Section Summary

Section Summary

13.1 Temperature

  • Temperature is the quantity measured by a thermometer.
  • Temperature is related to the average kinetic energy of atoms and molecules in a system.
  • Absolute zero is the temperature at which there is no molecular motion.
  • There are three main temperature scales: Celsius, Fahrenheit, and Kelvin.
  • Temperatures on one scale can be converted to temperatures on another scale using the following equations:
    TºF=95TºC+32TºF=95TºC+32 size 12{T rSub { size 8{°F} } = { {9} over {5} } T rSub { size 8{°C} } +"32"} {}
    TºC=59TºF32TºC=59TºF32 size 12{T rSub { size 8{°C} } = { {5} over {9} } left (T rSub { size 8{°F} } - "32" right )} {}
    TK=TºC+273.15TK=TºC+273.15 size 12{T rSub { size 8{K} } =T rSub { size 8{°C} } +"273" "." "15"} {}
    TºC=TK273.15TºC=TK273.15 size 12{T rSub { size 8{°C} } =T rSub { size 8{K} } - "273" "." "15"} {}
  • Systems are in thermal equilibrium when they have the same temperature.
  • Thermal equilibrium occurs when two bodies are in contact with each other and can freely exchange energy.
  • The zeroth law of thermodynamics states that when two systems, A and B, are in thermal equilibrium with each other, and B is in thermal equilibrium with a third system, C, then A is also in thermal equilibrium with C.

13.2 Thermal Expansion of Solids and Liquids

  • Thermal expansion is the increase, or decrease, of the size—length, area, or volume—of a body due to a change in temperature.
  • Thermal expansion is large for gases, and relatively small, but not negligible, for liquids and solids.
  • Linear thermal expansion is
    ΔL=αLΔT,ΔL=αLΔT, size 12{ΔL=αLΔT} {}
    where ΔLΔL size 12{ΔL} {} is the change in length LL size 12{L} {}, ΔTΔT size 12{ΔT} {} is the change in temperature, and αα size 12{α} {} is the coefficient of linear expansion, which varies slightly with temperature.
  • The change in area due to thermal expansion is
    ΔA=2αAΔT,ΔA=2αAΔT, size 12{ΔA=2αAΔT} {}
    where ΔAΔA size 12{ΔA} {} is the change in area.
  • The change in volume due to thermal expansion is
    ΔV=βVΔT,ΔV=βVΔT, size 12{ΔV=βVΔT} {}
    where ββ size 12{β} {} is the coefficient of volume expansion and ββ size 12{β approx 3α} {}. Thermal stress is created when thermal expansion is constrained.

13.3 The Ideal Gas Law

  • The ideal gas law relates the pressure and volume of a gas to the number of gas molecules and the temperature of the gas.
  • The ideal gas law can be written in terms of the number of molecules of gas
    PV=NkT,PV=NkT, size 12{ ital "PV"= ital "NkT"} {}
    where PP size 12{P} {} is pressure, VV size 12{V} {} is volume, TT size 12{T} {} is temperature, NN size 12{N} {} is number of molecules, and kk size 12{k} {} is the Boltzmann constant
    k=1.38×1023 J/K.k=1.38×1023 J/K. size 12{k=1 "." "38" times "10" rSup { size 8{–"38"} } " J/K"} {}
  • A mole is the number of atoms in a 12-g sample of carbon-12.
  • The number of molecules in a mole is called Avogadro’s number NANA size 12{N rSub { size 8{A} } } {}:
    NA=6.02×1023mol1.NA=6.02×1023mol1. size 12{N rSub { size 8{A} } =6 "." "02" times "10" rSup { size 8{"23"} } `"mol" rSup { size 8{ - 1} } } {}
  • A mole of any substance has a mass in grams equal to its molecular weight, which can be determined from the periodic table of elements.
  • The ideal gas law can also be written and solved in terms of the number of moles of gas
    PV=nRT,PV=nRT, size 12{ ital "PV"= ital "nRT"} {}
    where nn size 12{n} {} is number of moles and RR size 12{R} {} is the universal gas constant
    R=8.31J/molK.R=8.31J/molK. size 12{R=8 "." "31"`"J/mol" cdot K} {}
  • The ideal gas law is generally valid at temperatures well above the boiling temperature.

13.4 Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature

  • Kinetic theory is the atomistic description of gases as well as liquids and solids.
  • Kinetic theory models the properties of matter in terms of continuous random motion of atoms and molecules.
  • The ideal gas law can also be expressed as
    PV=13Nmv2¯,PV=13Nmv2¯, size 12{ ital "PV"= { {1} over {3} } ital "Nm" {overline {v rSup { size 8{2} } }} ,} {}
    where PP size 12{P} {} is the pressure (average force per unit area), VV size 12{V} {} is the volume of gas in the container, NN size 12{N} {} is the number of molecules in the container, mm size 12{m} {} is the mass of a molecule, and v2¯v2¯ size 12{ {overline {v rSup { size 8{2} } }} } {} is the average of the molecular speed squared.
  • Thermal energy is defined to be the average translational kinetic energy KE¯KE¯ size 12{ {overline {"KE"}} } {} of an atom or molecule.
  • The temperature of gases is proportional to the average translational kinetic energy of atoms and molecules
    KE¯=12mv2¯=32kTKE¯=12mv2¯=32kT size 12{ {overline {"KE"}} = { {1} over {2} } m {overline {v rSup { size 8{2} } }} = { {3} over {2} } ital "kT"} {}


    v2¯=vrms=3kTm.v2¯=vrms=3kTm. size 12{ sqrt { {overline {v rSup { size 8{2} } }} } =v rSub { size 8{"rms"} } = sqrt { { {3 ital "kT"} over {m} } } "." } {}
  • The motion of individual molecules in a gas is random in magnitude and direction. However, a gas of many molecules has a predictable distribution of molecular speeds, known as the Maxwell-Boltzmann distribution.

13.5 Phase Changes

  • Most substances have three distinct phases: gas, liquid, and solid.
  • Phase changes among the various phases of matter depend on temperature and pressure.
  • The existence of the three phases with respect to pressure and temperature can be described in a phase diagram.
  • Two phases coexist, that is, they are in thermal equilibrium, at a set of pressures and temperatures. These are described as a line on a phase diagram.
  • The three phases coexist at a single pressure and temperature. This is known as the triple point and is described by a single point on a phase diagram.
  • A gas at a temperature below its boiling point is called a vapor.
  • Vapor pressure is the pressure at which a gas coexists with its solid or liquid phase.
  • Partial pressure is the pressure a gas would create if it existed alone.
  • Dalton’s law states that the total pressure is the sum of the partial pressures of all of the gases present.

13.6 Humidity, Evaporation, and Boiling

  • Relative humidity is the fraction of water vapor in a gas compared to the saturation value.
  • The saturation vapor density can be determined from the vapor pressure for a given temperature.
  • Percent relative humidity is defined to be
    percent relative humidity=vapor densitysaturation vapor density×100.percent relative humidity=vapor densitysaturation vapor density×100. size 12{ size 11{"percent relative humidity"= { { size 11{"vapor density"}} over { size 11{"saturation vapor density"}} } times "100" "." }} {}
  • The dew point is the temperature at which air reaches 100 percent relative humidity.