Thermodynamics

thermodynamics - Boltzman equationA knowledge of thermodynamics is essential to nuclear engineers, who deal with nuclear power reactors. A nuclear power plant (nuclear power station) looks like a standard thermal power station with one exception. The heat source in the nuclear power plant is a nuclear reactor. As is typical in many conventional thermal power stations the heat is used to generate steam which drives a steam turbine connected to a generator which produces electricity.
Thermodynamics is the science that deals with energy production, storage, transfer and conversion. It studies the effects of work, heat and energy on a system. Despite the fact it is a very broad subject that affects most fields of science including biology and microelectronics, we will concern mostly with large scale observations. Small scale interactions will be described in the kinetic theory of gases.

Historically, thermodynamics was born in the 19th century as scientists were first discovering how to build and operate steam engines. Particularly through the work of French physicist Nicolas Léonard Sadi Carnot who introduced the concept of the heat-engine cycle and the principle of reversibility in 1824. Scottish physicist Lord Kelvin was the first to formulate a concise definition of thermodynamics in 1854. Carnot’s work concerned the limitations on the maximum amount of work that can be obtained from a steam engine operating with a high-temperature heat transfer as its driving force. In later years the laws of thermodynamics were developed. Thermodynamics is principally based on a set of four laws which are universally valid when applied to systems that fall within the constraints implied by each.

engineering thermodynamics

Rankine Cycle – Thermodynamics as Energy Conversion Science

Thermodynamics is both a branch of physics and an engineering science. The physicist is normally interested in gaining a fundamental understanding of the physical and chemical behavior of fixed quantities of matter at rest and uses the laws of thermodynamics to relate the properties of matter. Engineers are generally interested in studying energy systems and how they interact with their surroundings. To facilitate this, engineers extend the subject of thermodynamics to the study of open systems, in which heat, work and mass can be directed into or out of the control volume.

Our goal here will be to introduce thermodynamics as the energy conversion science, to introduce some of the fundamental concepts and definitions that are used in the study of engineering thermodynamics. These fundamental concepts and definitions will be further applied to energy systems and finally to thermal or nuclear power plants.

Nuclear power plant description

Main features of nuclear power plants with PWR-type (Pressurized Water Reactor) reactor.

A typical nuclear power plant has an electric-generating capacity of 1000 MWe. The heat source in the nuclear power plant is a nuclear reactor. As is typical in all conventional thermal power stations the heat is used to generate steam which drives a steam turbine connected to a generator which produces electricity. The turbines are heat engines and are subject to the efficiency limitations imposed by the second law of thermodynamics. In modern nuclear power plants the overall thermodynamic efficiency is about one-third (33%), so 3000 MWth of thermal power from the fission reaction is needed to generate 1000 MWe of electrical power.

In the following sections we will deal with the problem, how to transform the thermal energy generated inside the reactor into the electrical energy in a most effective way.

Laws of Thermodynamics

There are four laws of thermodynamics that define fundamental physical quantities (temperature, energy, and entropy) and that characterize thermodynamic systems at thermal equilibrium. These are considered as one of the most important laws in all of physics. The laws are as follows:

Zeroth law of thermodynamics:

If two systems are both in thermal equilibrium with a third then they are in thermal equilibrium with each other.  

This law provides a definition and method of defining temperatures, perhaps the most important intensive property of a system when dealing with thermal energy conversion problems.

First law of thermodynamics:

The increase in internal energy of a closed system is equal to the heat supplied to the system minus work done by it.  

This law is the principle of conservation of energy. It is the most important law for analysis of most systems and the one that quantifies how thermal energy is transformed to other forms of energy. It follows, perpetual motion machines of the first kind are impossible.

Second law of thermodynamics:

The entropy of any isolated system never decreases. In a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems increases.  

This law indicates the irreversibility of natural processes. Reversible processes are a useful and convenient theoretical fiction, but do not occur in nature. From this law follows that it is impossible to construct a device that operates on a cycle and whose sole effect is the transfer of heat from a cooler body to a hotter body. It follows, perpetual motion machines of the second kind are impossible.

Third law of thermodynamics:

The entropy of a system approaches a constant value as the temperature approaches absolute zero.

Based on empirical evidence, this law states that the entropy of a pure crystalline substance is zero at the absolute zero of temperature, 0 K and that it is impossible by means of any process, no matter how idealized, to reduce the temperature of a system to absolute zero in a finite number of steps. This allows us to define a zero point for the thermal energy of a body.

Popular Version of the Laws of Thermodynamics

0. You must play the game.

1. You can’t win; you can only break even.

2. You can only break even at absolute zero.

3. You can’t reach absolute zero.

Popular version of the consequences of the first, second, and third laws of thermodynamics:

0. You must play the game.

1. You can’t win. (consequence of first law of thermodynamics)

2. You can’t break even. (consequence of second law of thermodynamics)

3. You can’t even get out of the game. (consequence of third law of thermodynamics)

It is sometimes stated as a general adage without specific reference to the laws of thermodynamics.

Another variant:

1. You can’t win; you can only break even.

2. You can only break even at absolute zero.

3. You can’t reach absolute zero.

Extensive Properties – Intesive Properties

Thermodynamic properties can be divided into two general classes:

  • Extensive properties: An extensive property is dependent upon the amount of mass present or upon the size or extent of a system. Mass, total volume and energy are examples of extensive properties. The value of an extensive property varies directly with the mass. Thus, if a quantity of matter in a given state is divided into two equal parts, each part will have the same value of intensive property as the original and half the value of the extensive property. Extensive properties are additive for subsystems. The system could be divided into any number of subsystems and the value of the property for the system would be the sum of the property for each subsystem.
  • Intensive property: An intensive property is independent of the amount of mass and may vary from place to place within the system at any moment.  For example, the temperature of a system in thermal equilibrium is the same as the temperature of any part of it. If the system is divided the temperature of each subsystem is identical. Temperature, pressure, specific volume, and density are examples of intensive properties. Specific quantities are also referred to as intensive variables, though there are some intensive variables that have no extensive counterpart, such as pressure or temperature. Intensive properties may be functions of both position and time, whereas extensive properties vary at most with time.
Specific properties of material are derived from other intensive and extensive properties of that material. For example, the density of water  is an intensive property and can be derived from measurements of the mass of a water volume (an extensive property) divided by the volume (another extensive property). Also heat capacity, which is an extensive property of a system can be derived from heat capacity, Cp, and the mass of the system. Dividing these extensive properties gives the specific heat capacity, cp, which is an intensive property.

Specific properties are often used in reference tables as a means of recording material data in a manner that is independent of size or mass. They are very useful for making comparisons about one attribute while cancelling out the effect of variations in another attribute.

Specific properties - thermodynamics

Table of some specific properties

Nuclear and Reactor Physics:

  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. Kenneth S. Krane. Introductory Nuclear Physics, 3rd Edition, Wiley, 1987, ISBN 978-0471805533
  7. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  8. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  9. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2. 
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.