PY 131 Chapter 16: Heat Transfer

Heat Transfer

  • Heat moves due to temperature differences.
  • Heat energy always moves from hot to cold.
  • Heat is transferred from one object to another via three mechanisms:
      * Conduction
      * Convection
      * Radiation
  • During conduction the atoms/molecules of the object transferring the heat do not move.
      * Conduction is the only method of moving heat through a solid.
  • During convection the atoms/molecules do move.
      * Convection occurs in liquids and gases.
  • During radiation heat (energy) is transferred through space by electromagnetic waves (light) or gravitational waves.

Conduction

  • Conduction is the flow of energy between objects or from one object to another due to collisions between the atoms/molecules and without net motion of the material.
      * No net motion means the body does not move as a whole i.e. there is no bulk flow.
  • Conduction can occur in solids, liquid and gases.
  • In a solid the atoms are largely confined and collisions are the main mechanism by which the heat flows.
  • In a liquid or gas the heat flows due to collisions of the atoms/molecules but also atoms/molecules can diffuse.
  • Materials through which heat travels easily are called ==(thermal) conductors.==
      * Examples include metals, diamond (diamond is 250% better thermal conductor than copper).
  • Materials through which heat travels with difficulty are called ==(thermal) insulators.==
      * Examples include glass, wood, plastic, air.
EXAMPLE 1

If you hold one end of a metal bar against a piece of ice, the end in your hand will become cold. In which direction is energy moving?

  • ==From your hand to the ice==

Convection

  • Convection is heat transfer through an object due to the bulk motion of the material.
  • Convection requires there be a net force on a fluid element.
  • Convection can occur in different ways depending upon the force e.g. buoyant convection or forced convection.
      * In buoyant convection, the force is buoyancy so buoyant convection requires there be gravity – without it buoyant convection cannot occur.
      * Forced convection is when you blow or pump the fluid.
  • Consider a ‘fluid element’ with density ρb
      * Here b stands for ‘bubble’.
  • The surrounding fluid has the same density ρ.
  • What happens if this element moves upward by an amount Δy?
  • The density will change to ρb +Δρb .
  • At the new location, the surrounding fluid has a density ρ +Δρ.
  • If ρb +Δρb < ρ+Δρ then the element will continue to rise due to the buoyancy force and the fluid is unstable to convection.
  • Since ρb = ρ the criterion for instability is that Δρb < Δρ or Δρb Δ y ≀ Δρ Δ y A buoyantly convecting fluid forms BĂ©nard (convection) cells.

 

  • High-resolution images of the Sun show its surface is broken up into granules: http://www.youtube.com/watch?v=W_Scoj4HqCQ
  • The BĂ©nard cells on the Sun are huge: each is ~1000 km across and lives for ~ 10 minutes.
  • Careful observations indicate there are also supergranuales which are of order 30,000 km in size.
      * It is thought these may be the imprint of deeper lying convective cells.
  • Convection is responsible for sea breezes.
      * The land heats the air above it better than the water heats the air above it.
      * The density of the air over the land decreases causing it to float (rise).
      * The air over the sea is pushed in by pressure forces in to replace it.

Newton’s Law of Cooling

  • Consider two points in space separated by a distance Δx and with a temperature difference ΔT.
  • The ratio of ΔT to Δx is called the temperature gradient.
      * ΔT/Δx
  • The temperature gradient (which is a vector) will cause an amount of heat ΔQ to flow between the points in a time Δt.
  • The thermal current I is
      * I= ΔQ / Δt
  • It is found from the experiment that the thermal current is proportional to the temperature gradient.
      * I ∝ - (ΔT/Δx)
      * The minus sign is because heat flows from hot to cold.
  • This relationship is called ==Newton’s Law of Cooling.==
  • The larger the temperature difference, the faster a hot object loses energy or a cool object gains it.
  • As the object cools, the heat flow slows down.
  • In addition to the temperature gradient, the thermal current depends on the contact area and what the material is.
      * The smaller the contact area the smaller the heat flow.
      * Heat finds it harder to pass through some materials than others.
  • Newton’s Law of Cooling works well for conduction. For convective cooling it works if the cooling liquid/gas is pumped/forced/blown: if the convective cooling is buoyancy driven then it doesn’t work as well.
      * It doesn’t take into account the fluid speed.
EXAMPLE 1

Why does it take an ice cube longer to melt on a winter day than on a summer day?

  • ==The atmosphere is cooler==

Radiation

  • Heat Transfer by Radiation is the transfer of heat via the emission and absorption of light.
  • All objects with a temperature emit light.
      * This is not the light reflected from a light source e.g. the Sun.
  • Usually, we don’t notice this radiation because, at typical everyday temperatures, the emitted light is mostly infrared.
      * It takes temperatures of ~ 500 Celsius before the emitted light starts to
        become visible light.
      * At very high temperatures the emitted light can be UV or X-rays.
  • The emission of radiation causes an object to cool.
      * it’s the emission of radiation into space that cools the Earth at night.
  • The temperature of an object is related to the frequency or wavelength of the light it emits which has the maximum intensity

 

  • This relationship is known as ==Wien's Displacement Law==.
  • When radiation is incident upon an object, some of the light is absorbed, some is reflected, and some passes through.
      * The absorbed radiation will cause an increase in the object’s
        temperature.
      * The absorption of radiation emitted by the Sun heats the Earth during the day.
  • An object which absorbs all the radiation incident upon it is called a blackbody.
  • Objects which are good emitters of radiation are also good absorbers of radiation (and vice versa).
  • To make life complicated, the amount of radiation absorbed and emitted depends on the type of light.
      * Some objects reflect visible light well but absorb all the IR, for example.
  • Assuming a black object is black for all types of light, and a white object is white for all types of light, a black object radiates energy faster than a white object.
  • An object’s opacity is a measure of the amount of light it absorbs as light travels through the object.
  • The opacity can change with the ‘type’ of light.
      * an object (e.g. glass) can be very transparent to visible light but not transparent (opaque) to infrared or UV.
  • The opacity of the atmosphere is very important to astronomers.
      * If the atmosphere is opaque, a telescope can’t see through it.

 

The Greenhouse Effect

  • It is the difference of the opacity of the atmosphere to visible and infrared light which keeps Earth warmer than it should be given our distance from the Sun.
  • If Earth were a blackbody with no atmosphere it would have an average temperature of ~ +5 °C.
  • Given that Earth reflects about 30% of the incident sunlight, an Earth without an atmosphere would have an average temperature of ~ -20 °C.
  • Earth’s actual average temperature is ~ +15 °C.
  • The Sun emits a lot of its light as visible light. Visible light can largely pass through the atmosphere and be absorbed by the Earth causing Earth to be heated.
  • Earth emits most of its radiation as infrared light.
  • This should cool the Earth but the atmosphere is opaque to infrared light so energy gets absorbed.
  • The heated atmosphere radiates some of its energy back toward the Earth.
  • The net effect is that radiation finds it difficult to escape and the Earth is warmer than it would be if it could easily escape.
  • This is called the ==Greenhouse Effect.==
      * Even though actual greenhouses work slightly differently.
  • The same effects occur on other planets or moons with atmospheres.
      * On Venus the Greenhouse Effect has runaway and the temperature is 450 °C.
  • The gases in Earth’s atmosphere which absorb most of the infrared radiation are water vapor and carbon dioxide.
  • The amount of these gases in the atmosphere changes over time due to natural processes such as volcanoes, ice ages, sun cycles etc.
      * It even changes over the cycle of the year.
  • Over the last 200 years the amount of carbon dioxide in the atmosphere has roughly doubled.
  • Since 1960 the average temperature of the Earth has increased by ~1 °C.