Chapter 16: Heat Transfer

Two objects at different temperatures can share their energies through Heat Transfer where energy flows (heat transferred) from the higher temperature material to the lower temperature material through one of three mechanisms: conduction, convection, and/or radiation transport.

The transfer lasts as long as a temperature difference exists. The transfer is not instantaneous; it takes a finite amount time. The time taken for temperatures to equalize is given by the mechanism which transports the energy. The nature of heat transfer gives rise to a conundrum in the field of cosmology, a problem known as the Horizon Problem.

At left, examples of each mode of transport are shown: heat is conducted by the metal pan, heat is convected by the roiling water, and energy is transferred by the radiation produced by the hot embers of the fire.


Conduction

Heat transfer through Conduction usually refers to heat flow through solids, however, it also applies to liquids and gases under certain conditions. The flow of heat in conductions is carried by paticles, such as electrons.

The flame is applied to the left end of the bar. The bar gets hotter ===> particles start to vibrate and move and around faster (at higher energies).

The excited particles then collide with neighboring particles sharing their energy. This causes heat transfer to the right. For most materials, it is the light, mobile electrons that drive the transfer.

The efficiency of the transfer depends on how freely the electrons can move, which depends strongly on the stuctures of the materials (because this depends on how electrons are bond or not bond to their atoms or molecules).

Some materials are very adept at transporting energy, Conductors (most metals), others are not Insulators (things like wood, paper, styrofoam, and most gases and liquids).


Convection

Heat transfer through Convection refers to heat flow through liquids and gases, materials that can flow acted by some force, such as gravity. The flow of heat in convection is not carried by the motions of individual paticles such as was the case for conduction. The flow of heat in convection is carried by large-scale motions of the fluid.

The flame is applied to the bottom (in the sense that gravity points downward) of the pan. The fluid at the bottom of the pan gets hotter ===> particles start to move around faster (at higher energies) and expand and gets less dense. If conduction was efficient enough to transport heat and keep the fluid cool, no motions would arise. However, it turns out conduction is not efficient enough and the fluid heats and expands ===> buoyancy grows and makes the fluid rise as it heats and becomes less dense than the surrounding, cooler gas.

Eventually, the fluid loses heat (cools), and becomes denser than its surrounding and sinks. This process sets up a circulation pattern.

Convection drives several important processes on the Earth, for example, Plate Tectonics, atmospheric circulation.

Usually on the Earth, convection transports heat upward (opposite to gravity's pull). It does not transfer heat downward. This is different from conduction which can transport heat downward.


Coastal Breezes

The heat capacity of water is large compared to the heat capacity of soil (land). This has consequences for coastal winds.

  • During the day, the land heats more quickly (to higher T) than the ocean because the heat capacity of the land is smaller than that of the ocean. The higher T means that the pressure over land is higher and the air expands a little, gets less dense and rises. The warm rising air is replaced by cooler air which flows in from the ocean. The warmer air circulates over the ocean where it cools and flows downard to eventually cycle inward.

  • At night, the land cools more quickly (to lower T) than the ocean because the heat capacity of the land is smaller than that of the ocean. The higher T over the ocean means that the pressure over the water is larger and the warmer material expands a little, gets less dense and rises. The warm rising air is replace by cooler air which flows from the land. The warmer air circulates over the land where it cools and flows downard to eventually cycle outward.


Radiation Transport

We see the Sun because it produces electromagnetic radiation (see Chapter 26, Electromagnetic Radiation). I can see you (and you can see me) because electromagnetic is reflected off of you and is directed to me, The warmth of a fire can be felt by campers because of electromagnetic radiation produced by the burning wood. This form of heat transfer, radiation transport, is the last of those that play large roles in our daily lives.

Here, we do not consider the nature of electromagnetic radiation other than to say it is produced by charged particles and travels through space as a wave, an electromagnetic wave.

The wavelength of a wave is the distance between the crests of the wave. The frequency of a wave is the rate at which waves pass by. Because all electromagnetic waves travel at the same speed, the speed of light, short wavelength waves have high frequency.

The energy carried by electromagnetic radiation depends on the wavelength of the radiation; the shorter the wavelength (the greater the frequency), the more energy the wave carries.

Electromagnetic radiation of different wavelengths (frequencies) are called by different names. This is an arbitrary distinction. The electromagnetic radiation to which our eyes are sensitive is the visible portion of the electromagnetic spectrum. In order of increasing wavelength (decreasing frequency and energy) the parts of the electromagnetic spectrum are gamma-rays, x-rays, ultraviolet (UV), visible (optical), infrared (IR), microwave, and radio waves.

Although light from the Sun appears white and colorless, it is actually a blend of wavelengths (colors) which is apparent when we separate the light using some sort of device (such as a prism or a water droplet).


Heating and Cooling By Radiation

Hot dense objects like stars (and the Universe, see left) radiate in a manner similar to materials known as Blackbodies. Blackbodies are defined not by their emission properties but rather, by their ability to absorb electromangetic radiation. Above, we see objects coated with aluminum, silicon, and aluminum nitride, and an object coated with the blackest material yet made (reflects < 0.1 % of incident light).

    Blackbodies are materials that are perfect absorbers of radiation. No radiation which strikes a blackbody is reflected, 100 % of it is absorbed. This leads to the materials name, blackbody. The material appears black because it reflects no electromagnetic radiation. Lighter colored objects likely reflect light, absorb electromagnetic radiation less effectively.

    Q: What is a better color to wear in sunny climates? in cold climates?

The processes of absorption and emission are opposites (inverses) of each other. It turns out that good absorbers are also expected to be good emitters of radiation. This property allows us to calculate the emission properties of blackbodies. The theory for blackbody radiation was worked out in the 1800s by Planck. Planck's theory for these idealized objects capable of perfect absorption and so perfect emission led to the development of Quantum Mechanics and to one of the major physics revolutions in the early 1900s.


Heating and Cooling

An object gains heat by absorbing radiation (H) and loses heat by emitting radiation (C). So, whether an object heats or cools is determined by which process wins.

  • If H > C ===> object heats
  • If H < C ===> object cools

The rate at which an object heats or cools is determined by

  • The difference in temperature of the object and its source of heating. If there is no difference in temperature, then H and C will be in balance and no cooling or heating occurs.

    The rate at which heating and cooling takes place is roughly proportional to the difference in temperatures, Newton's Law.

Q: Does a cup of hot black coffee cool at a faster rate than a cup of lukewarm black coffee? Which cup takes longer to cool to room temperature?

Q: Does a cup of hot black coffee cool at a faster rate than a cup of hot coffee with milk? Which cup takes longer to cool to room temperature?

Q: Does a bowl of hot water cool at a faster rate than a bowl of cold water in the freezer of your refrigerator? Which takes longer to freeze (to turn to ice)?


Greenhouse Effect

An important effect in which radiation transport plays a huge role is the Greenhouse Effect. Venus has a Runaway Greenhouse Effect while the Earth has a mild Greenhouse Effect. The Greenhouse Effect raises the surface temperature of a planet. Today Venus has a surface temperature of 462 degrees Celsius while the Earth has an average surface temperature of around 14 degrees Celsius. Although low, the current temperature on the Earth would be much lower if we had no atmosphere (and no Greenhouse Effect), the expected temperature would be below the freezing point of water.

We are saved by our mild Greenhouse Effect


How Does the Greenhouse Effect Work?

Sunlight and Wien's Law

The Sun has surface temperature 5,527 degrees Celsius (5,800 Kelvin) while the surface temperature of the Earth is around 10-15 degrees Celsius (283 Kelvin).

Does this large temperature difference have an effect?

Yes. The temperature of a hot, dense object like the Sun and the surface of the Earth, controls the energy of the electromagnetic radiation produced. We can estimate the radiation properties of such objects because they resemble the idealized materials known as Blackbodies, the perfect absorbers of radiation mentioned above. For blackbodies, we know that the hotter is a source of radiation, the more energetic will be the electromagnetic radiation produced (the higher the resultant frequency of the peak radiation produced). The precise relationship for blackbodies and thus objects like the Sun is given by Wien's Law (shown in the Figure to the right of the Sun). The Sun (temperature of around 5,700 Kelvin) has peak power output in the visible band of the electromagnetic spectrum, according to Wien's Law. The temperature of the Earth, on average, is 10-15 degrees Celsius (temperature of 280-290 Kelvin) and the Earth radiates lower energy radiation at peak output than does the Sun. The Earth radiates Infrared radiation (IR) according to Wien's Law.

    Q: At what energies would a person radiate electromagnetic energy?

What are the consequences of the different energies for Solar and Terrestrial radiation?

The Greenhouse Effect

The atmosphere of the Earth is made up of 79 % nitrogen molecules, 21 % oxygen molecules with trace amounts of water vapor and carbon dioxide. The water vapor and carbon dioxide are both Greenhouse Gases. The materials in the atmosphere of the Earth allow visible light and parts of the UV from the Sun to pass through the atmosphere and to strike the surface of the Earth. This includes the water vapor and carbon dioxide. Because the temperature of the Earth is 10-20 degrees Celsius, the absorbed energy is re-radiated in the Infrared (IR) portion of the electromagnetic spectrum.

This has the following consequences:

  • The water vapor and carbon dioxide are efficient absorbers of IR and so they trap radiant energy in the atmosphere.

  • This heats the atmosphere and causes it to re-radiate energy; half going upward and half going downward. This is bad because only one-half of the energy is re-radiated to space; the Earth experiences a net gain of energy and so is out-of-balance.

    What happens?

    The energy directed downward gets absorbed by the surface, heating the surface. This causes the surface to heat a little more and to re-radiate energy at a slighter greater rate. This slightly increases the energy radiated to space.

  • This process continues to heat the surface of the Earth until the energy radiated to space exactly equals the energy input at the top of the atmosphere.

  • When the surface heats to the point where half of its re-radiated energy balances the heat input, it stops heating.

    • On Venus, because the atmopsheric pressure is 90 bars (and so very massive compared to the Earth) and the atmosphere is composed of 96 % carbon dioxide, this is a huge effect and there is a fierce Greenhouse Effect.

    • On the Earth with our trace amounts of water and carbon dioxide, we have only a mild Greenhouse Effect.