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The concept of energy is central to the study of engineering in general and thermodynamics in particular. A concise definition of energy is the capacity to do work. If a system has the capacity to do work, it possesses at least one form of energy that is available for transformation to another form of energy. For example, a compressed spring possesses a type of energy referred to as potential energy. As the term implies, potential energy is a type of stored energy that has the potential for producing some useful external effect. Consider a mass attached to a compressed spring, as illustrated in Figure 7. When the compressed spring is released, the stored energy in the spring will begin to resume its original undeformed length, imparting a velocity to the mass. As the spring elongates, the potential energy in the spring is converted to kinetic energy. Actually, a small portion of the potential energy in the spring is converted to thermal energy (heat) because there is friction between the mass and the surface and within the spring itself. The important thing to realize is that all the potential energy in the compressed spring is converted to other forms of energy; i.e., the total energy of the transformation is constant. No energy is produced or destroyed during the energy transformation, in accordance with the first law of thermodynamics.

Energy can exist in many forms. For purposes of thermodynamic analysis, energy is classified into two broad categories, macroscopic energy and microscopic energy. Macroscopic forms of energy are those that a whole system possesses with respect to a fixed external reference. In thermodynamics, the macroscopic forms of energy are potential energy and kinetic energy. Potential and kinetic energy are based on external position and velocity references, respectively. Microscopic forms of energy are those that relate to the system on a molecular or atomic level. There are several types of microscopic energies, so we conveniently group them together into a single category referred to as internal energy. Internal energy is the sum of all the various forms of microscopic energies possessed by the molecules and atoms in the system. Potential, kinetic, and internal energy warrant further discussion.

1 Potential Energy

In thermodynamics, there are primarily two forms of potential energy, elastic potential energy and gravitational potential energy. Elastic potential energy is the energy stored in a deformable body such as an elastic solid or a spring. Gravitational potential energy is the energy that a system possesses by virtue of its elevation with respect to a reference in a gravitational field. Elastic potential energy is usually of minor importance in most thermodynamics work, so gravitational potential energy is emphasized here. Gravitational potential energy, abbreviated PE, is given by the relation

where m is the mass of the system (kg), g is gravitational acceleration (m/s²), and z is the elevation (m) of the center of mass of the system with respect to a selected reference plane. The location of the reference plane is arbitrary but is usually selected on the basis of mathematical convenience. For example, consider a boulder poised on the edge of a cliff, as illustrated in Figure 8. The center of mass of the boulder is 20 m above the ground. A reasonable reference plane is the ground because it is a convenient origin. If the boulder's mass is 1500 kg, the gravitational potential energy of the boulder is

2 Kinetic Energy

Kinetic energy is the energy that a system possess as a result of its motion with respect to a reference frame. Kinetic energy, abbreviated KE, is given by the relation

where m is the mass of the system (kg) and v is the velocity of the system (m/s). When the boulder in Figure 8 is pushed off the cliff, it begins to fall toward the ground. As the boulder falls, its velocity increases, and its potential energy is converted to kinetic energy. If the velocity of the 1500-kg boulder is 10 m/s at a point between the cliff and ground, the boulder's kinetic energy at this point is

Immediately before the boulder impacts the ground, all the boulder's potential energy has been converted to kinetic energy. What happens to the boulder's kinetic energy during the impact with the ground?

3 Internal Energy

Internal energy is the sum of all the microscopic forms of energy of a system. Unlike potential energy and kinetic energy, which relate to the energy of a system with respect to external references, internal energy relates to the energy within the system itself. Internal energy, denoted by the symbol U, is a measure of the kinetic energies associated with the molecules, atoms, and subatomic particles of the system. Suppose the system under consideration is a polyatomic gas. (A polyatomic gas is a gas that consists of two or more atoms that form a molecule, such as carbon dioxide, CO₂. A monatomic gas consists of only one atom, such as helium, He, and argon, Ar.) Because gas molecules move about with certain velocities, the molecules possess kinetic energy. The movement of the molecules through space is called translation, so we refer to their kinetic energy as translational energy. As the gas molecules translate, they also rotate about their center of mass. The energy associated with this rotation is referred to as rotational energy. In addition to translating and rotating, the atoms of polyatomic gas molecules oscillate about their center of mass giving rise to vibrational energy. On a subatomic scale, the electrons of atoms “orbit” the nucleus. Furthermore, electrons spin about their own axis, and the nucleus also possesses a spin. The sum of the translational, rotational, vibrational, and subatomic energies constitutes a fraction of the internal energy of the system called the sensible energy. Sensible energy is the energy required to change the temperature of a system. As an example of sensible energy, suppose that we wish to boil a pan of water on the stove. The water is initially at a temperature of about 20°C. The stove burner imparts energy to the water, increasing the kinetic energy of the water molecules. The increase in kinetic energy of the water molecules is manifested as an increase in temperature of the water. As the burner continues to supply energy to the water, the sensible energy of the water increases, thereby increasing the temperature, until the boiling point is reached.

If sensible energy is only a fraction of the internal energy, what kind of energy constitutes the other fraction? To answer this question, we must recognize the various forces that exist between molecules, between atoms, and between subatomic particles. From basic chemistry, we know that various binding forces exist between the molecules of a substance. When these binding forces are broken, the substance changes from one phase to another. The three phases of matter are solid, liquid, and gas. Binding forces are strongest in solids, weaker in liquids, and weakest in gases. If enough energy is supplied to a solid substance, ice for example, the binding forces are overcome and the substance changes to the liquid phase. Hence, if enough energy is supplied to ice (solid water), the ice changes to liquid water. If still more energy is supplied to the substance, the substance changes to the gas phase. The amount of energy required to produce a phase change is referred to as latent energy. In most thermodynamic processes, a phase change involves the breaking of molecular bonds only. Hence, the atomic binding forces responsible for maintaining the chemical identity of a substance are not usually considered. Furthermore, the binding energy associated with the strong nuclear force, the force that binds the protons and neutrons in the nucleus, is relevant only in fission reactions.

4 Total Energy

The total energy of a system is the sum of the potential, kinetic, and internal energies. Thus, the total energy, E, is expressed as

As a matter of convenience, it is customary in thermodynamics work to express the energy of a system on a per unit mass basis. Dividing Equation 6-12 by mass, m, and noting the definitions of potential and kinetic energies from Eqs. (6-10) and (6-11), we obtain

where e=E/m and u=U/m. The quantities e and u are called the specific total energy and specific internal energy, respectively.

In the analysis of many thermodynamic systems, the potential and kinetic energies are zero or are sufficiently small that they can be neglected. For example, a boiler containing high temperature steam is stationary, so its kinetic energy is zero. The boiler has potential energy with respect to an external reference plane (such as the floor on which it rests) but the potential energy is irrelevant because it has nothing to do with the operation of the boiler. If the potential and kinetic energies of a system are neglected, internal energy is the only form of energy present. Hence, the total energy equals the internal energy, and Equation 6-12 reduces to E=U.

The analysis of thermodynamic systems involves the determination of the change of the total energy of the system because this tells us how energy is converted from one form to another. It does not matter what the absolute value of the total energy is because we are interested only in the change of the total energy. This is paramount to saying that it does not matter what the energy reference value is because the change of energy is the same regardless of what reference value we choose. The reference value is arbitrary. Returning to our falling boulder example, the change of potential energy of the boulder does not depend on the location of the reference plane. We could choose the ground as the reference plane or some other location, such as the top of the cliff or any other elevation for that matter. The change of potential energy of the boulder depends only on the elevation change. Hence, if potential and kinetic energies are neglected, the change of total energy of a system equals the change of internal energy, and Equation 6-12 is written as

Professional Success: Dealing With Engineering Professors

As a new engineering student, you may believe that engineering professors are probably not that much different from professors in other disciplines on campus. Perhaps you think that they are not even that much different from people outside higher education who work in nonteaching occupations. However, after you have taken a few engineering courses, your opinion will probably change. Engineering professors are unique. It may even be said that they are somewhat odd. Some engineering professors are overly serious, while others may seem rather light-minded. Some engineering professors dress very neatly, wearing a suit, tie, polished shoes, etc., while others come to school looking more like a student, wearing jeans, a sweatshirt, and sneakers. Regardless of their personalities and personal appearances, the majority of engineering professors are genuinely interested in their students and desire to see them succeed in their engineering studies. Engineering professors are very knowledgeable people in their disciplines, and they want to share that knowledge with students. They were students once, so they understand what you are going through. Professors are teachers, and quality instruction is what students expect from them. However, as a student, you should realize that most professors are involved in numerous activities outside the classroom that may or may not relate directly to teaching. Much of your professor's time is spent developing and improving the engineering curriculum. Depending on the availability of graduate teaching assistants, grading may also occupy a considerable fraction of the professor's time. Some colleges and universities, particularly the larger ones, are referred to as research institutions. At these schools, engineering professors are expected to conduct research and publish the results of their research. In addition to publishing research papers, some engineering professors write textbooks. Because most engineering professors specialize in a certain aspect of their discipline, some professors work part-time as consultants to private or governmental agencies. Most colleges and universities expect their faculty to render service to the institution by serving on various campus committees. Some professors, in addition to their research, writing, and service activities, serve as department or program advisors to students. Professors may even be involved with student recruitment, fund raising, professional engineering societies, and a host of other activities.

What does all this mean to you, the engineering student? It means that there are right ways and wrong ways of dealing with your professors. Here are a few suggestions:

Be an active member of your professor's class. Attend class, arrive on time, take notes, ask questions, and participate. Being actively engaged in the classroom not only helps you learn but it also helps the professor teach!
If you need to obtain help from your professor outside of class, schedule an appointment during an office hour and keep the appointment. Unless your professor has an “open door” policy, scheduling appointments during regular office hours is preferred because your professor is probably involved in research or other activities.
Engineering professors appreciate students who give their best efforts in solving a problem before asking for help. Before your go to the professor's office, be prepared to tell your professor how you approached the problem and where the potential errors are. Many engineering professors become irritated when the first thing a student says is, “Look at this problem, and tell me what I'm doing wrong” or “I just can't get the answer in the back of the book.” Preparing to ask the right questions before the visit will enable your professor to help you more fully.
Do not call professors at home. If you need assistance with homework, projects, etc., contact your professor at school during regular office hours if possible or by special appointment. Like students, professors try to have a personal life apart from their day-to-day academic work. How would you like it if your professors called you at home to assign additional homework?
Address professors by their appropriate titles. Do not call them by their first names. Most engineering professors have a PhD degree, so it is appropriate to address these individuals as “Dr. Jones” or “Professor Jones”. If the professor does not have a doctorate, the student should address the professor by “Professor Jones,” “Mr. Jones,” or “Ms. Jones.”

Forms of Energy

Objectives

1 Potential Energy

2 Kinetic Energy

3 Internal Energy

4 Total Energy

Professional Success: Dealing With Engineering Professors