Heat and Thermodynamics

AP Physics Rapid Learning Series - 13
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H t d Th d iHeat and Thermodynamics
Physics Rapid Learning Series
www.RapidLearningCenter.com/
© Rapid Learning Inc. All rights reserved.
Wayne Huang, Ph.D.
Keith Duda, M.Ed.
Peddi Prasad, Ph.D.
Gary Zhou, Ph.D.
Michelle Wedemeyer, Ph.D.
Sarah Hedges, Ph.D.

Learning Objectives
Temperature: Understand the
definition of temperature.
By completing this tutorial, you will learn:
Energy in Thermal Processes.
Understand the relationship
between heat and internal
energy.
Thermal Processes in your
world. Global warming and
greenhouse gasses.
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Laws of Thermodynamics.
Apply the laws of
thermodynamics to real life
problems such as engines and
human metabolism.
Concept Map
Physics
Studies
Previous content
New content
Thermodynamics
The field of
Matter and EnergyMatter and Energy
Heat Energy
One type of energy is
2nd Law1st Law
Expansion
Thermal
Expansion
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Heated objectsHeated objects
expand
Energy is
destroyed
Energy is
neither created nor
destroyed
Entropy
increases
Entropy
always
increases
States thatStates that States that

ThermodynamicsThermodynamics
and Thermal
Expansion
Thermometers and Temperature Scales.
Thermal expansion of Solids and Liquids
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Thermal expansion of Solids and Liquids
Thermodynamics and Temperature
How does temperature affect materials and how is
this used to measure temperature?
Linear expansion
Volume expansion
The physics of thermostats
The physics of
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thermometers

Definition - Thermodynamics
Thermodynamics - The branch of
physics that deals with conversionsphysics that deals with conversions
between heat energy and other forms
of energy.
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Thermal Expansion
As solids and liquids are heated, they expand because
their molecules gain kinetic energy and move around
more.
Expansions of solids can be
predicted using the linear
expansion equation.
Expansions of liquids can be
predicted using the volume
expansion equation.
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p q
The ticking noises heard after a
hot car is shut down are due the
shape changes of engine parts as
they cool.

Linear Expansion Equation
The linear expansion equation is of the form:
Where:
L = length of object
T = temperature
∆TαL∆L ××=
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p
α = coefficient of linear expansion [units = per degree]
∆ = Greek letter “delta”, change in.
Volume Expansion Equation
Similarly, the volume expansion equation is of the form:
∆TβV∆V ××=
Where:
V = volume of object
T = temperature
∆TβV∆V ××=
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ß = coefficient of volume expansion [units = per degree]
∆ = Greek letter “delta”, change in.

Expansion Coefficients
Note the units of the expansion coefficients:
1∆L
α ×=
1∆V
β ×=
The linear and volume expansion coefficients are
Thus, length and volume cancel. Both expansion
coefficients have units of “per degree”
∆TL
α ×
∆TV
β ×
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The linear and volume expansion coefficients are
related to each other by the following relationship:
Typical values for expansion coefficients may be
found in your physics textbook.
α3β ×=
Sample Problem: Thermal Expansion
Question: How much will the volume of a 2 cm3 aluminum
cube change if the temperature changes from 12°C to 32°C?
The linear expansion coefficient, α, of aluminum is 23x10-6/°C.
S l tiSolution:
Step 1: Use the volume expansion equation.
∆V = Vß * ∆T
Step 2: Calculate ∆T.
∆T = Tfinal –Tinitial = 32°C – 12°C = 20°C
St 3 C l l t ß
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Step 3: Calculate ß.
ß = 3α = 3 * 23 x10-6/°C = 69 x 10-6/°C
Step 4: Plug in the values.
∆V = Vß * ∆T = (2cm3) * (69x10-6/°C) * (20°C)
Answer: ∆V = 2.76x10-3 cm3

Note - Units and Temperature Change
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Thermostats - 1
Thermostats are designed to measure temperature
by applying the principle of linear expansion.
A thermostat uses two fused
strips of metal, each with a
different linear expansion
coefficient.
As the strip heats up one strip
lengthens faster so the strips
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bend away from the longer
strip.
Typically the bent strips will
make contact with a circuit.

Thermostats - 2
Imagine a thermostat made up of two metal strips
as shown below. The yellow strip has a larger
linear expansion coefficient.
Heat
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Heat
The strip bends towards the side with the lower
linear expansion coefficient.
Thermometers
Thermometers are designed to measure
temperature by applying the principle of thermal
expansion.
Most home thermometers use
mercury or alcohol inside a
narrow glass tube.
As the temperature rises, both
the glass and liquid expand.
The liquid has a higher volume
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The liquid has a higher volume
expansion coefficient than the
glass tube so it rises within the
tube to tell you the temperature.

Thermal Expansion: Stop-And-Think
Question: Why would engineers need to take
thermal expansion into account in the design
of bridges?
On hot days, the metal supports of a bridge will
expand and buckle if the bridge is not designed
to expand. Similarly, the bridge will crack as
the supports shrink on a cold day.
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Energy in Thermal
Processes
Heat and Internal Energy
Specific Heat
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Specific Heat
Calorimetry
Latent Heat and Phase Change
Energy Transfer
Global Warming and Greenhouse Gasses

System vs. Surroundings
Calculations of heat and internal energy are based
on the definition of a system and its surroundings.
System - The system
refers to the object
being studied.
Surroundings -
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g
Everything not
included in the system.
Example - System v. Surroundings
Example: a beaker
The system refers to
the contents of the
beaker.
Th di f
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The surroundings refer
to everything else.

Heat and Internal Energy Equation
Internal energy of a system is defined as:
1) The ability to do work on an object.
2) The ability to transfer heat to an object.
U = q + w
Heat
Heat energy of the
system
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q
Internal Energy
Work
System internal
energy
Work done on the
system or energy
available for the
system to do work.
Definition - Energy Units
Calorie (cal) - Heat is measured in
calories. A calorie is the amount of
heat required to heat 1 gram of water
1°C.
Joule (J) - Energy is measured in
Joules. One calorie (cal) is equal to
4 18J
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4.18J.
4.18 J = 1 cal

Definition - State Function
State Function - n. A state function is
a quantity of the object that isa quantity of the object that is
dependent on the current state. A
state function is independent of the
path taken to reach the current state.
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Temperature, kinetic energy, and
potential energy are all state functions.
Temperature is a State Function
Temperature is an example of a state function.
Your coffee can be 40°C whether you heated it in
the microwave or on the stove.
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40°C

Note: the Food Calorie
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Definition - Specific Heat
Specific Heat (CP) - n. Specific heatp ( P) p
is a material property that defines the
quantity of heat, q, required to raise
1g of a specific material 1°C.
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units of cp = [cal/gram*K]

Specific Heat Equation
T T
The specific heat may be used as follows:
Q = CPm * ∆T
Specific Heat
Change in
Temperature
Tfinal - Tinitial
(K) or (°C)
Proportionality
Constant
J/g*K or cal/g*K
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P
Heat
Total Heat Energy
(J)
Mass
Mass of Object
(g)
Interpretation of Specific Heat
What are the practical implications of specific heat?
High Specific Heat Low Specific Heat
Large amount of energy to
change temperature
Small amount of energy can
change temperature
Heats up slowly
Cools down slowly
Small temperature changes with
condition changes
e g Water Cast iron
Heats up quickly
Cools down quickly
Quickly readjusts to new
conditions
e g Air aluminum foil
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e.g. Water, Cast-iron e.g. Air, aluminum foil
A pool takes a long time to warm up and remains fairly warm over night.
The air warms quickly on a sunny day, but cools quickly at night
A cast-iron pan stays hot for a long time after removing from oven.
Aluminum foil can be grabbed by your hand from a hot oven
because it cools so quickly

Specific Heat and Heat Capacity
Thus, if the specific heat and the mass of any
object are known, then the amount of heat need to
raise the temperature by any given amount may be
calculated.
The heat capacity C of an object may be
determined from its specific heat CP and its mass
m as follows:
CmC ×
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C = heat capacity
CP = specific heat
m = mass of object
pCmC ×=
Definition - Heat Capacity
Heat Capacity (C) - The amount of heat Q
required to raise the temperature of an
object by ∆T is given by:
Q = C * ∆T
Heat Capacity
Proportionality
Constant
J/K or cal/K
object by ∆T is given by:
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Q = C * ∆T
Heat Change in Temperature
Tfinal - Tinitial
(K) or (°C)
Total Heat Energy
(J)

Definition - Enthalpy (H)
Enthalpy of Reaction (H) - The enthalpy of a
reaction is the heat energy (J) gained or lost
during a reaction. Enthalpy is a state function.during a reaction. Enthalpy is a state function.
Reaction
Bonds of reactants
broken. Bonds of
products formed.
Bonds of reactants have
hi h th
Bonds of products have
higher energy than
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higher energy than
bonds of products.
higher energy than
bonds of reactants.
Exothermic Endothermic
Heat given
off by system
Heat
absorbed by
system
Endothermic vs. Exothermic
Exothermic - If the system looses net
heat during a reaction, the reaction isg ,
exothermic.
Endothermic - If the system gains net
∆Hsystem = Hfinal – Hinitial < 0
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y g
heat energy during a reaction, the
reaction is endothermic.
∆Hsystem = Hfinal – Hinitial > 0

Definition - Calorimetry
Calorimetry. n.
Calorimetry is aCalorimetry is a
laboratory technique
used to determine the
amount of heat Q
taken up or given off
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by a reaction.
Procedure - Calorimetry
A small beaker is immersed in an insulated1
How to determine the heat of a reaction using
calorimetry.
beaker filled with a known amount of water.
The initial temperature of the water is noted.
A known amount of the reactants are
placed in the small reaction beaker.
The temperature of the water is recorded at
1
2
3
4
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regular intervals as the reaction proceeds.
The change is temperature is plotted versus time.
4
5
6
The heat given off by the reaction is calculated
from the total change in temperature of the water.

Example - Calorimetry
(1) Large,
insulated beaker
(2) Water initial(2) Water, initial
temperature Tinitial
(3) Reaction beaker
(4) Initiate reaction
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(5) Flow of heat energy
to water
(6) Measure final water
temperature, Tfinal
(7) Calculate ∆H from
∆Twater and the specific
heat of water, CP.
Endothermic vs. Exothermic Reactions
Endothermic Exothermic
Heat moves from Heat moves from system
surroundings to system
Internal energy of
system increases
KEAVE of system
molecules increases
Internal energy of system
decreases
KEAVE of the system
decreases
to surroundings.
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Temperature of the
system increases
Bonds of reaction
products have greater
energy than bonds of
reactants
Temperature of the
system decreases.
Chemical bonds of
reactants have greater
energy than bonds of
products.

Stop and Think- Calorimetry
Question: If the temperature of the water in a
l i t i t i i th ticalorimetry experiment rises, is the reaction
endothermic or exothermic?
Answer: The reaction is exothermic because heat
energy is moving from the system (the reaction) to
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energy is moving from the system (the reaction) to
the surroundings (the water).
A rise in temperature
Internal energy increases
When a solid is heated it undergoes the following:
Internal energy increases
Molecules oscillate more rapidly
A phase change from solid to liquid
Molecules oscillate so rapidly they loose their crystalline form
There is no increase in temperature during the transition
Another rise in temperature
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Another rise in temperature
A phase change from liquid to gas
Molecules oscillate so rapidly they escape the intermolecular
forces that bind them together and enter the gas phase
There is no increase in temperature during the transition.

Heats of Fusion and Vaporization
The amount of heat Qfus needed to melt m grams of a
substance is given by the following equation:
fusfus Lm∆Q ×=
Qfus = heat energy = [calories]
m = mass = [grams]
Lfus = Heat of Fusion = [calories/gram]
The amount of heat Qvap needed to vaporize m grams
of a substance is given by the following equation:
fusfus Lm∆Q ×
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Qvap = heat = [calories]
m = mass = [grams]
Lvap = Heat of Vaporization = [calories/gram]
of a substance is given by the following equation:
vapvap Lm∆Q ×=
Gas
Temperatureof
Substance
Phase
Liquid
Phase
Solid
Tboil
Tmelt
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Increase in Heat Energy, ∆Q
Solid
Phase
Qmelt
Qboil

Example - Heats of Transformation
Question: How much heat energy is required for 10 grams of ice
at 0°C to transition to liquid? To evaporate? The heat of fusion
for water is 333 KJ/kg. The heat of vaporization is 2256 KJ/kg.
Solution:Solution:
1) Calculate the heat energy required to melt 10 grams (0.01Kg) of ice.
Qfus = Lfus * m = 333 KJ/kg * 0.01 Kg = 3.33 KJ
2) Calculate the heat energy needed to raised the temperature of the
water from 0°C to 100°C.
Q = 0.00418 KJ/g*°C * 10.0 g * (100-0)°C = 4.18 kJ
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3) Calculate the heat energy required to vaporize 10g of water.
Qvap = Lvap * m = 2256 KJ/kg * 0.01Kg = 22.56 KJ
4) The total heat required is the sum of 1-3.
Qtot = 3.33 KJ + 4.18 KJ + 22.56 KJ = 30.07 KJ
Answer: Qtot = 30.07 KJ
Stop-and-think- Sweating
Question: Why is sweating an effective cooling
mechanism?
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Answer: As sweat evaporates from your skin it
transitions from the liquid to the gas phase. This
phase transition requires a transfer of heat energy
from the skin to the liquid, cooling the skin.

Global Warming & Greenhouse Gases
1) Heat energy radiates from the
sun to the earth
2) Some of the heat energy is
reflected off greenhouse gasesreflected off greenhouse gases
in the earth’s atmosphere.
3) Some of the heat energy is
reflected of the earth’s surface.
4) Some of the energy reflected off
the surface is trapped by
greenhouse gases in the
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atmosphere.
5) As the concentration of
greenhouse gases is increased
due to emissions from cars and
factories, the temperature of the
earth rises.
The Laws of
Thermodynamics
The Zeroth Law of Thermodynamics
Work in Thermodynamic Processes
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Work in Thermodynamic Processes
The First Law of Thermodynamics
Heat, Engines, and the Second Law of
Thermodynamics
Entropy
Human Metabolism

Heat Energy and the Laws of Thermodynamics
The Zeroth Law of Thermodynamics
states that objects in thermal
ilib i t th
The laws of thermodynamics govern energy
exchanges:
equilibrium are at the same
temperature.
The internal energy of a system is the
sum of the heat energy of the system
and the work done on or by the system.
The 1st Law of Thermodynamics states
that energy can change state but cannot
45/67
gy g
be created or destroyed.
The 2nd Law of Thermodynamics states
that the total entropy, or disorder, of the
universe can increase or stay the same
but never decrease. The universe tends
towards disorder.
Definition: Thermal Equilibrium
Thermal Equilibrium - Two objects are
thermal equilibrium are at the sameq
temperature. That is, when put in contact
they remain at the same temperature and
no longer exchange net heat energy.
A and B areIf A is placed inThe temperature
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A and B are
said to be in
thermal
equilibrium.
p
contact with B,
they both
remain at 10C°.
The temperature
of A is 10C° and
the temperature
of B is 10C°
Note that if objects are in thermal equilibrium, their
molecules also have the same average kinetic energy

Zeroth Law of Thermodynamics
Zeroth Law - If object A is in thermal
equilibrium with object B and object C,
then objects B and C are also in thermalthen objects B and C are also in thermal
equilibrium.
A
10 degrees
Celsius
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B C
10 degrees
Celsius
10 degrees
Celsius
Note that if B and C are in thermal equilibrium with A,
then they must also be at 10 degrees Celsius.
Work in Thermodynamics
As mentioned before:
U = q +U = q + w
U = system internal energy
q = heat energy
w = work done on or by the system
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Pressure-Volume Work
For constant pressure:
∆W = -P * ∆V
∆W = work done on or by the system
P = pressure
∆V = volume change of the system
One common type of application of this equation
is in calculating pressure-volume work done by
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engines.
Applied Pressure-Volume Work
If the system expands, work is done by
the system on the surroundings. The
internal energy of the systeminternal energy of the system
decreases.
If the system contracts, work is done
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by the surroundings on the system.
The internal energy of the system
increases.

The First Law of Thermodynamics
Energy in a reaction may be changed
from one form to another but it is neither
t d d t d ti fcreated nor destroyed – conservation of
energy.
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Application of The 1st Law
This implies that:
Q Q
∆U = ∆q + ∆w
Change in Heat Energy
W k d t b
Qinitial -Qfinal
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Change in System
Internal Energy
Work done to or by
the system
Ufinal - Uinitial Win -Wout

Work and the 1st Law
There are 4 special applications of the
1st Law:
1) Adiabatic: Q = 0, ∆U = -W
2) Constant-volume: W = 0, ∆U = Q
3) Cyclical: ∆U = 0, Q = -W
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4) Free expansion processes: ∆U = Q = W
Adiabatic Work
An example of adiabatic work is a closed system with a
piston. If pressure is applied rapidly to depress the
piston, the volume of the system will decrease. Work W
is done on the system by the surroundings, but there is
∆V ≥ 0
Q = 0, ∆U = -W = -P*∆V
is done on the system by the surroundings, but there is
no change in heat Q so the change in internal energy ∆U
is equal to –W.
W
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W
Vinitial
Vfinal

Constant-Volume Work
An example of constant-volume work is heating a
sealed cylinder. There is no volume change so the
change in internal energy is equal to the change in heat
energyenergy.
Tinitial Tfinal
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∆V = 0 so W = 0
∆T ≥ 0 so Q ≥ 0
∆U = Q
Cyclical Work and Engines
In an engine, heat is used to increase pressure leading to an
increase in volume. The change in volume does work on the
surroundings. The work energy is transferred back from the
surroundings to compress the cylinder back to its original size
and the cycle repeatsand the cycle repeats.
∆U = 0
Q W
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Q = -W

Free Expansion Work
Connecting a pressurized system to a vacuum is an
example of free-expansion work. The gas from the
pressurized system will immediately and irreversibly
expand to fill the vacuum The process occurs rapidlyexpand to fill the vacuum. The process occurs rapidly,
but unlike adiabatic work the process is irreversible.
∆U = Q = W = 0
Heating an open beaker may be considered free-
i k Th t th t t f th
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expansion work. The system, the contents of the
beaker, are open to the surroundings so there can be no
volume changes or heat exchanges.
Energy Calculations: Example
Question: If the volume of a sealed balloon
increases from 10mL to 100mL when heated and
then shrinks back to 10mL as it cools, what
f tapplication of the 1st Law is this?
Constant-volume
Adiabatic
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Cyclical

Energy Calculations: Answer
Question: If the volume of a sealed balloon
increases from 10mL to 100mL when heated and
then shrinks back to 10mL as it cools, what
f tapplication of the 1st Law is this?
Constant-volume
Adiabatic
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Cyclical
Definition - Entropy
Entropy (S) - n. Entropy is a measure of
the disorder of a system or its
surroundings.surroundings.
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A landfill possesses lots of entropy!

The 2nd Law of Thermodynamics
The 2nd Law of Thermodynamics states that the
total entropy of the universe can never decrease,
it can only increase or stay the same.
∆Stotal ≥ 0
Note that the entropy of the system may
decrease, so long as the entropy of the
s rro ndings increases b an eq al or greater
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surroundings increases by an equal or greater
amount.
Thus,
∆Ssys + ∆Ssur ≥ 0
Relative Entropies
Low entropy states are more organized than high
entropy states.
Lower Entropy Higher Entropy
Your clean bedroom Your room after finals
Solids Liquids
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Liquids
Salt tablets in water
Gases
Dissolved salt in water

Definition - Engine Efficiency
In a real combustion engine such as your car, some of the
work energy is lost to the surroundings as heat rather than
transferred to pressure-volume work which moves a piston.
The efficiency of an engine is the ratio of the heat energy put
in (for example by combustion) to the work output by the
engine (such as movement of the wheels of a car).
ε = Wout / Qin
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If the efficiency of an engine is 0.7, the 30% of the heat
from combustion is lost as heat to the surroundings. In
the real world, this would be a very efficient engine!!!
Entropy and Human Metabolism
Question: Metabolic processes in the body, such as
the building of proteins and DNA, lead to increased
order. How does this not violate the 2nd Law?
Answer: Although the building of
structural proteins in the body lead
to increased order in the system,
which is the body, they lead to
increased disorder in the
surroundings through loss of heat.
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surroundings through loss of heat.
Metabolic processes are usually
linked to a catabolic process such
as the combustion of glucose or
the flow of ions down a
concentration gradient.

Entropy: Stop-and-Think Question
Question: When an ice cube melts, does system
entropy increase, decrease, or remain the same?
Pick the best answerPick the best answer.
A. Remain the same because
there is no reaction, only a
state change.
B. Increase because the
molecules are changing
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g g
from an ordered crystalline
state to a disordered liquid
state.
C. Decrease because heat
is absorbed to melt the ice.
Entropy: Stop-and-Think Answer
Question: When an ice cube melts, does system
entropy increase, decrease, or remain the same?
Pick the best answerPick the best answer.
A. Remains the same because
there is no reaction, only a
state change.
B. Increases because the
molecules are changing
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g g
from an ordered crystalline
state to a disordered liquid
state.
C. Decreases because heat
is absorbed to melt the ice.

Entropy is aEntropy is a
Expansion
coefficients
measure how
Expansion
coefficients
measure how
The 2nd Law
states that net
entrop can
The 2nd Law
states that net
entrop can
Learning Summary
Heat energy mayHeat energy may
measure of
disorder.
measure of
disorder.
measure how
much objects
expand when
heated.
measure how
much objects
expand when
heated.
entropy can
never
decrease.
entropy can
never
decrease.
The 1st LawThe 1st Law
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Heat energy may
be gained or lost
to the
surroundings
during work.
Heat energy may
be gained or lost
to the
surroundings
during work.
The 1 Law
states that
energy is never
created or
destroyed.
The 1 Law
states that
energy is never
created or
destroyed.
Congratulations
Y h f ll l t dYou have successfully completed
the tutorial
Heat and
Thermodynamics
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Wh t’ N t
Chemistry :: Biology :: Physics :: Math
What’s Next …
Step 1: Concepts – Core Tutorial (Just Completed)
Step 2: Practice – Interactive Problem Drill
Step 3: Recap – Super Review Cheat Sheet
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Heat and Thermodynamics

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