparts 250 kJ of work to the liquid while 700 kJ of heat is lost from the liquid to the surroundings. What is the final internal energy of the liquid?   Diagram A diagram representing the system is illustrated in Figure 20. The system is the liquid in the tank. Energy transferred across the system boundary as work and heat is shown. . System for Example 6.4.   Assumptions . The system is closed. The tank is stationary, so PE=KE=0. Energy change in the paddle wheel is negligible.   Governing Equations The governing equation for this problem is the first law of thermodynamics for a closed system.   Calculations From the diagram, we see that but there is no heat input and no work output. Thus, Substituting known quantities into the first law, we have Solving for U2, the final energy of the liquid, we obtain   Solution Check No errors are found.   Discussion The final internal energy of the liquid is 1050 kJ, a decrease of 450 kJ. The internal energy of the liquid must decrease because more energy (700 kJ) is removed from the system than is supplied (250 kJ) to the system.

EXAMPLE

Problem Statement The air in a small house is maintained at a constant temperature by an electric baseboard system that supplies 5.6 kW to the house. There are ten light fixtures in the house that each dissipate 60 W, and the major electrical appliances (dishwasher, range, clothes dryer, etc.) have a total dissipation of 2560 W. The house is occupied by four people who each dissipate 110 W. Find the total heat loss from the house to the surroundings.   Diagram . The diagram for this problem is shown in Figure 21. The air in the house is the system. Power supplied to the house by the baseboard system, shown as an electrical resistor, is represented on the diagram by electrical power input, The rate of heat dissipation by lights, people and appliances is shown on the diagram as , and the heat loss from the house to the surroundings is shown as . A careful reading of the problem statement indicates that the change in internal energy of the system is zero because the baseboard system maintains the air in the house at a constant temperature. . System for Example 6.5.   Assumptions . The system is closed. Energy change in the contents of the house is zero. All energy transfer rates are constant.   Governing Equations The governing equation for this problem is the first law, in rate form, for a closed system. Because the house is maintained at a constant temperature, U=0. Thus, we have   Calculations There are ten 60-W lights, 4 people who dissipate 110 W each, and appliances that dissipate a total of 2560 W. The total rate of heat transfer into the house is The electrical power supplied to the house by the baseboard system is but there is no work output, so =0. Substituting known quantities into the first law, we have Solving for the heat loss, , we obtain   Solution Check No errors are found.   Discussion The heat loss of 9.2 kW represents the rate of heat transfer from the house to the surroundings. Heat is lost from the house through the walls, roof, windows, doors, and any other building member that is part of the system boundary. Because the air in the house is maintained at a constant temperature, the rate of energy supplied to the house must equal the rate of energy lost by the house.

 

Practice!

1. A 2500-kg boulder is pushed off a 75-m high cliff. What is the velocity of the boulder immediately before it strikes the ground? How does the boulder's mass affect the solution?
2. Just before striking the ground, the boulder in practice problem 1 converts all its potential energy to kinetic energy (assuming negligible aerodynamic friction). After colliding with the ground, the boulder comes to rest, converting its kinetic energy into other energy forms. What are these forms?
3. The fluid in a closed-pressure vessel receives 500 kJ of heat while a shaft does 250 kJ of work on the fluid. If the final internal energy of the fluid is 1100 kJ, what is the initial internal energy of the fluid?
4. The fluid in a closed tank loses 600 Btu of heat to the surroundings while a shaft does 850 Btu of work on the fluid. If the initial internal energy of the fluid is 250 Btu, what is the final internal energy of the fluid?
5. A small house is to be air-conditioned. The house gains 18,000 Btu/h of heat from the surroundings while lights, appliances and occupants add 6000 Btu/h from within the house. If the house is to be maintained at a constant temperature, what is the required rating of the air conditioner?
6. A piston-cylinder device containing water is heated. During the heating process, 300 J of energy is supplied to the water while 175 J of heat is lost through the walls of the cylinder to the surroundings. As a result of the heating, the piston moves, doing 140 J of boundary work. Find the change in the internal energy of the water for this process.

 

 

Professional Success: Knowing the Practical Side of Engineering

Engineering is the business of designing and producing devices and systems for the benefit of society. People who practice engineering for a living design and manufacture things-practical things that are useful in specific applications. Given the applied nature of engineering, one would assume that engineering education is likewise applied. After all, an engineering education is supposed to prepare students for engineering practice, right? While an engineering education does indeed prepare students for industrial practice, the nature of that preparation may not be what you expect. Generally speaking, engineering courses are very theoretical and mathematical in nature. If you have a few engineering courses under your belt already, you have no doubt discovered this. Engineering courses are usually deep in theory but shallow in practical aspects. As a result, an electrical engineering student may know how to analyze a circuit using a schematic diagram, but may not be able to recognize an actual electrical component such as resistor, capacitor, inductor, or integrated circuit. Similarly, a mechanical engineering student may be very comfortable with performing a first law analysis of a boiler, compressor, turbine, or heat exchanger, but would not recognize one of these devices if he or she saw one. So, why is the emphasis placed on theory at the expense of the practical aspects? One of the main reasons is that many professors who are teaching you how to become a practicing engineer have never practiced engineering themselves. This may sound bizarre, but many engineering professors took a teaching position directly out of graduate school after receiving their PhD degree, have been teaching ever since, and therefore have little or no industrial experience. This situation is not likely to change significantly in the near future, so it is up to the engineering student to acquire some practical, hands-on experience. Here are some ways: Enroll in a vocational or technical course at the university, the local community college, or trade school. Technical programs usually offer a wide variety of very practical courses such as welding, machining, refrigeration repair, auto repair, pipe fitting, electrical wiring, small engine repair, and computer servicing. You should take these courses when they will not interfere with your engineering course work, such as during the summer. Take additional laboratory courses. Some engineering courses have laboratories associated with them. The engineering laboratory is a good place to acquire practical engineering skills. Read engineering and technical-related magazines and journals. These publications contain articles about real engineering systems that will help you bridge the gap between engineering theory and engineering practice. Participate in engineering projects and competitions sponsored by your school and professional engineering societies. The American Society of Mechanical Engineers (ASME), the Society of Automotive Engineers (SAE), the Institute for Electrical and Electronics Engineers (IEEE), the American Institute of Aeronautics and Astronautics (AIAA), and other professional societies sponsor various engineering competitions. Local participation in National Engineers Week, held annually in February, is an excellent opportunity for students to bolster their practical engineering skills. Tinker with various mechanical and electrical devices. Find an old electric hand drill, and disassemble it. Figure out how it works. Do the same for a telephone, computer hard drive and a small kitchen appliance. Disassembling, studying and reassembling things will help you discover how actual devices work. You may even want to perform service on your own automobile such as replacing the brakes, doing a tuneup, or installing a sound system.