www.lsmsa.edu teacher Robert Dalling's Physics Lectures (see also www.ushumans.net)

Heat

            Phenomena that involve heat are now seen to be yet another example of motion and so are not a unique or independent aspect of nature. The equations for phenomena involving heat were obtained in the last three centuries. These equations provide mathematical relationships between an object's temperature, pressure, volume, and its type of material and physical structure. It has been found that a material's temperature is a measure of the speed of its constituent atoms. The atoms of a gas bounce around, colliding with other atoms and with the walls of the container. The pressure of a gas is due to the force of the atoms colliding with the container walls. In this way it has been found that heat phenomena are also described by Newton's motion equation. That is, heat is not a separate phenomenon but is another aspect of motion. The atoms of a hotter material are jiggling faster than are those of cooler ones. When a fast moving atom runs into a slow moving atom, it is slowed by the collision; the slower atom’s speed is increased. This transfer of the speed-of-motion from one atom to another is the flow of heat. Your food heats as its slower-moving atoms are brought in contact with the more energetic atoms of the surrounding fire or air. (A microwave oven passes electromagnetic waves through food in order to make the atoms of the food wiggle more quickly and become hotter.) Other examples of heat machines include steam, gasoline, and diesel engines.

                        Temperature and Heat

When one particle bounces off a wall it imparts a force on the wall that is equal and opposite to the force of the wall on it, which is F = dp/dt. These two forces are equal and oppposite.

F(wall on particle) - F(particle on wall)

or

dp(wall)/dt = -dp(particle)/dt

Both share the same time so we can cancel dt. Remember p=mv.

dpwall=-dpparticle = -( pfinal - pinitial )

but pfinal = - pinitial so the right hand side is

                       = 2pinitial

Consider a particle in a cubical box whose sides have length l.

The particle's motion equation is x=vxt. The time needed to travel from one wall to the other is t(traverse box) = l/vx. If we want to consider only the right-hand wall then the particle has to travel a distance 2l between collisions, and then the number of right-hand wall collisions per second the particle makes is

1/2t(traverse) = vx/(2l). The time between right-hand wall collisions is 2l/vx.

These collisions result in a force per unit time of

        dp(wall)=2pinitial

Fwall = ------- ---------

         time time

        = 2mvx = mvx2/l

          ---

          2l/vx

When many molecules, Nm, are bouncing off the wall we have the total force from the total momentum change is

Fwall = Nmmvx2/l

A particle bounces around the box colliding with other particles, its direction of movement will sometimes be along x, sometimes along y, and sometimes along the z axis.

Or, we can believe that just one-third of the particles will be moving along the x-axis, one-third along the y-axis, and one-third along the z-axis. So we divide this force on one wall by one-third to switch from one- to three-dimensional force.

Or, since v = vx + vy + vz and vx=vy=vz on average then in Fwall you can replace vx with v/3 to switch from 1-dimensional vx to three dimensional velocity v.

The pressure (big 'P') P = force / area of all these collisions is

Pressure=Fwall/Area = Nmmv2/3l3 = Nmmv2/3V where V=Volume of box=l3.

         = 2/3 times NmK/V where K = kinetic energy of the particle.

If this wall were a piston inside a car motor or some hydraulic machine, then the wall can be pushed to the right. You can connect rod and geared wheels to harness this kinetic energy. If you alternatingly heat and cool the gaseous contents of the container then the force on the right-hand wall or piston increases and decreases. The wall moves back and forth and makes a gear rotate.

So we have

PV = 2/3 Nm K

   = 2/3 Ktot, where Ktot = Nm K

This is two-thirds of the total kinetic energy of the atoms in the gas. Daniel Bernoulli derived this in 1738 for a colection of Nm particles--before atoms were known.

Think of using those spring-loaded guns to shoot a huge number of metal spheres at the wall. The force per unit area will be 2/3 the total kinetic energy.

Since Nm = ( number of moles )( Avogadro's number, which is particles per mole ) = n Na we can write PV as

PV = 2/3 nNa K

It was experimentally found that PV=nRT at room temperatures achievable during the 1650s-1850s. This is the "Ideal Gas Law." We can identify

RT = 2/3 Na K (1)

Notice that temperature is a measure of average v2 or K of the atoms within the gas.

R is the ideal gas constant

R = 8.31 J / mol K°

  = 0.08207 liter atm per mole per K°

R is the energy added to each mole to increase its temperature by one degree.

But temperature T must be expressed in Kelvin degrees,

where Kelvin degrees = Centigrade degrees + 273

See problem 2A on page 278: K° = 150°C + 273 = 423 K (no degree sign needed)

The ratio R/Na occurs frequently and has been named k, the Boltzmann constant 8.31 J / mol K°

with kB = R/Na we get for (1) kNaT = 2/3 Na K

cancel Na and arrange as K = 1/2 mv2 = 3/2 kBT (2)

This means that the average kinetic energy per molecule depends only on it temperature, not on the pressure or volume. The speeds here are average speeds. The Maxwell velocity distribution gives probability of particular speeds.

It turns out that any energy going as the square of a coordinate contibutes 1/2kT to the total energy, e.g potential energy of a spring. We get 3/2kt from vx2+vy2+vz2. A molecule consisting of two atoms held together by electrical attraction act as two masses on a spring. Count the number of degrees of freedom of a system.

If you mix gases of two differing chemicals, equating their temperatures in (2) means that T1=T2 or 2/3 K1/k = 2/3 K2/k or K1=K2 or m1v12 = m2v22 or v12/v22 = m2/m1

The ratio of squares of average speeds is inversely proportional to masses. The lighter species diffuses more quickly across a room. (Separate chemicals by diffusion.) Took a one square mile building to do this in 1942 to get enough fissionable U235 or 238. Other nations are kept from building uranium bombs by monopolizing the world's uranium supply. Quickly smash two 11-kg halves together and you get a bomb.

Fisher went north and hated Feynman. He worked on device making it explode at the desired height above ground using air pressure. His wife wrote a book about cooking at 8000 foot elevation.

Separate two cubes of gas, each at a different temperature.

Heat is the flow of kinetic energy from one material to another.

Two separated containers of differing temperatures.

       ┌─────────┬┬────────┐

       │ ││ │

       │ T1 ││ T2 │

       │ ││ │

       │ ││ │

       └─────────┴┴────────┘

T1 > T2 so K1 > K2

Remove the division and collisions transfer speed to colder side. This flow of kinetic energy is the flow of heat.

Difference between heat and temperature.

Temperature gives the kinetic energy of an atom. Heat is a measure of total energy. There is more heat in a bucket of water at 50° than in a cup at 50° because there are more atoms moving at speed 1/2mv2 = 3/2 kT.

The adjacent atoms forming solid matter can be viewed to be held together by springs: a 3-d cube of spring-held atoms. Atoms oscillate about their home location within the crystal. The electric force can be modelled as a spring force. The more their kinetic energy the more their temperature. When they get enough energy an atom will break free from its neighbors=melt. When an atom gets moe than a couple of atoimic diameters away then it can no onger be held in place.

The total energy of constituent particles = kinetic energy of motion plus stored potential energy.

In an ideal gas, the stored energy is zero so total energy = K

PV=nRT

We'll get back to PV=nRT in the next chapter.

Heat transfer by conduction, convection, radiation.

Conduction: flow of kinetic energy through collisions. How much energy flows across an area:

The heat gained or lost Q by a mass m when going from an initial to a final temperature is

Q = mCdt = mC( Tfinal - Tinitial )

Q absorbed is positive (dt>0), negative is heat released (dT<0)

C = measured specific heat capacaity = joules per centigrade degree per kilogram of matter. See table of C values on page 279. for water, C=4186 J/kgC°

Example: problem 23 page 296. Raise temperature of 0.050 kg of water from 4.5 to 83.0 °C? Q=mC(Tf-Ti)=(0.050 kg)(4186 J/kgC°)(83.0-4.5C°) = 16400 J.

CQ: problem 25 page 296.

How much heat absorbed when m=0.4 kg glass at T=20.0°C placed into water at T=100.0 °C?

Q=mCdt=(0.4 kg)(664 J/kgC°)(80.0 - 20.0 C°)=15900 J.

            Mixing substances of differing temperatures

Combine 2 kg of water at 80 °C with 6 kg of water at 20 °C. What is the final temperature of the mix?

Conservation of energy:

Heat lost by hoter water = Heat absorbed by cooler water

mhCdth = mcCdtc

(cancel Cs, most problems involve differing materials and Cs)

mh(Th-T) = mc(T-Tc)

mhTh-mhT = mcT-mcTc

mhTh + mcTc = mcT + mhT = (mc + mh)T

so T= (mhTh + mcTc)/(mc + mh)=(2x80 + 6x20)/(2+6)=35 °C which is an intermediate temperature.

Who already mixed two materials at differing temperature in a cup in chemistry class?

                              Melting

Water freezes at 0°C. Heat ice from -50°C to 0°C, then at 0° it turns out tht heat continues to be absorbed as electrical-spring bonds are being broken within the solid crystal structure, without a further increase of temperature until all the ice is melted. Then the now liquid material's temperature wil again increase as heat continues flowing into the water. (Change of phase indicated by a region of constant temperature during continued heat absorption--true in elementary particle physics, too.) Keep heating the water until it begins to boil. Stays at same temperature until all is boiled. See figure on page 286.

Hf = heat of fusion = heat needed to melt a kg

For ice, Hf = 3.34 x 105 J/kg

Heat of vaporaiztion = energy needed to vaporize (turn to steam)

For water, Hv = 2.26 x 106 J/kg

See chart on page 287 for measured H values needed for homework.

Example, problem 32 on page 297:

Ice box differs from fridgerator. How much heat is absorbed to melt 20 kg of ice. Q = mHf = (20 kg)(3.34 x 105 J/kg) = 6.68 x 106 J. The temperature of the melted ice is stil 0 °C. The temperature of this melted water can then begin to rise to room temperature.

Some homework problems begin with ice and end with steam. You'll hve to raise its temperature to melting point, then melt it, then raise it to vaporization point, then raise it beyond.

                   The Maxwell speed distribution

              . cold T

  │ . .

  │ . ° warm T

  │ . ° . °

  │  °

  │ . °  .  ° hot T

  │ °. ° 

  └──────────────────────────────────

The distribution of instantaneous speeds within a gas follow a Maxwellian curve. f(v)=constant times (m/T)**3/2 v2 exp(-mv2/2kT), where T can be written in terms of the average speed or average kinetic energy 1/2mv2=3/2kT. This distribution is measured by driling a small hole in a container. Those atoms moving along +x axis (hole) escape the container and pass through a couple plates then into a hole in another container having a rotating drum. The fast and slow molecules take difering times to traverse to the other side of the rotating drum where they stick and pile up. Measuring the thickness of the deposited silver gives f(v). Or have two rotating slits to select velocites traversing the separation between those disks.

On our skin, the faster moving molecules escape (evaporate) first leaving slower ones behind with a lower temperature. Evaporation is a cooling effect. We sweat to cool off. We have sweat glands all over. Less voluminous mammals have greater surface area per unit mass and want to retain heat so they have fewer sweat glands. A dog cools off by evaporating from its tongue not its skin. Its tongue provides enough cooling while we need to sweat from our entire bodies.

                           Heat examples

C = specific heat = ability to hold heat or energy needed to raise temp. Water holds more heat than metal. A potato takes longer to heat up and to then cool down. Thermal bump of a city because concrete and such holds more heat than simple landscape of bushes and trees. A lake moderates temperature swings of nearby area. Animals hold heat in their volume and radiate it through their surface. A 100-lb dog is the transistion between radiating and holding heat. Elephants are all volume. Before moon landings one scientist measured surface rate of heating and cooling during sun appearance-disappearance of potential moon landing locations to know if the surface consisted of house-sized boulders or fine grains. Didn't want the spaceship to crash land on boulders. Also, the lunar lander was very shiny so that it would reflect sunlight, otherwise its temperature would go to 100 °F. This had to be thought out before going. Black car interior gets hotter than does a white interior.

Takes a long time to cook food or boil water. Temperature changes slowly. Heat moves slowly = flow of kinetic energy from atomic collisions. Many processes occur in so little time that no heat flows in or out of the system: the P, V, and T of a little cube of air as a sound wave passes through it. An explosion occurs in too little time for heat to flow in or out. A cube of air might flow up and then down a 100 foot tall hill in a few minutes without heat flowing in or out.

Heat passes rapidly through a metal because of its "free" electrons. Put a metal rod through a potato and it will cook more quickly.

            From ushumans: After talking about the effects of us humans on our own environment, let’s talk about the direct effects of our environment on our appearance. We do this by taking a brief digression on physics to help explain the size, shape, and color of objects which are the most effective at removing excessive heat or cold. A warm object cools by releasing heat through its surface. An object retains warmth if it has lots of volume but little surface area. For this reason, the size and shape of humans varies with climate. At the warm, sunny equator we are tall and thin so that we are more easily cooled. In polar areas, we retain more heat by being shorter and rounder so that we have more volume and less surface area. We humans are also found to have darker colored skin when living near the equator and lighter colored skin when living near the poles. Dark skin helps reflect sunlight–especially ultraviolet light–while light skin absorbs more sunlight. Light skin also avoids the rickets caused by a lack of sunlight–as occurs in northern, cloud-filled latitudes. The color of our skin shows our relationship to the Earth and its latitudes. One anthropologist made a globe of the Earth with each region colored like that of local human skin. Humans are also about 10 percent smaller in height and size whenever we live in year-round highly-humid locations because the decreased sweat evaporation makes a larger volume harder to cool.

                              Entropy

Count the number of ways in which the total energy of a system can be divided among the constituents of the system. In any process, this count always increases. Entropy is the log of this number of ways to divy the energy of an evolving system. The log is the number of digits needed to write down the number of ways to divy. Entropy is the number of digits needed to write down the number of ways to divy the energy. This entropy is also a measure of the amount of information known about a system.

The number of ways you can divide the (kinetic) energy of a collection of atoms in a gas is given by the Maxwellian speed distribution.

T cold is narrow. There isn't much range in the speeds so there is a smaller number of ways of dividing up the energy than occurs with T hot. We see that the colder distribution has fewer speeds (kinetic energies) than the hotter temperature. More disorder or randomness seen in T hot than in T cold.

This determines the number of ways to divide the energy. Add up all the f(v) to get total number of speeds, take the log.

macroscopically delta S = delta Q / T

Consider a 1-d tube with momentum-reflecting ends. The tube contains two particles having speeds v1 and v2 and masses m1 and m2. Given initial v1 and v2 what combinations of v1 and v2 will occur through time? How many different vs are possible when 3 atoms repeatedly collide? n? with lots o atoms, there is more chance that a head on collision will result in a zero speed. The T hot curve has a more evenly spread out distribution and has more at the edges. The T cold shows most atoms having the middle speed and few at the extremes.

Poetically, entropy is a measure of the disorder or randomness in a system, as in a photo of a junk yard or the bedroom on page 293. This is vague, misleading, and subject to wild misinterpretation.

The Second Law of Thermodynamics states that natural processes go in the way that maintains or increases the total entropy of the system. Lost energy in a cycle of a heat engine appears as increased entropy.

                    First Law of Thermodynamics

A gas contains an internal energy that is the sum of the kinetic energies of the constituent atoms.

For a gas pushing a piston a distance d outward:

W=Fd=PA delta d=P delta V.

The work is done by a gas expanding its volume. This decreases the internal energy of the gas. The atoms rebound with decreased speed after colliding with the piston that then moves outward.

The internal energy of a gas increases if heat Q flows inward. This inward flow of heat means faster moving atoms brought into contact with the gas resulted in increased kinetic energies of the gas atoms.

Thermal energy of a meterial increased by doing work on it or heating it. (Doing work is negative, releasing heat is negative).

The first law of thermodynamics is a statment of the conservation of energy: dU = dQ - PdV = heat flow in minus work done by the system.

Picture the gas expanding against the piston. The gas is heated by burning fuel within and then does work to move the piston. The burnt fuel is then exhausted, new fuel brought in, and repeated.

When a material freezes, its stored energy is released. The surroundings will warm a bit. Move the frozen material to another place and let it melt and that region will absorb energy.

A refrigerator does the heat releasing expansion outside the container, then moves the cooler fluid into the container to absorb heat from the contents. The contents are cooling but the room is warming. Leave the door open and you'll heat the room.

The heat engine always consists of a cycle. It starts and ends in the same situation. Some useful work is done with each cycle. The second law says we can't convert 100% of stored heat energy to useful work. Yuo can dissipate energy of motion entirely into heat but you can't convert heat energy entirely into motion. Systems or processes (nature) flows in one direction. The arrow of time. Salt dissolves in water but never undissolves. Heat moves from hot to cold, not in reverse.

                  The Second Law of Thermodynamics

Heat flows from a hot body to a cold one and never in the reverse direction. In a cyclic engine, some energy is always waisted.

                               PV=nRT

PV=nRT: ( or P=density times rT)

Volume = understood

n=number of moles

Pressure: one atmosphere is the weight of air above a square meter of ground = 1.013 x 105 N/m2 or pascals (Pa) = 14.7 lbs/in2. This is the weight of water 32 feet = highest vacuum distance. Pascal made a barometer out of 40 feet of red wine. To avoid having smelly, spoiled wine, he had to replace the red wine each day.

Pressure studied as vacuum pumps were being made. In 1655, Otto von Guericke connected two hal-spheres and then removed the air from them. And it required 8 horses on each side to pull them apart.

Robert Hook improved vacuums, and found srping force law F=-kx. Robert Boyle (1627-1691) did more experiments. Boyle's law pv=constant at constant temperature (1660 a.d.)

Joseph Gay-Lussac found that at constant pressure, T1/V1 = T2/V2 (or V proportional to T), that is, all gases--regardless of which chemical--expand by 1 part in 273 for each 1 degree rise in temperature. Who would guess that would happen. Solids don't all expand by the same fraction with each one degreee rise in temperature.

To solve these PV=nRT homework problems, read to see which things are constant. Isolate them on one side of the equal sign. Solve for unknown.

For example, 1 liter of gas at 1 atm pressure expands at constant temperature to twice its original volume. What is its new pressure?

PV=nRT=constant so P1V1=P2V2 or P2=V1/V2 P1 = 1/2 P1 = 1/2 atm

Inside a constant volume container, the temperature of gas is raised from 300 K to 350 K. If its initial pressure was 2 atm what will be its new pressure?

P/T=nR/V=constant so

P1/T1=P2/T2 so P2 = T2/T1 P1 = 350/300 X 2 = 1.17 atm.

Heat increses length:

Hot water faucet turns itself off.

Max-temp thermometer as Hg expands forcibly through a restriction. Needs shaken to get back.

Neck temperature drop when you open a bottle.

Dirty snow melts first.

geyser.

How do geysers like old faithful work anyway? Deep cylinder with lots of pressure, boiling bubbles push up water into a large and wide pool, releases weight, allows violent ejection of water when pressure removed.

Serway 10.12

Through the day, a 2.168 cm diameter gold ring is heated from 0 to 25°C. How much will its diameter increase when heated?

dL = αL(Tf-Ti) = (1.42x10-5/C°)(2.168 cm)(25 - 0 C°)=0.000770 cm

10.17

A 3.196 cm diameter hollow cylindrical tube at 0°C is heated until it fits over a 3.212 cm diamter shaft. To what temperature must the outer sleeve be heated?

dL = αL(Tf-Ti) so Tf = dL / (αL) + Ti

Tf = (3.212-3.196 cm) / [(19x10-6/C°)(3.196 cm)] + 0 C°= 263.5 °C

or cool the inner cylinder down to -262.2 °C

10.14

At 20°C the 1.3000 meter long brass grandfather clock pendulum is 1.3000 meter long. What is its length at 0°C?

dL = αL(Tf-Ti) = (19x10-6/C°)(1.3000 cm)(0 - 25 C°)=-4.94x10-4 cm so its new length is 1.2995 m. Its period is T = 2πsqrt( l / g ) and its change in period is Th - Tc= 2πsqrt( lh / g ) - 2πsqrt( lc / g ) = - 0.00044 seconds or it looses one second every 1/0.00044 = 2272 sec = 37.87 hours. Not so important to have a temperature compensated pendulum.

Our grandparents would heat a 1-m diameter iron wheel to fit over a 0.995 meter diameter wooden wheel. On a 20°C day, how hot must the iron become in order to fit? When cooled the iron is snugly attached to the inner wooden wheel.

dL = αL(Tf-Ti) so

Tf = dL / (αL) + Ti

Tf = (0.005 m) / [(11x10-6/C°)(1 m)] + 20 C°= 475 °C

Also put green wood chair legs into seat holes. As the wood dries it expands and makes a tightly fitting leg.

Cheapos like me buy gas when it is coldest in the underground tank and let it expand in our warmer car gas tanks. Sleep in line at the gas station to be there when it first opens.

light radiation in physics 108 book

16 Heat Transfer

Conduction, convection, and radiation

Conduction

Heat conducts from hot to cold objects as kinetic energy (1/2mv2) is transferred from faster moving atoms to more slowly moving atoms. Heat is the flow of kinetic energy of motion. Its not temperature that flows and heat does not flow from cold to hot.

The heat energy per unit time (=power=watts) flowing across a slab of material is proportional to the area of the slab annd the difference in temperature on its front and back sides: H/t = k dt/L, where L is the thickness of the slab and k is a constant that depends on the material.

L

thicker walls mean heat is more slowly transmitted, so that it takes longer for the interior of your home to heat or cool to temperature of the outdoors.

dt

The larger the difference in temperature (atomic speeds) across the slab the more heat energy flows across the slab per second.

A

More area means more atomic collisions are occurring and so more heat energy (kinetic energy) can flow. It takes more time to conduct heat through a thicker salb having greater L.

Wine glass has little area to restrict the flow of heat from your hand to the wine.

k

Metal more readily conducts heat than does wood because of the free electrons in the metal bound to the entire metal structure but not to a single atom. We put low-conduction wooden handles on metal pans. Air conducts very poorly and makes a good insulator. Coats, wool, fur, snow (eskimos homes and frozen lake tops, paper (match burns but fingers don't, or heat the end of metal or wood stick with a match and heat more quickly travels along the metal to burn your hand), and feathers are full of air and conduct little. We use two window panes to take advatage of the low-conducting air trapped between them. Glass conducts heat less rapidly than does metal.

Metal feels colder than wood when they at the same temperature because metal more rapidly conducts heat from your hand or foot.

Walking across a few foot of wood coals does not burn your feet because wood is such a poor conductor. Frost or snow stays longer on wooden logs or on wooden fence posts than on the metal fence. Frost stays longer on low-conducting grass than on the adjacent walkway.

Insulation is meant to slow the rate of heat flow. After snow covers the roofs of our homes we can see where the heat is flowing through the roofs.

We cool a car engine by conducting heat from the metal to the cooling water. We heat food by conducting heat through the pan.

If you seperate two slabs by a vacuum then no heat can conduct because no atomic collisions are occurring.

Convection

occurs when the heated material itself flows, carrying the heat with it.

Blow hot air past food to heat it more quickly. Moving hot air heats us more quickly; cold air that is moving cools us more quickly (wind chill). If you place something 100° into air at 50° then its temperature soon cools to 50°. Its temperature doesn't go below 50°, it just cools to that temperature in less time. Moving water feels cooler than stationary water but isn't.

Fans cool you by convecting heat away from the surface area of your body. They do not lower the room temperature. Their electrical energy use means they would slightly warm the air.

The Earth's ocean (and air) currents conduct heat from warm equatorial waters toward cooler poles.

Hot air conducts out of our homes as cold air enters through cracks. You can feel air around electrical outlets and windows and such. The entire air within the house exchanges a couple times per hour. The house soon becomes stale otherwise. A heat exchnager is used (rarely) to transfer heat of outgoing air to the incoming, freshening air. Spending $100 on insulation and caulking and you'll save that money in one year.

An upwind tree can slow airflow past your home and save heating. Trees also cool in summer by blocking sunlight and heat in winter by reflecting heat back to your home.

Radiation.

Sunlight is heat radiation = light.

We feel the heat from a fireplace by holding out our hands. We are not touching the fire but its heat is traveling through the space between us. The heat intensity decreases with distance in a 1/r2 manner because the surface of the enclosing sphere increases as r2. A metal plate at the back of a fireplace heats the room by radiation. Most of the fire's heat goes out the chimney. (You can buy a video of a fireplace. Remember to periodically clean yor chimney by dropping a couple of wing-flapping chickens down it.)

This word is used for any emission, including heat, light, nuclear radiation. Light travels through a vacuum.

Light is another form of energy. When an object emits light, it is cooling.

Heat a piece of metal in an oven and it soon becomes red hot, then white hot. Its jiggling atoms are emitting increasingly energetic light. Its color indicates its temperature. This is the way we know the temperature of stars without having to go stick a thermometer in them. Microwave ovens heat food by sending light through them.

Place a car under a roof without sides and the car windows will take much longer to frost over.

Clouds keep the air warmer between the cloud and ground.

Clear nights are colder because the heat escapes into space and doesn't get bounced back.

The lake under a bridge is last to freeze becuase the heat radiation bounces back and forth between the water and the bridge above.

A thermos bottle has shiny interior wall to reflect heat radiation back into the material and has an evacuated gap between two containers.

             Expanding air cools, compressed air heats

As warm air rises it is carrying heat upward. As it moves into higher elevations it finds less pressure and expands and cools and then begins falling nerby. Imagine a paddle smacking a ping pong ball to increase its speed (or a piston moving inward to compress a gas and heat it through collisions with piston and atoms). If a moving ping pong ball hits a receding paddle or piston then its speed decreases. A gas cools as it expands. With your mouth open blow onto the back of your hand. Your breath is warm. Blow onto your hand through compressed lips. The air expands after emerging from your lips, and it cools while expanding. Air expands and cools when moving up a mountain side to higher elevations of less pressure. Air is compressed and heated when it comes down the mountain side. Fog develops when cooling below dew point and rain occurs on the upward slope leaving a "rain shadow" on the downslope side of the mountain. Nevada is desert beyond wet sierra Nevada mountains.

A bicycle pump heats as air is compressed within.

see the little half sheet for discussions of homework problems

see White Sands 108 course for more radiation and solar power stuff