Heat Transfer

Background on Heat Transfer

Last week we were introduced to the concept of heat. We saw that Heat is the total internal kinetic energy of the atoms and molecules that make up a substance. Since heat is a form of energy, it is measured in Joules.

• 1 Joule = 1 N*m = 1 kg m/s² * m
• 1 calorie is the heat energy needed to raise 1 gram of water by 1 degree Celsius.
• 1 calorie = 4.186 Joules.
• 1 Calorie = 1000 calories.

The transfer of heat is normally from a high temperature object to a lower temperature object. Heat transfer changes the internal energy of both systems involved according to the First Law of Thermodynamics.

Heat can be transferred by:

• Conduction
• Convection
• Advection
• Radiation

Conduction

Conduction is the transfer of heat within a substance, molecule by molecule. If you put one end of a metal rod over a fire, that end will absorb the energy from the flame (this is radiation transferring energy). The molecules at this end of the rod will gain energy and begin to vibrate faster. As they do their temperature increases and they begin to bump into the molecules next to them. The heat is being transfered from the warm end to the cold end.

                       
The measurement of how well a material can conduct heat depends on how it's molecules are structurally bonded together. This is a listing of the heat conductivity of various substances:

As you can see air does not conduct heat very well. This is the idea behind a styrofoam coolers, the air pockets between the styrofoam beads do not conduct heat very well. On the other hand, metals do conduct heat very well. This is why metal seems cold when you touch it. The metal molecules are conducting your body heat away from your hand quickly.

Convection

Convection is heat transfer by the mass movement of a fluid in the vertical (up/down) direction. This type of heat transfer takes place in liquids and gases. This occurs naturally in our atmosphere.

Warm air is less dense than cold air, making cold air heavier than warm air. On a sunny day, the surface of the Earth is heated by radiation from the Sun. The thin layer of molecules touching the surface are heated by conduction. We know air is a poor conductor of heat, so this warm mass of air near the surface can not immediately transfer its heat away from the surface by conduction. This warm air mass is buoyant and wants to rise upward because it is less dense, the heavy cold air takes the place of the warm bubble. This rising warm light air is called a thermal in meteorology.

In lecture you learned that the pressure of the air decrease with height. This is an important fact for the life of these rising thermals. Recall, ^P/_ρT = R, from the ideal gas law. For a rising thermal, you can think of this thermal as a parcel or a balloon, there will be less pressure exerted on its wall as it rises. Therefore, the parcel will expand and the temperature within the parcel will decrease.

These warm thermals cool as they rise. In fact, the cooling rate as a parcel rises can be calculated:

If the thermal consists of dry air, it cools at a rate of 9.8°C/km as it rises.

Advection

Advection is the transfer of heat in the horizontal (north/east/south/west) direction. In meteorology, the wind transports heat by advection. This happens all the time on Earth, heat is transported in many ways. For example, wind blowing over a body of water will pick up evaporated water molecules and carry them elsewhere, when the air with these water molecules cools, the water will condense and release latent heat. The heat is being transfered by the wind.

Advection is very similar to Convection, however, it is in the horizontal and not vertical.

Radiation

Radiation allows heat to be transfered through wave energy. These waves are called Electromagnetic Waves, because the energy travels in a combination of electric and magnetic waves. This energy is released when these waves are absorbed by an object. For example, energy traveling from the sun to your skin, you can feel your skin getting warmer as energy is absorbed.

The energy a wave carries is related to its wavelength (measured from crest to crest). Shorter wavelengths carry more energy than longer wavelengths. Wavelengths are measured in terms of meters:

• 1 (millimeter) mm = .001 m = 10^-3 m
• 1 (micrometer) μm = .000001 m = 10^-6 m
• 1 μm is 1 millionth of a meter. One-hundredth the diameter of a human hair.
• 1 (nanometer) nm = .000000001 m = 10^-9 m

All things with a temperature above absolute zero emit radiation. Everything, your body, your desk, your house, grass, snow, the atmosphere, the moon, they all emit a wide range of radiation. The source of this electromagnetic radiation are vibrating electrons that exist in every atom that makes an object.

Emitted radiation can be:

• Absorbed
  Increasing the internal energy of the gas molecules.
• Reflected
  Radiation is not absorbed or emitted from an object but it reaches the object and is sent backward. The Albedo represents the reflectivity of an object and describes the percentage of light that is went back.
• Scattered
  Scattered light is deflected in all directions, forward, backward, sideways. It is also called diffused light.
• Transmitted
  Radiation not absorbed, reflected, or scattered by a gas, the radiation passes through the gas unchanged.

The temperature of an object can tell us something about the emitted radiation.

• The Stefan-Boltzmann law tells us that as the temperature of an object increases, more radiation is emitted each second.
  E = σT⁴
  where σ is a constant, T is the temperature of an object in Kelvin and E is the maximum rate of radiation emitted per meter².
• Wien's law describes the maximum wavelength that an object emits based on it's temperature.
  λ_max = ^θ/_T
  where λ_max is the wavelength in micrometers (μm) at which the maximum radiation emission occurs, θ is a constant equal to 2897 μm K, and T is the temperature in Kelvin.

For the Earth, T~300 K:

λ_max = ^θ/_{300 K} ~ 10 μm
For the Sun, T~6000 K:

λ_max = ^θ/_{6000 K} ~ 0.5 μm
The Sun emits in shortwave radiation where as the Earth emits in longwave radiation.
                  

Our eyes are sensitive to visible light, with wavelengths between 0.4 and 0.7 μm. This happens to be the range at which the Sun emits its peak wavelengths of radiation. In fact, 44% of the Sun's radiation is within the visible spectrum. Over time, our eyes have evolved to see this peak wavelength.

Kirchhoff's Law says that good absorbers of a particular wavelength are also good emitters of that wavelength, and poor absorbers of a wavelength are also poor emitters at the same wavelength.

Our atmosphere has a several gases that are selective absorbers of radiation. These gases include:

• Water vapor (H₂O)
• Carbon Dioxide (CO₂)
• Nitrous Oxide (N₂O)
• Methane (CH₄)
• Ozone (O₃)

How does Earth's atmosphere deal with solar radiation?

Out of 100% how much is reflected to space? How much is absorbed by the atmosphere? by the surface?
                  

Summary

Describe what is going on and how each method of heat transfer works in this example:

Heat Transfer and the Atmosphere