Thermal Expansion

8 Key excerpts on "Thermal Expansion"

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  eBook - ePub

  Physics for O.N.C. Courses

  • R.A. Edwards(Author)
  • 2014(Publication Date)
  • Pergamon

    (Publisher)

  CHAPTER 6

  Thermal Expansion

  Publisher Summary

  This chapter presents the concept of Thermal Expansion and its different properties. Most substances expand when they are heated. The expansion that any substance undergoes when heated through a few tens of degrees, Celsius, is usually quite small relative to the total bulk of the substance and, particularly, in the case of solids, may be far from being apparent by direct observation. The problem of the measurement of Thermal Expansion, at least for solids and liquids, is a problem of the accurate measurement of very small dimensions. Coefficient of linear expansion can be defined as the fractional increase in length of the solid per unit temperature rise. The chapter also presents the results of the experimental determination of the coefficient of expansion of liquids. Sufficient accuracy of measurement for most practical purposes of the linear coefficient of expansion of solids, particularly of metals, may be obtained using the micrometer screw gauge method. A thermostat is any device that regulates automatically the supply of heat to, and in consequence controls the temperature of, any system. Many thermostats operate by the expansion of liquids and solids or, in particular, the difference in expansion between one metal and another.

  6.1 Introduction

  Most substances expand when they are heated although this is not always the case, a notable exception being that of water when heated between 0° and 4°C. Water contracts when heated over this range, but beyond 4°C expansion occurs and continues right up to the boiling point at 100°C. A given mass of water thus has a minimum volume at 4°C, i.e. water has a maximum density at this temperature (Fig. 6.1 ). The original definition of the unit of mass known as the kilogram was the mass of a cubic decimetre of water (1 litre of water) at 4°C.

  FIG. 6.1

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  eBook - ePub

  Electronic Materials

  Principles and Applied Science

  • Yuriy M. Poplavko(Author)
  • 2018(Publication Date)
  • Elsevier

    (Publisher)

  T and measured in degrees of Kelvin (K). The average energy of particles in a body is proportional to the absolute temperature.

  The heat capacity, denoted as C and measured in (J/deg) or in [cal/(deg mol)], is the heat absorbed from external sources when the temperature increases. In active dielectrics and ordered magnetics, the heat capacity is dependent on the mechanical and electrical boundary conditions of a crystal.

  The coefficient of thermal conductivity , denoted as λ and measured in [W/(deg m)] or [cal/(deg s cm)], is a characteristic property of a heat-conducting material; numerically, it is equal to the amount of heat passing through a unit area per unit time at a unit temperature gradient.

  The coefficient of Thermal Expansion , denoted α and measured in unit [deg− 1 ] = [K− 1 ], represents the alterations in a solid body's relative dimensions when the temperature changes by 1 K.

  The next section presents some examples of the application of thermodynamics in solid-state physics. The focus is on three thermal properties of solids: Thermal Expansion, heat capacity, and thermal conductivity. These are properties that have the greatest practical importance.

  3.2 Thermal Expansion of Solids

  Changes in the dimensions and volume of a crystal with a temperature variation are a result of the asymmetry in the interaction of its particles in a crystal lattice. Quantitatively, the degree of a change in the volume is characterized by the volumetric coefficient of Thermal Expansion, α V . According to general definition, this coefficient is the relative change of volume V in a body on heating by 1° of temperature at constant pressure P , and it can be written as:

  α V

  =

  1 / V

  ∂ V / ∂ T

  P

  .

  Very often, Thermal Expansion in crystals is anisotropic and, sometimes, it is negative [2] . This means that when the temperature increases, a crystal can expand differently in various crystallographic directions; moreover, in some directions, the crystal may even be compressed with an increase in the temperature. Therefore, besides the volumetric expansion, the linear expansion coefficient αl

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  eBook - ePub

  Commonly Asked Questions in Physics

  • Andrew Rex(Author)
  • 2014(Publication Date)
  • CRC Press

    (Publisher)

  Over reasonably small temperature ranges, the expansion in any direction (or in volume) is fairly linear as a function of temperature. A common example of Thermal Expansion is the liquid in a liquid-bulb thermometer, in which you see a liquid moving along a linear temperature scale marked on the tube. Different materials exhibit different rates of expansion. The coefficient of volume expansion measures a material’s fractional volume change per degree of temperature change. Generally, liquids expand more than solids over the same temperature range. Liquid water is an interesting exception. At temperatures of 4°C and above, water behaves normally and expands as its temperature rises. But between 0°C (the freezing point) and 4°C, water has the opposite behavior, expanding as it gets colder. This unusual behavior affects the formation of ice. Near the freezing point, colder water has lower density, which makes ice form at the water’s surface rather than below. Once the ice forms, it stays at the surface because its density (about 920 kg/m 3) is lower than water’s (1000 kg/m 3). The surface ice insulates the water below, which restricts the rate of ice formation. This keeps an entire lake from freezing and allows aquatic life to survive below the ice through the winter. When the water is warmer (all above 4°C), the cooler water is denser and hence closer to the bottom, making it cooler as you dive down. Engineers and construction workers need to take Thermal Expansion into account or else catastrophic failure can result. Bridges, road surfaces, and railroad tracks have to be built with gaps that allow the materials to expand on hot days. If those gaps are too small, the expanding material can buckle and deform

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  eBook - ePub

  Materials Under Extreme Conditions

  Recent Trends and Future Prospects

  • A.K. Tyagi, S. Banerjee, A. K. Tyagi(Authors)
  • 2017(Publication Date)
  • Elsevier

    (Publisher)

  Thus it can be inferred that the Thermal Expansion of solids is nothing but expansion of chemical bonds. In other words, Thermal Expansion of solids is related to their chemical bonding strength, which in turn is related to the lattice energy. The crystal structure also has a dominant role in governing Thermal Expansion behavior, which will be discussed in a subsequent section of this chapter. In summary, the Thermal Expansion of a solid can be correlated with the nature and strength of the chemical bond, mass of the vibrating atoms, melting point, and crystal structure (e.g., packing fraction). It may be added here that all of these factors that influence Thermal Expansion behavior are also interrelated. 3. Experimental Techniques for Thermal Expansion Measurements The instrumentation for measurement of Thermal Expansion of solids has a rich history. In an early stage, marker comparison methods were used for this purpose, which were rather crude and were applicable for materials exhibiting larger expansion. Presently, sophisticated and automated Thermal Expansion measurement instruments like the thermodilatometer and interferometers are being employed. The principles and procedures of measurement of Thermal Expansion of solids have been elaborated extensively [ 13 – 17 ]. As discussed earlier, Thermal Expansion can be classified as bulk and lattice Thermal Expansion. The measurement of bulk Thermal Expansion involves a direct measurement of the change in dimension as a function of temperature, which can be done by a thermodilatometer or interferometer. As far as the lattice Thermal Expansion is concerned, diffraction methods like variable temperature X-ray or neutron diffraction are used. Usually Thermal Expansion of a material at a given temperature is measured with respect to a reference temperature, which is often room temperature

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  eBook - ePub

  Understanding Physics

  • Michael M. Mansfield, Colm O'Sullivan(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  −2 .

  For problems based on the material presented in this section visit up.ucc.ie/11/ and follow the link to the problems.

  11.8 Thermal Expansion

  To a greater or lesser extent most substances expand on being heated; for example, the expansion of the liquid in a glass thermometer. While the amount of expansion of a solid or a liquid can be relatively small, gases can expand considerably even for small rises in temperature. When the rise in the temperature of a body is not too large, it is found experimentally that the fractional increase in the volume is directly proportional to the rise in temperature, that is

  or

  (11.9)

  the constant of proportionality being characteristic of the material involved. Since changes in volume can also be produced by changing the pressure on the body (elastic deformation, as discussed in Section 10.2 ), it is clear that the experimental result quoted above can only be valid if ΔV is caused by the change in temperature only; that is if the pressure is held constant throughout the experiment. The constant of proportionality in Equation (11.9) is called the cubic expansion coefficient of the material and is defined as

  Note the use of the partial derivative notation (Appendix A.6.3 ) to indicate the change in volume with respect to a change in one variable (temperature in this case) while another (pressure) is held constant. From its definition, the SI unit of

  αV

  can be seen to be

  K−1

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  Experiments and Demonstrations in Physics

  Bar-Ilan Physics Laboratory

  • Yaakov Kraftmakher(Author)
  • 2014(Publication Date)
  • WSPC

    (Publisher)

  equilibrium point defects in crystal lattice. The Thermal Expansion of materials is very important for many technical applications.

  The linear Thermal Expansion of a solid, ΔL, is a nonlinear function of temperature:

  where L0 is the length of the sample at a reference temperature, usually 293 K.

  The coefficient of linear Thermal Expansion, or linear expansivity, is

  The expansivity usually increases with temperature. For anisotropic crystals, the linear expansivity depends on the orientation of the sample. At temperatures below the Debye temperature, the expansivity rapidly decreases when decreasing temperature. For metals, the higher the melting temperature Tm , the lower the mean expansivity. For many metals, the total linear expansion from the absolute zero to the melting point amounts to 2–3%. This simple rule may serve for estimating the mean expansivity of metals. As an example, values of the linear expansivity of copper and tungsten recommended by White and Minges (1997) are shown (Fig. 1 ). For both metals, the total expansion from absolute zero to melting points is nearly 2.5%. The significant nonlinear increase of the expansivity of tungsten at high temperatures is probably caused by the formation of equilibrium point defects (vacancies) in the crystal lattice. For copper, the effect is not so strong. The reason is that the maximum equilibrium vacancy concentration (at the melting point) in copper is much less than in tungsten. Similar nonlinear effects at high temperatures are seen in the specific heat of metals (Kraftmakher 2000a).

  Brief review of dilatometeric techniques. Modern methods for measuring the dilatation of solids provide sensitivity of the order of 10–10 m and even better. Along with a significant progress in traditional dilatometry

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  eBook - ePub

  The Handy Physics Answer Book

  • Charles Liu(Author)
  • 2020(Publication Date)
  • Visible Ink Press

    (Publisher)

  THERMODYNAMICS

  What is thermodynamics?

  Thermodynamics is the study of the change of thermal energy in objects and materials that makes them warm and cold, how they interact with each other, and the relationship between energy, heat, and work. It can be a challenging area of physics, in part because most of the vocabulary dates from the time before scientists understood what makes an object hot. Terms like “heat,” “heat capacity,” and “latent heat” suggest that warm objects contain some material that reacts to temperature. It wasn’t until the early 1800s that our present understanding started to develop. Some 200 years later, our common usage of these terms is still based on earlier ideas.

  What is thermal energy?

  Thermal energy is the random kinetic energy of the moving particles—such as atoms and molecules—that make up matter. Objects expand when heated, so the bonds holding the particles together stretch. That means they have more elastic energy. So, thermal energy is the sum of the kinetic and elastic energy of the atoms and molecules and the bonds that hold them together. It is energy that is inside the object, so it is called a form of internal energy.

  THERMAL PHYSICS

  Who discovered what makes an object hot?

  Benjamin Thompson, Count Rumford (1753–1814), who was born in the Massachusetts Bay Colony but did most of his scientific work in the Kingdom of Bavaria (which is now part of Germany), deserves a great deal of credit in discovering what makes things hot. Before his experiments, most scientists thought that hot objects contained an invisible fluid called caloric. Experiments done before Rumford showed that when you heated an object it didn’t gain weight, so caloric must be weightless as well as invisible. This result made many scientists suspicious of the caloric explanation.

  In 1789 Rumford drilled holes in bronze cannons through which a cannonball would be shot. He found that both the cannon and the metal chips that resulted from the drilling became hot. He determined the amount of water that could be raised to the boiling point by both the cannon bodies and the chips and showed that the caloric theory did not agree with his results. He finally concluded that in hot objects, the particles that made up the material moved faster than they moved in cold objects. Using our present terminology, they had more kinetic energy. In their motion they vibrate back and forth; they do not move together from one place to another like a thrown ball.

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  eBook - ePub

  Physics I Workbook For Dummies with Online Practice

  • (Author)
  • 2021(Publication Date)
  • For Dummies

    (Publisher)

  Part 4

  Obeying the Laws of Thermodynamics

  IN THIS PART … Discover how heat makes items expand. See how heat is produced, and understand the relationship among the pressure, volume, and temperature of a gas. Check out the laws of thermodynamics that govern heat processes.

  Passage contains an image Chapter 12

  You’re Getting Warm: Thermodynamics

  IN THIS CHAPTER

  Converting between temperature scales

  Working with linear expansion

  Calculating volume expansion

  Using heat capacities

  Understanding latent heat

  Thermodynamics is the study of heat. It’s what comes into play when you drop an ice cube into a cup of hot tea and wait to see what happens — if the ice cube or the tea wins out.

  In physics, you often run across questions that involve thermodynamics in all sorts of situations. This chapter refreshes your understanding of the topic and lets you put it to use with practice problems that address thermodynamics from all angles.

  Converting between Temperature Scales

  You start working with questions of heat by establishing a scale for measuring temperature. The temperature scales that you work with in physics are Fahrenheit, Celsius (sometimes called centigrade), and Kelvin.

  Fahrenheit temperatures range from 32° for freezing water to 212° for boiling water. Celsius goes from 0° for freezing water to 100° for boiling water. Following are the equations you use to convert from Fahrenheit (F) temperatures to Celsius (C) and back again:

  The Kelvin (K) scale is a little different: Its 0 corresponds to absolute zero, the temperature at which all molecular motion stops. Absolute zero is at a temperature of −273.15° Celsius, which means that you can convert between Celsius and Kelvin this way:

  To convert from Kelvin to Fahrenheit degrees, use this formula:

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