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 Bénard (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 Bénard 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.

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