107
•Temperature
•Thermal Expansion
•Ideal Gas Law
•Kinetic Theory
•Heat
•Heat Transfer
•Phase Changes
•Specific Heat
•Calorimetry
Zeroeth Law
• Two systems individually in thermal
equilibrium with a third system (such as a
thermometer) are in thermal equilibrium
with each other.
• That is, there is no flow of heat within a
system in thermal equilibrium
1st Law of Thermo
• The change of internal energy of a system
due to a temperature or phase change is
given by (next chapter):
Temperature Change: Q = mcT
Phase Change: Q = mL
• Q is positive when the system GAINS heat
and negative when it LOSES heat.
2nd Law of Thermo
• Heat flows spontaneously from a substance
at a higher temperature to a substance at a
lower temperature and does not flow
spontaneously in the reverse direction.
• Heat flows from hot to cold.
• Alternative: Irreversible processes must
have an increase in Entropy; Reversible
processes have no change in Entropy.
• Entropy is a measure of disorder in a system
3rd Law of Thermo
It is not possible to
lower the
temperature of any
system to absolute
zero.
9( ) ( ) 32
5T F T C
5( ) ( ) 32
9T C T F
( ) ( ) 273.15T K T C
Temperature is measured by a thermometer.
Kelvin is the Absolute Scale.
What is "room temperature" (68 degrees F) in Celsius and Kelvin?
5( ) ( ) 32
9T C T F
( ) ( ) 273.15T K T C
568 32
9 20 C
293.15K
Do book quiz 2!
30 is HOT.
20 is NICE.
10 is CHILLY.
Zero is ICE!
•Heat Energy is a flow of energy from hotter to colder because of a
difference in temperature. Objects do not have heat. [Heat] = Joule
• Internal Energy of a system is a measure of the total Energy due to
ALL random molecular motions INTERNAL of the system
(Translations KE, Rotational KE, Vibrational KE) and internal
POTENTIAL energies due to interactive forces (electromagnetic,
strong, weak, gravitational) Objects have energy.
•Mechanical Energy is due to the kinetic and potential energies of
the system itself in an external reference frame.
•Mechancial Equivalent of Heat: mechanical energy converted to
heat energy by doing work on the system: 1.000 kcal = 4186J
A 10,000 kg truck applies the
brakes and descends 75.0 m at
a constant speed, causing the
brakes to smoke as shown. If
the brakes have a mass of
100.00 kg and a specific heat of
800 J/kgC, calculate the
temperature increase of the
brakes. truck brakesm gh m c T
92.0truck
brakes
m ghT C
m c
•Heat Energy is a flow of energy from hotter to colder because of a
difference in temperature. Objects do not have heat. [Heat] = Joule
•Heat Energy entering or leaving a system will cause either a
Temperature Change: Q = mcT or a Phase Change: Q = mL
• The change of internal energy of a system due to a temperature or phase change is given by:
Temperature Change: Q = mcT
Phase Change: Q = mL
• Q is positive when the system GAINS heat and negative when it LOSES heat.
Specific Heat: Thermal Inertia
The Specific Heat of a substance is the amount of Energy it
requires to raise the temperature of 1 kg, 1 degree Celsius.
Q mc T 0
Q Jc
m T kg C
•The higher the specific heat, the more energy it takes and
the longer it takes to heat up and to cool off.
•The lower the specific heat, the less energy it takes and the
quicker it takes to heat up and cool off.
•Substances with HIGH specific heat STORE heat energy
and make good thermal moderators. (Ex: Water, Oceans)
Some Specific Heat Values
More Specific Heat Values
Specific Heat
Why does water have such a high
specific heat?
Heat goes into other modes of energy so
that temperature changes slowly.
0
0
0
4186
2410
452
water
glycerin
iron
Jc
kg C
Jc
kg C
Jc
kg C
Q mc T
How much heat is required to raise the temperature of a
0.750kg aluminum pot containing 2.50kg of water at 30ºC to
the boiling point?
Al Al w wQ m c T m c T
.75 (900 / ) 2.5 (4186 / ) (70 )kg J kg C kg J kg C C
Al Al w wm c m c T
57.798 10Q x J
Phase Change Q mL
•A change from one phase to another
•A phase change always occurs with an exchange of energy!
•A phase change always occurs at constant temperature!
Sample Latent Heat Values
Q mL
Phase Change
Energy goes into the system and breaks molecular bonds..
Energy is given up by the system by forming molecular bonds
Melting: Energy goes into the system and breaks molecular bonds..
Freezing: Energy is given up by the system by forming molecular bonds
Phase Change: Melting & Freezing
Phase Change: Melting & Freezing
Phase Change: Melting & Freezing
•Melting: Solid to Liquid @ the melting temperature
•Melting is a cooling process
•Freezing: Liquid to Solid @ the melting temperature
•Freezing is a warming process.
Why do farmers spray peaches with water to
save them from frost?
Freezing is a warming process!
If you were in an igloo on a freezing
night. You would be warmed more by
a) a bucket of ice melting.
b) a bucket of water freezing
c) the same either way.
d) neither - are you nuts?
Phase Change: Evaporation •Takes place at the surface of a liquid due to escaping
molecules.
•Occurs at all temperatures
•Evaporation occurs when water vapor pressure in the liquid
exceeds the pressure of water vapor in the surrounding air.
•Evaporation is a cooling process.
Evaporation is a Cooling Process
Phase Change: Boiling •Boiling is evaporation under the surface of the liquid.
•Liquid boils at the temperature for which its vapor pressure
exceeds the external pressure (mostly atmospheric pressure.)
•Boiling point depends on temperature AND pressure:
•@ 1 atm, bp of water is 100ºC, @ 5atm, bp of water is 374
ºC
•Boiling is a cooling process.
•At low pressures, liquids are boiled (‘freeze-dried’) into
solids.
Phase Change: Condensation
•Gas molecules condense to form a liquid.
•Condensation is a warming process
•Why is a rainy day warmer than a cloudy or clear day in
winter?
•Why do we feel uncomfortable on a muggy day?
Condensation is a Warming Process
Phase Change: Humidity
•Vapor is the gas phase of a substance below its boiling
temperature.
•Air can ‘hold’ only so much water vapor before it becomes
saturated and condensation occurs. Humidity is a measure of
vapor density.
•Warm air can hold more water vapor. More condensation occurs
at cooler temperatures because the molecules are moving slower.
Slow moving water molecules coalesce upon collision.
Windward: Wet
Leeward: Dry
Warm
Humid
Air
Pushed
Up
Cools and condenses at Top
Warm
Dry
Air
Falls
Down
Stormy Weather
When warm air rises, it expands and cools.
The water vapor in the air soon condenses
into water droplets, which form clouds and
eventually these droplets fall from the sky as
rain.
Phase Change:Sublimation
The conversion of a solid directly to a gas & visa versa
Examples: snowflakes, Moth Balls, dry ice
Phase Change: Triple Point
A temperature and pressure at which all three
phases exist in equilibrium.
Freezing-Melting Evaporation
-Condensation
Sublimation
Lines of
equilibrium
Phase Change
Phase change occurs at a Constant Temperature!
Latent Heats of: Fusion & Evaporation Lf, Lv
Q mL
334 / solid-liquid
2256 / liquid-gas
f
v
L kJ kg
L kJ kg
Water:
Phase Change: Water
How much steam @ 100 °C does it take to melt 1kg of ice at -30 °C?
Q mL
0
0
334 /
2256 /
2090 /
4186 /
f
v
ice
water
L kJ kg
L kJ kg
c J kg C
c J kg C
•How much energy is needed to raise the ices to 0 °C
•How much energy is needed to melt 1kg of ice?
•How much energy is given up by the steam?
•What happens to the steam that is melting the ice?
Phase Change: Water
How much steam @ 100 °C does it take to melt 1kg of ice at -30 °C?
Q mL
0
0
334 /
2256 /
2090 /
4186 /
f
v
ice
water
L kJ kg
L kJ kg
c J kg C
c J kg C
How much energy is needed to raise the ices to 0 °C
0 0
1 1 (2090 / )(30 )Q kg J kg C C
62700J
Phase Change: Water
How much steam @ 100 °C does it take to melt 1kg of ice at -30 °C?
Q mL
0
0
334 /
2256 /
2090 /
4186 /
f
v
ice
water
L kJ kg
L kJ kg
c J kg C
c J kg C
How much energy is needed to melt 1kg of ice?
2Q mL
2 334Q kJ
1 (334 / )kg kJ kg
1 62700Q J
2 334Q kJ
Phase Change: Water
How much steam @ 100 °C does it take to melt 1kg of ice at -30 °C?
Q mL
0
0
334 /
2256 /
2090 /
4186 /
f
v
ice
water
L kJ kg
L kJ kg
c J kg C
c J kg C
1 62700Q J
2 334Q kJ
•How much energy is given up by the steam?
•What happens to the steam that is melting the ice?
397totalQ kJ
The First Law of Thermodynamics
• The First Law of Thermodynamics is a special case of the Law of Conservation of Energy
– It takes into account changes in internal energy and energy transfers by heat and work
• Although Q and W each are dependent on the path, Q + W is independent of the path
intE Q W
Work in Thermodynamics • Work can be done on a deformable
system, such as a gas
• Consider a cylinder with a moveable
piston
• A force is applied to slowly compress the
gas
– The compression is slow enough for
all the system to remain essentially in
thermal equilibrium
– This is said to occur quasi-statically
ˆ ˆ dW d F dy Fdy PA dy PdV F r j j
dW PdV
Work
• Interpreting dW = - P dV
– If the gas is compressed, dV is negative and the
work done on the gas is positive
– If the gas expands, dV is positive and the work
done on the gas is negative
– If the volume remains constant, the work done
is zero
• The total work done is:
f
i
V
VW P dV
PV Diagrams
• Used when the pressure and
volume are known at each step
of the process
• The state of the gas at each step
can be plotted on a graph called
a PV diagram
– This allows us to visualize the
process through which the gas is
progressing
• The curve is called the path
f
i
V
VW P dV
f
i
V
VW P dV
Problem
Work Done By Various Paths
( )f f iW P V V
f
i
V
VW P dV
( )i f iW P V V ( )W P V dV
The work done depends on the path taken!
Not necessarily
an isotherm!
Isothermal Process • At right is a PV diagram of an isothermal
expansion
• The curve is a hyperbola
• The curve is called an isotherm
• The curve of the PV diagram
indicates PV = constant
– The equation of a hyperbola
• Because it is an ideal gas and the
process is quasi-static,
PV = nRT and
f f f
i i i
V V V
V V V
nRT dVW P dV dV nRT
V V
ln i
f
VW nRT
V
Isobaric Processes
• An isobaric process is one that occurs at a
constant pressure
• The values of the heat and the work are
generally both nonzero
• The work done is W = -P (Vf – Vi) where P
is the constant pressure
intE Q W f
i
V
VW P dV PV nRT
Isovolumetric Processes
• An isovolumetric process is one in which there is
no change in the volume
• Since the volume does not change, W = 0
• From the first law, Eint = Q
• If energy is added by heat to a system kept at
constant volume, all of the transferred energy
remains in the system as an increase in its internal
energy
intE Q W f
i
V
VW P dV PV nRT
Isothermal Process
• An isothermal process is one that occurs at
a constant temperature
• Since there is no change in temperature,
Eint = 0
• Therefore, Q = - W
• Any energy that enters the system by heat
must leave the system by work
intE Q W f
i
V
VW P dV PV nRT
Adiabatic Process
• An adiabatic process is one during which no energy enters or leaves the system by heat: Q = 0
– This is achieved by: • Thermally insulating the walls of the system
• Having the process proceed so quickly that no heat can be exchanged
• Since Q = 0, Eint = W
• If the gas is compressed adiabatically, W is positive so Eint is positive and the temperature of the gas increases
• If the gas expands adiabatically, the temperature of the gas decreases
• Examples of adiabatic processes related to engineering are: – The expansion of hot gases in an internal combustion engine
– The liquefaction of gases in a cooling system
– The compression stroke in a diesel engine
– Adiabatic free expansion of a gas
• The gas expands into a vacuum, no piston: W = 0
• Since Q = 0 and W = 0, Eint = 0 : initial and final states are the same, no change in temperature is expected.
intE W
intE Q W f
i
V
VW P dV
Thermo Processes • Adiabatic
– No heat exchanged
– Q = 0 and Eint = W
• Isobaric
– Constant pressure
– W = P (Vf – Vi) and Eint = Q + W
• Isovolumetric
– Constant Volume
– W = 0 and Eint = Q
• Isothermal
– Constant temperature
Eint = 0 and Q = -W
intE Q W
ln i
f
VW nRT
V
Was ist das?
Fig. 20-9, p. 569
The First Law of Thermodynamics
• The First Law of Thermodynamics is a special case of the Law of Conservation of Energy
– It takes into account changes in internal energy and energy transfers by heat and work
• Although Q and W each are dependent on the path, Q + W is independent of the path
intE Q W
Cyclic Processes
• A cyclic process is one that starts and ends in the same state
– On a PV diagram, a cyclic process appears as a closed curve
• If Eint = 0, Q = -W
• In a cyclic process, the net work done on the system per cycle equals the area enclosed by the path representing the process on a PV diagram
intE Q W
A gas is taken through the cyclic process as shown.
(a) Find the net energy transferred to the system by heat during one complete cycle. (b) What If? If the cycle is reversed—that is, the process follows the path ACBA—what is the net energy input per cycle by heat?
intE Q W f
i
V
VW P dV
A sample of an ideal gas goes through the process as shown. From A to B, the process is adiabatic; from B to C, it is isobaric with 100 kJ of energy entering the system by heat. From C to D, the process is isothermal; from D to A, it is isobaric with 150 kJ of energy leaving the system by heat. Determine the difference in internal energy E(B) – E(A).
intE Q W f
i
V
VW P dV PV nRT
Problem
•Heat flows from HOT to COLD
•Conduction (solids)
•Convection (liquids & gases)
•Radiation (solids, gases, plasma)
Energy transferred via molecular collisions
•Good Conductors: Most Metals (free electrons!)
•Bad Conductors: Organic & Inert Materials
•Good Insulators: Air, Water, Wood
•Good Conductors are BAD Insulators
•& Visa Versa
Heat energy is transferred in solids
by collisions between free electrons
and vibrating atoms.
The heat Q conducted during a time t through a material with
a thermal conductivity k. dT/dx is the Temperature Gradient.
dTP kA
dx
Some Thermal Conductivities
Temperature Gradient
h cdT T T
dx L
The quantity |dT / dx| is called the temperature gradient
Q dTkA
t dx
Conduction Problem
A bar of gold is in thermal contact with a bar of silver of the
same length and area as shown. One end of the compound
bar is maintained at 80.0°C while the opposite end is at
30.0°C. When the energy transfer reaches steady state, what
is the temperature at the junction? Ignore thermal
expansion of the metals.
h cT TkA
L
In the same room, at the same
temperature, the tile floor feels
cooler than wood floor.
How can they be the same
temperature?
Hot Air rises, expands and cools, and then sinks back down
causing convection currents that transport heat energy.
Hot air rises because fast moving molecules tend to migrate toward
regions of least obstruction - UP - into regions of lesser density!
Rising air cools because a decrease in density
reduces number of collisions & speeds decrease.
As the air cools, it becomes denser, sinking down,
producing a convection current.
Uneven heating on the earth and over water cause convection
currents in the atmosphere, resulting in WINDS.
Global wind patterns (Trade Winds, Jet Streams) are due to
convection current from warmer regions (equator) to cooler
regions (poles) plus rotation of Earth.
Convection Currents in the Ocean (Gulf Stream)
transport energy throughout the oceans.
Air & Ocean Convection causes
the WEATHER.
Convection between water and land causes the Winds.
Sea Breeze
High Pressure
Dry Warm Weather
Low Pressure
Stormy Weather
Electromagnetic Radiation is emitted and absorbed via atomic
excitations. All objects absorb and emit EM waves.
Electromagnetic Radiation is emitted and absorbed via atomic
excitations. All objects absorb and emit EM waves.
When an object it heated it will
glow first in the infrared, then the
visible. Most solid materials break
down before they emit UV and
higher frequency EM waves.
Frequency ~ Temperature
Long
Short
Stefan’s Law
• P = σAeT 4
– P is the rate of energy transfer, in Watts
– σ = 5.6696 x 10-8 W/m2 . K4
– A is the surface area of the object
– e is a constant called the emissivity
• e varies from 0 to 1
• The emissivity is also equal to the absorptivity
– T is the temperature in Kelvins
A good absorber reflects little and appears Black
A good absorber is also a good emitter.
4P e T A
Radiant heat makes it impossible to stand close to a hot
lava flow. Calculate the rate of heat loss by radiation
from 1.00 m2 of 1200C fresh lava into 30.0C
surroundings, assuming lava’s emissivity is 1.
The net heat transfer by radiation is: 4 4
2 1( )P e A T T
4 4
2 1( )P e A T T
8 4 2 4 41(5.67 10 / )1 ((303.15 ) (1473.15 ) )x J smK m K K
266P kW
Fur is filled with air. Convection currents are slow
because the convection loops are so small.
How do fur coats keep you warm?
Any two systems placed in thermal
contact will have an exchange of heat
energy until they reach the same
temperature.
If the systems are in thermal
equilibrium then no net changes take
place.
Why is winter cold and summer
hot?
Intensity: The Radiation Power, P, passing through an area,
A.
2 2
W
4 m
PI
r
Why are cloudy nights warmer
than cold nights?
The heating effect of a medium such as glass or the Earth’s
atmosphere that is transparent to short wavelengths but opaque
to longer wavelengths: Short get in, longer are trapped!
CO2 & Temperature Change
Impacts of a Warming Arctic
The Arctic Climate Impact Assessment, a study
commissioned by the United States and the seven
other countries with Arctic territory, projects that
rising global concentrations of heat-trapping
emissions will drive up temperatures particularly
quickly at high latitudes.
RISING SEAS One of the most important
consequences of Arctic warming will be increased
flows of meltwater and icebergs from glaciers and
ice sheets, and thus an accelerated rise in sea
levels.
Forrest vs Tundra
Caught between rising seas on one side and expanding
shrub-filled zones to the south, tundra ecosystems around
the Arctic will likely shrink to their smallest extent in at
least 100 years, the scientists concluded. This could
reduce breeding areas for many tundra-dwelling bird
species and grazing lands for caribou and other mammals.
1 Meter Rise In Florida
ZEPO:A Melting Glacier in Tibet
"Thirty years ago, there was no river here.
If you come back here in another 30 years, one thing is for sure:
There will definitely be no more ice here."
-Dr. Yao Tandong,
Institute of Tibetan Plateau Research
Global Glacial Ice Melting
On Kilimanjaro in Kenya, an 11,700-year-old ice cap that
measured 4.3 square miles in 1912 had shrunk to 0.94 square
miles in 2000, and is projected to disappear altogether in
about 15 years. Melting of glaciers in Patagonia has doubled
in recent years.
Ice Caps Melting in Peru
In Peru, the Quelccaya ice cap retreated a rate of more than
600 feet a year from 2000 to 2002 - up from just 15 feet a year
in the 1960's and 70's - leaving a vast 80-foot-deep lake where
none had existed when his studies began.
Unless we change our
direction, we are likely to end
up where we are headed.
Happy Earth Day!
“The organic and inorganic components of Planet Earth have
evolved together as a single living, self-regulating system
Life maintains conditions suitable for its own survival.”
- James Lovelock
“It is much too late for sustainable
development; what we need is a sustainable
retreat.”
-James Lovelock, The Revenge of Gaia
“...we’re all astronauts aboard a little spaceship called Earth”
- Bucky Fuller
One island in one ocean...from space
Our Spaceship Earth
"We are on a spaceship; a beautiful one.
It took billions of years to develop.
We're not going to get another.”
- Bucky Fuller,
Operating Manual for Spaceship Earth
500,000 miles/hr 67,000 miles/hr
Space Ecology
Pressure Acts ONLY
Perpendicularly to the Surface
Pressure depends on depth.
Pressure IN a Fluid
•Is due to the weight of the fluid above you
•Depends on Depth and Density Only
•Does NOT depend on how much water is present
•Acts perpendicular to surfaces (no shearing)
•Pressure’s add
•At a particular depth, pressure is exerted equally in ALL directions
including sideways (empirical fact)
