Thermal Equilibrium

Thermal Equilibrium

A particularly important concept is thermodynamic equilibrium. In general, when two objects are brought into thermal contact, heat will flow between them until they come into equilibrium with each other.  When a temperature difference does exist heat flows spontaneously from the warmer system to the colder system. Heat transfer occurs by conduction or by thermal radiation. When the flow of heat stops, they are said to be at the same temperature. They are then said to be in thermal equilibrium.

For example, you leave a thermometer in a cup of coffee. As the two objects interact, the thermometer becomes hotter and the coffee cools off a little until they come into thermal equilibrium. Two objects are defined to be in thermal equilibrium if, when placed in thermal contact, no net energy flows from one to the other, and their temperatures don’t change. We may postulate:

When the two objects are in thermal equilibrium, their temperatures are equal.

This is a subject of a law that is called the “zeroth law of thermodynamics”.

Zeroth Law of Thermodynamics

We can discover an important property of thermal equilibrium by considering three systems. A, B, and C, that initially are not in thermal equilibrium. We separate systems A and B with an adiabatic wall (ideal insulating material), but we let system C interact with both systems A and B. We wait until thermal equilibrium is reached; then A and B are each in thermal equilibrium with C. But are they in thermal equilibrium with each other?

According to many experiments, there will be no net energy flow between A and B. This is an experimental evidence of the following statement:

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

This statement is known as the zeroth law of thermodynamics. It has this unusual name because it was not until after the great first and second laws of thermodynamics were worked out that scientists realized that this apparently obvious postulate needed to be stated first.

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. Temperature is a property of a system that determines whether the system will be in thermal equilibrium with other systems. When two systems are in thermal equilibrium, their temperatures are, by definition, equal, and no net thermal energy will be exchanged between them. Thus the importance of the zeroth law is that it allows a useful definition of temperature.

Temperature is a very important characteristics of matter. Many properties of matter change with temperature. The length of a metal rod, steam pressure in a boiler, the ability of a wire to conduct an electric current, and the color of a very hot glowing object. All these depend on temperature.

For example, most materials expand when their temperature is increased. This property is very important in all of the science and engineering, even in nuclear engineering. The thermodynamic efficiency of power plants changes with temperature of inlet steam or even with outside temperature. At higher temperatures, solids such as steel glow orange or even white depending on temperature. The white light from an ordinary incandescent lightbulb comes from an extremely hot tungsten wire. It can be seen temperature is one of the fundamental characteristics that describes matter and influences matter behaviour.

References:
Reactor Physics and Thermal Hydraulics:
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. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.

Temperature