Thermal Expansion

10 Key excerpts on "Thermal Expansion"

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  College Physics

  • Paul Peter Urone, Roger Hinrichs(Authors)
  • 2012(Publication Date)
  • Openstax

    (Publisher)

  The same happens in all liquids and gases, driving natural heat transfer upwards in homes, oceans, and weather systems. Solids also undergo Thermal Expansion. Railroad tracks and bridges, for example, have expansion joints to allow them to freely expand and contract with temperature changes. What are the basic properties of Thermal Expansion? First, Thermal Expansion is clearly related to temperature change. The greater the temperature change, the more a bimetallic strip will bend. Second, it depends on the material. In a thermometer, for example, the expansion of alcohol is much greater than the expansion of the glass containing it. What is the underlying cause of Thermal Expansion? As is discussed in Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature, an increase in temperature implies an increase in the kinetic energy of the individual atoms. In a solid, unlike in a gas, the atoms or molecules are closely packed together, but their kinetic energy (in the form of small, rapid vibrations) pushes neighboring atoms or molecules apart from each other. This neighbor-to-neighbor pushing results in a slightly greater distance, on average, between neighbors, and adds up to a larger size for the whole body. For most substances under ordinary conditions, there is no preferred direction, and an increase in temperature will increase the solid’s size by a certain fraction in each dimension. Linear Thermal Expansion—Thermal Expansion in One Dimension The change in length ΔL is proportional to length L . The dependence of Thermal Expansion on temperature, substance, and length is summarized in the equation (13.7) ΔL = αLΔT , where ΔL is the change in length L , ΔT is the change in temperature, and α is the coefficient of linear expansion, which varies slightly with temperature. Table 13.2 lists representative values of the coefficient of linear expansion, which may have units of 1 / ºC or 1/K.

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  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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  University Physics Volume 2

  • William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
  • 2016(Publication Date)
  • Openstax

    (Publisher)

  Thermal Expansion in Two and Three Dimensions Unconstrained objects expand in all dimensions, as illustrated in Figure 1.7. That is, their areas and volumes, as well as their lengths, increase with temperature. Because the proportions stay the same, holes and container volumes also get larger with temperature. If you cut a hole in a metal plate, the remaining material will expand exactly as it would if the piece you removed were still in place. The piece would get bigger, so the hole must get bigger too. Thermal Expansion in Two Dimensions For small temperature changes, the change in area ΔA is given by (1.3) ΔA = 2αAΔT where ΔA is the change in area A, ΔT is the change in temperature, and α is the coefficient of linear expansion, Chapter 1 | Temperature and Heat 15 which varies slightly with temperature. Figure 1.7 In general, objects expand in all directions as temperature increases. In these drawings, the original boundaries of the objects are shown with solid lines, and the expanded boundaries with dashed lines. (a) Area increases because both length and width increase. The area of a circular plug also increases. (b) If the plug is removed, the hole it leaves becomes larger with increasing temperature, just as if the expanding plug were still in place. (c) Volume also increases, because all three dimensions increase. Thermal Expansion in Three Dimensions The relationship between volume and temperature dV dT is given by dV dT = βV ΔT , where β is the coefficient of volume expansion. As you can show in Exercise 1.60, β = 3α . This equation is usually written as (1.4) ΔV = βV ΔT . Note that the values of β in Table 1.2 are equal to 3α except for rounding. Volume expansion is defined for liquids, but linear and area expansion are not, as a liquid’s changes in linear dimensions and area depend on the shape of its container. Thus, Table 1.2 shows liquids’ values of β but not α . In general, objects expand with increasing temperature.

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  Electronic Materials

  Principles and Applied Science

  • Yuriy 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 - PDF

  Introduction to Physics

  • John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
  • 2015(Publication Date)
  • Wiley

    (Publisher)

  The plate and the ball have the same temperature at all times. Should the plate and ball both be heated or both be cooled to prevent the ball from falling through the hole? 12.5 | Volume Thermal Expansion The volume of a normal material increases as the temperature increases. Most solids and liquids behave in this fashion. By analogy with linear Thermal Expansion, the change in volume DV is proportional to the change in temperature DT and to the initial volume V 0 , provided the change in temperature is not too large. These two proportionalities can be converted into Equation 12.3 with the aid of a proportionality constant b, known as the coefficient of volume expansion. The algebraic form of this equation is similar to that for linear expansion, DL 5 aL 0 DT. Volume Thermal Expansion The volume V 0 of an object changes by an amount DV when its temperature changes by an amount DT: DV 5 bV 0 DT (12.3) where b is the coefficient of volume expansion. Common Unit for the Coefficient of Volume Expansion: (C8) 21 The unit for b, like that for a, is (C8) 21 . Values for b depend on the nature of the ma- terial, and Table 12.1 lists some examples measured near 20 8C. The values of b for liquids are substantially larger than those for solids, because liquids typically expand more than solids, given the same initial volumes and temperature changes. Table 12.1 also shows that, for most solids, the coefficient of volume expansion is three times as much as the coefficient of linear expansion: b 5 3a. If a cavity exists within a solid object, the volume of the cavity increases when the ob- ject expands, just as if the cavity were filled with the surrounding material. The expansion of the cavity is analogous to the expansion of a hole in a sheet of material. Accordingly, the change in volume of a cavity can be found using the relation DV 5 bV 0 DT, where b is the coefficient of volume expansion of the material that surrounds the cavity.

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  Physics

  • John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
  • 2018(Publication Date)
  • Wiley

    (Publisher)

  The plate and the ball have the same temperature at all times. Should the plate and ball both be heated or both be cooled to prevent the ball from falling through the hole? 12.5 Volume Thermal Expansion The volume of a normal material increases as the temperature increases. Most solids and liquids behave in this fashion. By analogy with linear Thermal Expansion, the change in volume ΔV is proportional to the change in temperature ΔT and to the initial volume V 0 , provided the change in temperature is not too large. These two proportionalities can be converted into Equation 12.3 with the aid of a proportionality constant , known as the coefficient of volume expansion. The algebraic form of this equation is similar to that for linear expansion, ΔL = L 0 ΔT. A B C Brass Lead Steel (a) A B C Lead Brass Steel (b) FIGURE 12.18 Conceptual Example 7 discusses the arrangements of the three cylinders shown in cutaway views in parts a and b. CYU FIGURE 12.1 Aluminum frame Rod Small gap shows the lead cylinder as the outer cylinder C. It will fall off as the tem- perature is raised, since lead expands more than steel. The brass inner cyl- inder A expands more than the steel cylinder that surrounds it and becomes tightly wedged, as observed. Similar reasoning applies also to Figure 12.18b, which shows the brass cylinder as the outer cylinder and the lead cylinder as the inner one, since both brass and lead expand more than steel. 338 CHAPTER 12 Temperature and Heat VOLUME Thermal Expansion The volume V 0 of an object changes by an amount ΔV when its temperature changes by an amount ΔT: ∆V = βV 0 ∆T (12.3) where β is the coefficient of volume expansion. Common Unit for the Coefficient of Volume Expansion: (C°) –1 The unit for , like that for , is (C°) −1 . Values for  depend on the nature of the material, and Table 12.1 lists some examples measured near 20 °C.

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  Cutnell & Johnson Physics, P-eBK

  • John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler, Heath Jones, Matthew Collins, John Daicopoulos, Boris Blankleider(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  The algebraic form of this equation is similar to that for linear expansion, ΔL = L 0 ΔT. Volume Thermal Expansion The volume V 0 of an object changes by an amount ΔV when its temperature changes by an amount ΔT : ΔV =  V 0 ΔT (12.3) where  is the coefficient of volume expansion. Common unit for the coefficient of volume expansion: (C°) −1 The unit for  , like that for , is (C°) −1 . Values for  depend on the nature of the material, and table 12.1 lists some examples measured near 20 °C. The values of  for liquids are substantially larger than those for solids, because liquids typically expand more than solids, given the same initial volumes and temperature changes. Table 12.1 also shows that, for most solids, the coefficient of volume expansion is three times as much as the coefficient of linear expansion:  = 3. 324 Physics If a cavity exists within a solid object, the volume of the cavity increases when the object expands, just as if the cavity were filled with the surrounding material. The expansion of the cavity is analogous to the expansion of a hole in a sheet of material. Accordingly, the change in volume of a cavity can be found using the relation ΔV =  V 0 ΔT, where  is the coefficient of volume expansion of the material that surrounds the cavity. Example 8 illustrates this point. EXAMPLE 8 The physics of the overflow of an automobile radiator A small plastic container, called the coolant reservoir, catches the radiator fluid that overflows when an automo- bile engine becomes hot (see figure 12.19). The radiator is made of copper, and the coolant has a coefficient of volume expansion of  = 4.10 × 10 −4 (C°) −1 .

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  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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  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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  Physics

  • John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
  • 2015(Publication Date)
  • Wiley

    (Publisher)

  The algebraic form of this equation is similar to that for linear expansion, DL 5 aL 0 DT. Volume Thermal Expansion The volume V 0 of an object changes by an amount DV when its temperature changes by an amount DT: DV 5 bV 0 DT (12.3) where b is the coefficient of volume expansion. Common Unit for the Coefficient of Volume Expansion: (C8) 21 The unit for b, like that for a, is (C8) 21 . Values for b depend on the nature of the ma- terial, and Table 12.1 lists some examples measured near 20 8C. The values of b for liquids are substantially larger than those for solids, because liquids typically expand more than solids, given the same initial volumes and temperature changes. Table 12.1 also shows that, for most solids, the coefficient of volume expansion is three times as much as the coefficient of linear expansion: b 5 3a. If a cavity exists within a solid object, the volume of the cavity increases when the ob- ject expands, just as if the cavity were filled with the surrounding material. The expansion of the cavity is analogous to the expansion of a hole in a sheet of material. Accordingly, the change in volume of a cavity can be found using the relation DV 5 bV 0 DT, where b is the coefficient of volume expansion of the material that surrounds the cavity. Example 8 illustrates this point. Coolant reservoir Radiator Figure 12.19 An automobile radiator and a coolant reservoir for catching the overflow from the radiator. EXAMPLE 8 | The Physics of the Overflow of an Automobile Radiator A small plastic container, called the coolant reservoir, catches the radiator fluid that overflows when an automobile engine becomes hot (see Figure 12.19). The radiator is made of copper, and the coolant has a coefficient of volume expansion of b 5 4.10 3 10 24 (C8) 21 . If the radiator is filled to its 15-quart capacity when the engine is cold (6.0 8C), how much overflow will spill into the reservoir when the coolant reaches its operating temperature of 92 8C?

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