Lecture 26

• temperature

  • a quantitative measure of how hot or cold an object is relative to a standard reference
  • Kelvin (K) is the SI unit
  • Celsius is widely used
  • a change in temperature of 1 K is the same as a change of 1 C
  • two scales are offset 0 c = 273.15 K
  • temperature has a lower limit, absolute zero: 0 k = -273.15 C
  • no upper limit 100,000,000 K has been achieved in a lab
• triple point of water

  unique reference point 0.01 C 0.006 Atm more dependable than melting or boiling points used for precisely calibrating thermometers
• heat and energy

  thermal energy is associates with the energy of motion of molecules and atoms

  in a fluid this motion is free and random

  in a solid the average position of the molecule or atom stays the same and thermal energy is associated with vibrations
• adding heat to an object usually increases its temperature
• $dQ\ =$$\ c_pm\ \cdot\ dT$ where dQ is the heat added cpm is the thermal capacity and dT is the change in temperature
• the amount of heat Q (J) needed to increase the temperature of an object by 1 K depends on its mass m (kg) and a property of the material called its specific heat capacity cp (this is at constant pressure)
• latent heat

  materials can exist in different forms - solids, liquid, gas - called phases. at special temperatures, there will be a change of phase - melting or boiling. at the melting or boiling point, adding more heat converts the material from solid to liquid or from liquid to gas without changing the temperature
• the amount of heat needed to change unit mass from solid to liquid (e.g. ice to water) or vice versa is the latent heat of melting or latent heat of freezing
• the amount of heat needed to change unit mass from liquid to gas (e.g. water to steam) or vice versa is the latent heat of evaporation or latent heat of condensation
• heat flows from hot to cold bodies in three ways: conduction, convection and radiation
• conduction involves heat diffusing through a material that itself does not move. where the heat is applied, the atoms and molecules vibrate more energetically, knock against their neighbors and so make them vibrate too. thermal energy is passed on. this is the main heat transfer mechanism in the Earth's lithosphere (outer ~100 km)
• when a material is heated, it expands and so becomes less dense and therefore buoyant - it has a tendency to float up towards the surface. when it cools it contracts and becomes denser acquiring a tendency to sink. in a gas or liquid there are not forces holding the atoms or molecules in place, so this tendency is not resisted. a warm parcel of fluid will rise and a cold parcel will sink. this behavior is convection. this is the main heat transfer mechanism in the Earth's mantle and outer core
• energy is transmitted by electromagnetic radiation - all objects emit radiation (hotter objects emit more). radiation can pass through a vacuum (e.g. space) and is reflected/absorbed when it encounters matter - this limits passage of radiation through media e.g. light from the sun is absorbed/reflected by the atmosphere and surface of Earth. light penetrates a few 10s of metres into the oceans, ~1 m into ice but <1 mm into solid rocks. radiation is the dominant form of heat transfer in the atmosphere but can be largely neglected in the Earth's interior. electromagnetic radiation at longer wavelengths is used in various geophysical surveying methods
• observations that constrain deep Earth temperature

  from temperature measurements in mines and boreholes (within a few km of surface) T increases with depth at ~30 K/km implies center of Earth ~20,000 K (too high). seismology shows outer core is liquid and inner core is solid. mean density of Earth ~5500 km m^-3 so core must have high density and magnetic field - mainly iron so melting point of iron at core pressures constrains the temperature to a certain range. ellipsoidal shape - pressures in the Earth are near hydrostatic. lab experiments at high pressures can determine melting point of iron
• hydrostatic equation: dp/dz = ρg
• Iron’s melting point at 340-380 GPa is ~5500K (quite uncertain)
• $\frac{dT}{dz}=$$\frac{Tαg}{c_p}$ α is the volume coefficient of the expansion (fractional change in volume per unit change in temperature), cp is the specific heat capacity at constant p g changes with depth (and falls to zero at center of Earth)
• can also calculate theoretically how the melting temperature (solidus) varies with depth
• high T gradients indicate conduction in boundary layers e.g. near surface
• less steep gradients are near adiabatic and indicate convection
• newer estimates have hotter core and bigger jump at core-mantle boundary. also shallower T-gradient in mantle