Thermodynamics and Statistical Mechanics (eBook)

An Integrated Approach

Robert J. Hardy, Christian Binek (Autoren)

eBook Download: EPUB

2014
John Wiley & Sons (Verlag)
9781118676370 (ISBN)

Infos

Thermodynamics and Statistical Mechanics

Thermodynamics and Statistical Mechanics

An Integrated Approach

This textbook brings together the fundamentals of the macroscopic and microscopic aspects of thermal physics by presenting thermodynamics and statistical mechanics as complementary theories based on small numbers of postulates. The book is designed to give the instructor flexibility in structuring courses for advanced undergraduates and/or beginning graduate students and is written on the principle that a good text should also be a good reference.

The presentation of thermodynamics follows the logic of Clausius and Kelvin while relating the concepts involved to familiar phenomena and the modern student's knowledge of the atomic nature of matter. Another unique aspect of the book is the treatment of the mathematics involved. The essential mathematical concepts are briefly reviewed before using them, and the similarity of the mathematics to that employed in other fields of physics is emphasized.

The text gives in-depth treatments of low-density gases, harmonic solids, magnetic and dielectric materials, phase transitions, and the concept of entropy. The microcanonical, canonical, and grand canonical ensembles of statistical mechanics are derived and used as the starting point for the analysis of fluctuations, blackbody radiation, the Maxwell distribution, Fermi-Dirac statistics, Bose-Einstein condensation, and the statistical basis of computer simulations.

ROBERT J. HARDY and CHRISTIAN BINEK
Department of Physics, University of Nebraska-Lincoln, USA

Textauszug

Chapter 1
Fundamentals

As many of the terms of thermal physics are also used in everyday speech, it is important to understand their more restricted technical meanings. It is especially important to understand the fundamental distinction between heat and work, which describe the interaction of systems with each other, and the intrinsic property of individual systems called internal energy. Other important concepts are equilibrium, state, state function, process, and temperature.

1.1 PVT Systems

Pressure P, volume V, and temperature T are essential properties of solids, liquids, and gases. In scientific usage both liquids and gases are fluids, i.e., substances that flow to conform to the shape of their container. Before introducing two relatively simple mathematical models of PVT systems, we review the units used in the description of thermodynamic behavior.

Units

The SI units for pressure, volume, and temperature are the pascal (Pa) named after Blaise Pascal, the cubic meter (m3), and the kelvin (K) named after Lord Kelvin, who is also known as William Thompson. Other commonly used units for volume are the cubic centimeter (cm3), the liter (L), and the cubic foot (ft3).

1.1

One pascal equals one newton per square meter (). In many applications the convenient SI unit for pressure is the kilopascal (kPa). An important reference pressure is the standard atmosphere (), which is approximately .

1.2

Other units for pressure are the bar (), the pound per square inch (), the millimeter of mercury (mmHg), and the torr (1 torr = 1 mmHg) named after Evangelista Torricelli. The unit “mmHg” is based on the height of the mercury column in a barometer. These units are related by

1.3

The unit “atm” is sometimes called an atmosphere. The unit specifies a specific force per unit area and must not be confused with the less precise “atmospheric pressure,” which is the pressure of the atmosphere and is only approximately equal to 1 atm at elevations not too far above sea level.

The commonly used temperature scales are the Kelvin, Celsius, and Fahrenheit scales. The relationship between a Celsius temperature and a Kelvin temperature is

1.4

The relationship between a Fahrenheit temperature (in units of ) and a Celsius temperature (in units of ) is

1.5

The symbol is reserved for temperatures measured on an absolute temperature scale, a concept made precise in Chapters 7 and 8. The symbol Θ is used with other temperature scales. The Kelvin scale is an absolute temperature scale. (The symbol for the unit is K, not °K). The Celsius and Fahrenheit scales are not absolute scales. Although the numerical values of temperatures are different in units of K and °C, the values of the temperature differences are the same,

1.6

As indicated in (1.5), a temperature difference of five Celsius degrees is equivalent to a difference of nine Fahrenheit degrees.

Standard temperature and pressure (STP) refers to 273.15 K (0 °C) and 1 standard atmosphere. Room temperature and atmospheric pressure are not precisely defined. This book considers “room temperature” to be 300 K and “atmospheric pressure” to be 100 kPa.

Internal energy U is the thermodynamic property of a system that represents the sum of the kinetic and potential energies of its microscopic constituents. The SI unit for energy is the joule (J) named after James Prescott Joule. In thermal physics the calorie (cal) and kilocalorie (kcal) are convenient units for energy. The food Calorie (written with a capital C) is actually a kilocalorie. The British thermal unit (Btu) is used in engineering. The units of energy are related by

1.7

The internal energy and pressure of PVT systems can be expressed as functions of temperature and volume.1

1.8

It is helpful when explaining the concepts of thermodynamics to have explicit expressions for these functions. Ideal gases and simple solids are useful for this purpose.

Ideal Gases

A gas is a collection of molecules that move about in random directions with occasional collisions with each other and with the walls of their container. In many applications real gases are accurately modeled as ideal gases, which are also called perfect gases. In the ideal gas model the relationship between pressure, volume, and temperature is

1.9

where the function is . This is the ideal gas equation of state, and R is the universal gas constant.

1.10

and n is the number of moles.

One mole is the quantity of material that has a mass in grams equal to its molecular weight. The mass m of one molecule of a pure substance is

1.11

where the atomic mass constant is

and the number of molecules per mole is given by Avogadro's number named after Amadeo Avogadro.

1.12

The internal energy of an ideal gas depends on temperature only, which is a special case of the relationship indicated in (1.8). As there is no dependence on volume, it is expressed by

1.13

It is shown in Chapter 10 that this special case is a consequence of . Until then, equations (1.9) and (1.13) are considered the defining characteristics of an ideal gas.

Simple Solids

More than one type of model system is needed to illustrate the generality of thermodynamics. The functions for the internal energy and pressure of another type of system are

1.14

and

1.15

where , , , and are constants and is the mass of the system. Although less significant that the ideal gas model, the above equations give a useful description of the behavior of solids over the limited ranges of temperatures and pressures of interest in many applications. For this reason a system described by (1.14) and (1.15) will be referred to as a simple solid.

It is shown in Chapter 3 that the above equations describe the internal energy and pressure of a system whose coefficient of thermal expansion , bulk modulus , and specific heat are constant. Their values for a few solids are given in Table 1.2 on page 15. The equations that relate the , , and to , , and are , , and (see (3.28)). The constant is chosen so that (1.15) gives the pressure at some specific temperatures, such as and .

The significant differences in the functions for internal energy and pressure for ideal gases and simple solids reflect differences in their microscopic structures. The behavior of solids is dominated by the forces that bind the atoms into a rigid structure. These forces can be obtained from a potential energy function. An approximate expression for the internal energy function is

1.16

The term describes the kinetic and potential energies associated with the vibrational motion of the atoms. The static energy is the energy or the system when the atoms are stationary. The volume of a solid is changed by subjecting it to high pressure. The contribution to pressure resulting from the changes to is . An approximate expression for the pressure is

1.17

The term accounts for the tendency of solids to expand as temperature increases. The static energy is represented in the simple solid model by the term in (1.14), which implies that . Combining this with (1.17) yields the expression for pressure in (1.15).

1.2 Equilibrium States

System

Many of the systems that will be studied are homogeneous (uniform composition) and isotropic (same in all directions), such as the gas or liquid in a container or a sample of dielectric or magnetic material. Nevertheless, the concepts of thermal physics are applicable to much more complex systems, sometimes referred to as devices, such as engines, refrigerators, and electrical generating plants.

A system may be made up of smaller systems, called subsystems. We may refer to something as a subsystem at one time and as a system at another time. Sometimes we concentrate on one system and refer to everything it interacts with as its surroundings, or the environment. Since the focus of a discussion often changes, it is important to clearly identify the system to which the principles of thermodynamics are being applied.

A system with a fixed quantity of matter is a closed system, and one that can exchange matter with its surrounding is an open system. An automobile engine, which takes in fuel and air and exhausts combustion products, is an open system. The mass of a closed system is constant, and in the absence of chemical reactions the numbers of moles of its different constituents are constant.

Equilibrium

A system is in equilibrium if it does not spontaneously change. A glass of warm water with a cube of ice in it is not in equilibrium, as the ice will spontaneously melt until either the water cools to 0.0 °C or all of the...

Produkt-Details

• Erscheint lt. Verlag: 12.6.2014
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Thermodynamik
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Classical & Fluid Mechanics • Klassische u. Strömungsmechanik • Klassische u. Strömungsmechanik • Maschinenbau • mechanical engineering • Physics • Physik • Statistische Mechanik • Thermal Physics & Statistical Mechanics • thermodynamics • Thermodynamik • Wärmelehre u. Statistische Mechanik • Wärmelehre u. Statistische Mechanik
• ISBN-13: 9781118676370 / 9781118676370