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Section Summary

14.1 Heat

  • Heat and work are the two distinct methods of energy transfer.
  • Heat is energy transferred solely due to a temperature difference.
  • Any energy unit can be used for heat transfer, and the most common are kilocalorie (kcal) and joule (J).
  • Kilocalorie is defined to be the energy needed to change the temperature of 1.00 kg of water between 14.5 ºC14.5 ºC and 15.5 ºC15.5 ºC.
  • The mechanical equivalent of this heat transfer is 1.00 kcal=4186 J.1.00 kcal=4186 J.

14.2 Temperature Change and Heat Capacity

  • The transfer of heat QQ size 12{Q} {} that leads to a change ΔTΔT size 12{ΔT} {} in the temperature of a body with mass mm size 12{m} {} is Q=mcΔT,Q=mcΔT, size 12{Q= ital "mc"ΔT} {} where cc size 12{c} {} is the specific heat of the material. This relationship can also be considered as the definition of specific heat.

14.3 Phase Change and Latent Heat

  • Most substances can exist either in solid, liquid, and gas forms, which are referred to as phases.
  • Phase changes occur at fixed temperatures for a given substance at a given pressure, and these temperatures are called boiling and freezing—or melting—points.
  • During phase changes, heat absorbed or released is given by
    Q=mL,Q=mL, size 12{Q= ital "mL"} {}

    where LL size 12{L} {} is the latent heat coefficient.

14.4 Heat Transfer Methods

  • Heat is transferred by three different methods: conduction, convection, and radiation.

14.5 Conduction

  • Heat conduction is the transfer of heat between two objects in direct contact with each other.
  • The rate of heat transfer Q/tQ/t size 12{Q/t} {} (energy per unit time) is proportional to the temperature difference T2−T1T2−T1 size 12{T rSub { size 8{2} } - T rSub { size 8{1} } } {} and the contact area AA size 12{A} {} and inversely proportional to the distance dd size 12{d} {} between the objects
    Qt=kAT2−T1d.Qt=kAT2−T1d. size 12{ { {Q} over {t} } = { { ital "kA"` left (T rSub { size 8{2} } - T rSub { size 8{1} } right )} over {d} } } {}

14.6 Convection

  • Convection is heat transfer by the macroscopic movement of mass. Convection can be natural or forced and generally transfers thermal energy faster than conduction. Table 14.4 gives wind-chill factors, indicating that moving air has the same chilling effect of much colder stationary air. Convection that occurs along with a phase change can transfer energy from cold regions to warm ones.

14.7 Radiation

  • Radiation is the rate of heat transfer through the emission or absorption of electromagnetic waves.
  • The rate of heat transfer depends on the surface area and the fourth power of the absolute temperature
    Qt=σeAT4,Qt=σeAT4, size 12{ { {Q} over {t} } =σ`e`A`T rSup { size 8{4} } } {}

    where σ=5.67×10−8J/s⋅m2⋅K4σ=5.67×10−8J/s⋅m2⋅K4 is the Stefan-Boltzmann constant and ee size 12{e} {} is the emissivity of the body. For a black body, e=1e=1 whereas a shiny white or perfect reflector has e=0e=0, with real objects having values of ee between 1 and 0. The net rate of heat transfer by radiation is

    Q net t = σ e A T 2 4 − T 1 4 Q net t = σ e A T 2 4 − T 1 4 size 12{ { {Q rSub { size 8{"net"} } } over {t} } =σ`e`A` left (T rSub { size 8{2} } rSup { size 8{4} } - T rSub { size 8{1} } rSup { size 8{4} } right )} {}

    where T1T1 size 12{T rSub { size 8{1} } } {} is the temperature of an object surrounded by an environment with uniform temperature T2T2 size 12{T rSub { size 8{2} } } {} and ee size 12{e} {} is the emissivity of the object.