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Latent Heat

- When a solid melts or a liquid boils, energy must

be added but the temperature remains constant!

(This can be explained by considering that it

takes energy to break the bonds holding the

material together.) - The amount of energy it takes to melt or boil a

certain amount of material is called a latent

heat.

Latent Heat

- For water, the latent heat of fusion (heat needed

to melt ice to water) is 79.7 cal/gm. - For water, the latent heat of vaporization (heat

needed to boil water) is 540 cal/gm. - For alcohol, the latent heat of vaporization is

less at 204 cal/gm.

Latent Heat - Example

- Example how much energy does it take to

vaporize 1 liter of water if the water is

initially at a temperature of 98oF ?

Latent Heat - Example cont.

- First we need to find the energy to raise the

temperature of the water up to boiling - this involves the heat capacity
- (which for water is 1 cal/gmoC)
- (density of water is 1 gm/cc, 1 liter 1000 cc)
- C Q/(m?T) , with ?T (212-98)5/963oC
- Q (1 cal/gmoC)(1 gm/1cc)1000 cc63oC
- 63,333 cal (4.186 J/cal) 265,000 J .

Latent Heat - Example cont.

- Now we add in the latent heat
- (for water, this is 540 cal/gm)
- Q Lm (540 cal/gm)(1 gm/cc)(1000 cc)
- 540,000 cal (4.186 J/cal) 2,260,000 J
- Total energy required is 265,000 J 2,260,000

J 2,525,000 J .

Latent Heat - Example 2

- Question how much water would be needed to keep

cool for 4 hours by evaporation if the outside

temperature is 100 oF (essentially same as

bodys) and a power output of 200 Watts (doing

some work) is desired?

Latent Heat - Example cont.

- Since the body generates 200 Watts, or 200 Joules

a second, the body must evaporate water to carry

this energy away. - Q (200 J/sec)(4 hs)(3600 sec/hr) 2,880,000 J.
- From the previous considerations, evaporating 1

liter of water carries away 2,525,000 J. Thus we

need 2.88MJ / (2.525MJ/liter) - 1.14 liters of water.

Latent Heat - Example cont.

- Would more or less alcohol be needed to keep cool

for the same energy output? - (The heat capacity of alcohol is 2.4 J/gmoC the

density of ethanol .791 gm/cc the boiling

point is 78oC latent heat of vaporization is

854 J/gm). - From this you should be able to decide whether

water or alcohol is better for heat regulation.

Heat Transfer

- There are four ways of moving heat
- Evaporation (using latent heat - weve

already looked at this) - Convection (moving heat with a material)
- Conduction (moving heat through a material)
- Radiation
- Well develop equations for conduction and

radiation and talk about convection.

Heat Transfer Convection

- Heat Transfer by Convection is when you heat some

material and then move that material containing

the heat. - The amount of heat energy moved depends on the

heat in the material (heat capacity times amount

of material times the temperature difference) and

how much material you move per time. - The blood and hot air furnaces use this method.

Heat Transfer Conduction

- Heat will flow through a solid material from the

hot end to the cold end. What is flowing? No

matter is flowing! - We can think of energy as flowing in this case!

We measure the flow of energy as power 1 Watt

1 Joule/sec .

Heat Transfer Conduction

- Power Q/t kA?T/L
- where k is a constant that depends on the

material, called the thermal conductivity - where A is the cross sectional area
- where L is the distance from the hot end to

the cold end - and ?T is the temperature difference

between the hot and cold ends.

L

A

k

Thi

Tlow

Conduction - R values

- Units of thermal conductivity from
- Power Q/t kA?T/L
- k has units of Wm/(m2K) or J/(secmK), and k

depends only on the material. - Often a material is given an R value, where R

includes both the material and the thickness of

the material R L/k, and R has the units of

m2secK/J (or ft2oFhr/BTU, where 1

ft2oFhr/BTU 0.176 m2secK/J)

Conduction - R values

- P Q/t kA?T/L A?T / R
- where we define R L / k .
- where if we have several different materials and

thicknesses, we can simply add the individual Rs

to get the total R - Rtotal ?Ri .

Conduction - Conductivity

- approximate k values for some materials
- metals k 1 cal/(seccmoC)
- glass k 2 x 10-3 cal/(seccmoC)
- wood, brick, fiberglass
- k 1 x 10-4 cal/(seccmoC)
- air k 5 x 10-5 cal/(seccmoC)

Conduction - Example

- Lets calculate the R value of brick 4 inches in

thickness L 4 in (.0254 m/in) .10 m - k 1.5 x 10-4 cal/(seccmoC)
- (4.186 J/cal)(100 cm/m) .063 J/(secmoC)
- R L/k .10 m / .063 J/(secmoC)
- 1.6 m2K/Watt
- (1 ft2oFhr/BTU) /( .176 m2K/Watt)
- 9 (1 ft2oFhr/BTU)

Conduction - Example

- What is the heat loss through the brick walls

(assume no other insulation) of a house that is

50 ft x 30 ft (floor area 1500 ft2) x 8 ft when

the temperature inside is 72oF and the

temperature outside is 20oF ?

Conduction - Example

- P Q/t kA?T/L A?T / R
- A 50ft 8ft 30ft 8ft 50ft 8ft

30ft8ft 1280 ft2 (1 m2/10.76 ft2) 120 m2 . - ?T (72-20)oF (5K/9oF) 29 K
- R 1.6 m2K/Watt
- P 120 m2 29 K / 1.6 m2K/Watt
- 2175 Watts 2.175 kW.

Blackbody Radiation

- What is a blackbody?
- A BLACK object absorbs all the light incident on

it. - A WHITE object reflects all the light incident on

it, usually in a diffuse way rather than in a

specular (mirror-like) way.

Blackbody Radiation

- The light from a blackbody then is light that

comes solely from the object itself rather than

being reflected from some other source. - A good way of making a blackbody is to force

reflected light to make lots of reflections

inside a bottle with a small opening.

Blackbody Radiation

- If very hot objects glow (such as the filaments

of light bulbs and electric burners), do all warm

objects glow? - Do we glow? (Are we warm?
- Are you HOT?)

Blackbody Radiation

- What are the parameters associated with the

making of light from warm objects?

Blackbody Radiation

- What are the parameters associated with the

making of light from warm objects? - Temperature of the object.
- Surface area of the object.
- Color of the object ? (If black objects absorb

better than white objects, will black objects

emit better than white objects?)

Blackbody Radiation Color Experiment

- Consider the following way of making your stove

hot and your freezer cold

Color Experiment

- Put a white object in an insulated and evacuated

box with a black object. The black object will

absorb the radiation from the white object and

become hot, while the white object will reflect

the radiation from the black object and become

cool. - Put the white object in the freezer, and the

black object in the stove.

Color Experiment

- Does this violate Conservation of Energy?

Color Experiment

- Does this violate Conservation of Energy? NO
- Does this violate the Second Law of

Thermodynamics (entropy tends to increase) ?

Color Experiment

- Does this violate Conservation of Energy? NO
- Does this violate the Second Law of

Thermodynamics (entropy tends to increase) ?

YES - This means that a good absorber is also a good

emitter, and a poor absorber is a poor emitter.

Use the symbol ? to indicate the blackness (?1)

or the whiteness (?0) of an object.

Blackbody Radiation

- What are the parameters associated with the

making of light from warm objects? - Temperature of the object, T.
- Surface area of the object, A.
- Color of the object, ??

Blackbody Radiation

- Is the ? for us close to 0 or 1?
- (i.e., are we white or black?)
- We emit light in the IR, not the visible.
- So what is our ? for the IR?

Blackbody Radiation

- So what is our ? for the IR?
- Have you ever been near a fire on a cold night?
- Have you noticed that your front can get hot at

the same time your back can get cold? - Can your hand block this heat from the fire?
- Is this due to convection or radiation?

Blackbody radiation

- For humans in the IR, we are all fairly good

absorbers (black). An estimated value for ? for

us then is about .97 .

Blackbody Radiation Experimental Results

- At 310 Kelvin, only get IR

Intensity

IR

blue yellow red

UV

wavelength

Blackbody Radiation Experimental Results

- At much higher temperatures, get visible
- look at blue/red ratio to get temperature

Intensity

IR

blue yellow red

UV

wavelength

Blackbody Radiation Experimental Results

- Ptotal ??AT4
- where ? 5.67 x 10-8 W/m2

K4 - ??????????peak b/T where b 2.9 x 10-3 mK

Intensity

IR

blue yellow red

UV

wavelength

Blackbody Radiation Example

- Given that you eat 2000 Calories/day,
- your power output is around 100 Watts.
- Given that your body temperature is
- about 90o F , and
- Given that your surface area is about
- 1.5 m2,

Blackbody Radiation Example

- Given Ptotal 100 Watts
- Given that Tbody 90o F
- Given that A 1.5 m2
- WHAT IS THE POWER EMITTED VIA
- RADIATION?

Blackbody Radiation Example

- Pemitted ??AT4
- ? .97
- ?? 5.67 x 10-8 W/m2 K4
- T 273 (90-32)5/9 (in K) 305 K
- A 1.5 m2
- Pemitted 714 Watts
- (compared to 100 Watts generated!)

Blackbody Radiation Example

- need to consider power absorbed at room T
- Pabsorbed ??AT4
- ? .97
- ?? 5.67 x 10-8 W/m2 K4
- T 273 (72-32)5/9 (in K) 295 K
- A 1.5 m2
- Pabsorbed 625 Watts
- (compared to 714 Watts emitted!)

Blackbody Radiation Example

- Total power lost by radiation
- 714 W - 625 W 89 Watts
- (Power generated is 100 Watts.)
- Power also lost by convection (with air)
- and by evaporation.

Blackbody Radiation Example

- At colder temperatures, our emitted power stays

about the same while our absorbed power gets much

lower. This means that we will get cold unless - we generate more power, or
- our skin gets colder, or
- we reflect the IR back into our bodies.
- Use metal foil for insulation!

Thermodynamics

- The First Law of Thermodynamics is a fancy name

for the Law of Conservation of Energy applied to

thermal systems. It says - DU Q - W
- where DU indicates the change in the internal

energy of the system. This internal energy is

related to the temperature and heat capacity of

the system Q is the heat energy added to the

system and W is the work done by the system.

Thermodynamics

- The first law of thermodynamics, like the

conservation of energy, does not indicate the

direction. It does not explain why, when cold

milk is added to hot coffee, the cold milk warms

up and the hot coffee cools down. The

conservation of energy (first law of

thermodynamics) permits the possibility that the

milk would get even colder while the coffee gets

hotter after they are mixed.

Second Law of Thermodynamics

- It is the Second Law of Thermodynamics that

explains why the hot coffee does cool down and

the cold milk warms up when they are mixed. - To understand the second law, however, we need to

first look a little at probability.

Probability

- Consider flipping four coins. How many heads

would you expect to get (assuming they were

honest coins)? - Why do you expect this?
- Lets look at all the possible combinations of

flipping four coins

Flipping Four Coins

- Four heads (only one way) HHHH
- Three heads (four ways)
- THHH HTHH HHTH HHHT
- Two heads (six ways)
- TTHH THTH THHT
- HTTH HTHT HHTT
- One head (four ways)
- HTTT THTT TTHT TTTH
- Zero heads (only one way) TTTT

Probability

- We see that there are more ways of getting two

heads and two tails than any other combination. - The same argument can be made about the

distribution of energy among many molecules the

highest probability corresponds to the most ways

of having that outcome.

Probability

- In the case of distributing the thermal energy

between the hot coffee and the cold milk, there

are more ways of distributing the energy equally

among the many coffee and milk molecules than

there are ways of giving it all to just the

coffee or just the milk molecules.

Statement of 2nd Law

- A system will tend to go to its most probable

state. - To measure the ways of having the same state

(like determining the number of ways of having

two heads out of four coins), we use the concept

of entropy.

Another Statement

- Entropy is a measure of the probability of being

in a state. Since things tend to go to their

most probable state, we can write the 2nd Law of

Thermodynamics as systems tend to have their

entropy increase.

About the 2nd Law

- Note that this is not an absolute law like

Conservation of Energy. Rather it is a

probablistic Law. However, when dealing with

large numbers (recall that Avagadros Number is 6

x 1023, or almost a trillion trillion), the

probabilities become essentially certainties.

Heat Engines

- Heat engines are devices that convert some of the

heat into useful energies such as electrical.

These engines can only work, however, if there is

a difference in temperature. - We can think by analogy just as gravity tends

to bring masses together, and we can get work out

of a gravitational separation so entropy tends

to increase by bringing temperatures together,

and we can get work out of a separation of

temperatures.

Efficiency

- Efficiency is a measure of how much you get out

versus how much you put in. For heat engines,

then - Efficiency ? Work done / Heat Added
- By the first law, then, the work done is simply

the difference in the heat going into the engine

minus the heat coming out of the engine. The

total heat added is the heat going into the

engine. ? (Qhot - Qcold) /Qhot

Carnot Efficienty

- By considering the most efficient way of running

a heat engine, we come up with the Carnot cycle.

This is the best we can theoretically do with a

heat engine. For a Carnot efficiency, we have

the formula - ??Carnot (Thot - Tcold) / Thot .
- Note that these temperatures must be in absolute

(Kelvin), not oC or oF .

Heat Engines

- Our heat engines, whether fired by coal, oil or

nuclear energy, are all limited in their

efficiencies by this Carnot efficiency. In

practice we come very close to this theoretical

maximum. - Note that for the best efficiencies, we need Thot

to be very hot and Tcold to be very cold. Due to

material limitations on both Thot and Tcold, this

efficiency is about 30.

Heat Engines

- All heat engines, then, have to get rid of the

excess heat energy. Most major power stations do

this via water because of the high heat capacity

of water relative to air. - The biggest structure at nuclear power stations

is the cooling tower, and this is often depicted

as a symbol of nuclear power. Yet the same heat

dump is present at coal and oil facilities!

Heat Engines

- Your car is a heat engine, but it is only about

15 efficient compared to a major power plants

efficiency of 30. Your cars engine cannot

operate at the same high temperature as the power

plant! - Your car employs both a water transfer (via water

convection inside the engine) as well as an air

transfer (at the radiator) for the waste heat.