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Chapter 13 Learning Objectives

Concepts and Skills to Review

  • Energy conservation (Sections 6.3, 6.6, 6.7)
  • Momentum conservation (Section 7.4)
  • Collisions (Sections 7.7, 7.8)

Summary

  • Temperature is a quantity that determines when objects are in thermal equilibrium. The flow of energy that occurs between two objects or systems due to a temperature difference between them is called heat flow. If heat can flow between two objects or systems, the objects or systems are said to be in thermal contact. When two systems in thermal contact have the same temperature, there is no net flow of heat between them; the objects are said to be in thermal equilibrium.
  • Zeroth law of thermodynamics: if two objects are each in thermal equilibrium with a third object, then the two are in thermal equilibrium with each other.
  • The SI unit of temperature is the kelvin (symbol K, without a degree sign). The kelvin scale is an absolute temperature scale, which means that T = 0 is set to absolute zero.
  • Temperature in °C (TC) and temperature in kelvins (T) are related as follows:
     TC = T – 273.15 K(13-3)
  • As long as the temperature change is not too great, the fractional length change of a solid is proportional to the temperature change:
     <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/57996/image13_4.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> (13-4)
    The constant of proportionality, α, is called the coefficient of thermal expansion of the substance.
  • The fractional change in volume of a solid or liquid is also proportional to the temperature change as long as the temperature change is not too large:
     <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/57996/image13_7.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> (13-7)
    For solids, the coefficient of volume expansion is three times the coefficient of linear expansion: β = 3α.
  • The mole is an SI base unit and is defined as follows: one mole of anything contains the same number of units as there are atoms in 12 grams (not kilograms) of carbon-12. This number is called Avogadro's number and has the value
     NA = 6.02 × 1023 mol-1 
  • The mass of a molecule is often expressed in the atomic mass unit (symbol u). By definition, one atom of carbon-12 has a mass of 12 u (exactly).
     1 u = 1.66 × 10-27 kg(13-12)
    The atomic mass unit is chosen so that the mass of a molecule in 'u' is numerically the same as the molar mass in g/mol.
  • In an ideal gas, the molecules move independently in free space with no interactions except when two molecules collide. The ideal gas is a useful model for many real gases, provided that the gas is sufficiently dilute. The ideal gas law:
     microscopic form: PV = NkT(13-13)
     macroscopic form: PV = nRT(13-16)
    where Boltzmann's constant and the universal gas constant are
     k = 1.38 × 10-23 J/K(13-14)
     <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/57996/image13_15.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> (13-15)
  • According to kinetic theory, the pressure of a gas is proportional to the average translational kinetic energy of the molecules:
     <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/57996/image13_18.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> (13-18)
  • The average translational kinetic energy of the molecules is proportional to the absolute temperature:
     <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/57996/image13_20.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> (13-20)
  • The speed of a gas molecule that has the average kinetic energy is called the rms speed:
     <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/57996/image13_21.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> (13-21)
  • The distribution of molecular speeds in an ideal gas is called the Maxwell-Boltzmann distribution.
  • If the activation energy for a chemical reaction is much greater than the average kinetic energy of the reactants, the reaction rate depends exponentially on temperature:
     <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/57996/image13_24.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> (13-24)
  • The mean free path (Λ) is the average length of the path traveled by a gas molecule as a free particle (no interactions with other particles) between collisions:
     <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/57996/image13_25.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> (13-25)
  • The root mean square displacement of a diffusing molecule along the x-axis is
     x2rms = <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/57996/image13_26b.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a> (13-26)
    where D is a diffusion constant.







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