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## Latent Heat

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### 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 ... – PowerPoint PPT presentation

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Title: Latent Heat

1
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.

2
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.

3
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 ?

4
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 .

5
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 .

6
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?

7
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.

8
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.

9
Heat Transfer
• There are four ways of moving heat
• Evaporation (using latent heat - weve
• Convection (moving heat with a material)
• Conduction (moving heat through a material)
• Well develop equations for conduction and

10
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.

11
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 .

12
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
13
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)

14
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 .

15
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)

16
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)

17
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 ?

18
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.

19
• 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.

20
• 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.

21
• 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?)

22
• What are the parameters associated with the
making of light from warm objects?

23
• 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?)

24
• Consider the following way of making your stove

25
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.

26
Color Experiment
• Does this violate Conservation of Energy?

27
Color Experiment
• Does this violate Conservation of Energy? NO
• Does this violate the Second Law of
Thermodynamics (entropy tends to increase) ?

28
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.

29
• 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, ??

30
• 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?

31
• 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?

32
• For humans in the IR, we are all fairly good
absorbers (black). An estimated value for ? for
us then is about .97 .

33
• At 310 Kelvin, only get IR

Intensity
IR
blue yellow red
UV
wavelength
34
• At much higher temperatures, get visible
• look at blue/red ratio to get temperature

Intensity
IR
blue yellow red
UV
wavelength
35
• 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
36
• Given that you eat 2000 Calories/day,
• your power output is around 100 Watts.
• Given that your body temperature is
• about 90o F , and
• 1.5 m2,

37
• Given Ptotal 100 Watts
• Given that Tbody 90o F
• Given that A 1.5 m2
• WHAT IS THE POWER EMITTED VIA

38
• 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!)

39
• 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!)

40
• 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.

41
• 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!

42
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.

43
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.

44
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.

45
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

46
Flipping Four Coins
• Four heads (only one way) HHHH
• THHH HTHH HHTH HHHT
• TTHH THTH THHT
• HTTH HTHT HHTT
• HTTT THTT TTHT TTTH
• Zero heads (only one way) TTTT

47
Probability
• We see that there are more ways of getting two
heads and two tails than any other combination.
distribution of energy among many molecules the
highest probability corresponds to the most ways
of having that outcome.

48
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.

49
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.

50
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.

51
• 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.

52
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.

53
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

54
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 .

55
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

56
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!

57
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.