PHYSICS 220
Lecture 24
Heat
Textbook Sections 14.4 – 14.5
Lecture 25
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Exam 2
Average: 96.7
out of 150
Std Dev: 30.5
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Overview
• Last Lecture
– Thermal Expansion
• ΔL = α L0 ΔT (linear expansion)
• ΔV = β L0 ΔT (volume expansion)
– Kinetic Theory of Monatomic Ideal Gas
• <Ktr> = 3/2 kB T
• Today
– Heat
– Specific Heat
– Phase Transitions
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Quiz
1) A pendulum is made from an aluminum rod with a mass
attached to its free end. If the p
pendulum is cooled does the
pendulum's period
A) increase
B) decrease
d
C) stay the same
2) A steel tape measure is marked in such a way that it gives
accurate length measurements at a normal room
temperature off about 20°C.
20°C Iff this tape measure is used
outdoors on a cold day when the temperature is 0°C, are
its measurements
A) too long
B) too short
C) accurate
t
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Internal Energy
• Energy of all molecules including
– Random
R d
motion
ti off iindividual
di id l molecules
l
l
• <Ktr> = 3/2 k T
for ideal gas
• Vibrational energy of molecules and atoms
– Chemical energy in bonds and interactions
• DOES NOT INCLUDE
– Macroscopic
M
i motion
ti off object
bj t
– Potential energy due to interactions with other objects
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Heat
• Definition: Flow of energy between two objects
due to difference in temperature
– Note: similar to WORK
– Object does not “have”
have heat (it has energy)
• Units: calorie
– Amount of heat needed to raise 1g of water 1ºC
– 1C
Calorie
l i = 1 kkcall = 1000 call = 4186 JJoules
l
• Heat flows from a system at higher temperature
to one at lower temperature
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Heat
• The energy that flows between the systems is called heat or
heat energy
– Heat is energy that passes from one system to another by virtue of a
temperature difference
• The terms heat and heat energy are often used
interchangeably
– In physics, they always refer to the transfer of energy between
systems
• According to the principle of conservation of energy
energy, the
amount of heat energy that “leaves” system 1 must equal the
amount of heat energy
gy that “enters” system
y
2
• The transfer can take place in different ways
• The direction of the transfer depends
p
only
y on the temperature
p
difference
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Units of Heat
• The SI unit of heat is the same as for energy, the
Joule (J)
• A unit called the calorie is widely used for heat
– 1 cal = 4.186 J
• The Calorie, with an uppercase “C,” is used to
measure the energy content of food
– 1 Calorie = 1000 calories
– So 1 food Calorie is a kcal
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Heat and Mechanical Energy
• James Joule measured the
“
“mechanical
h i l equivalent”
i l ” off
heat energy
• The apparatus
apparat s he used
sed is
similar to the one shown
• As the mass fell,
fell its potential
energy rotated the paddle,
raising
g the temperature
p
of the
liquid
• Joule could then relate the
mechanical energy to the
heat energy
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Heat Capacity and Specific Heat
• Heat capacity is the ratio between the heat energy
added to a system and the resulting change in
temperature
Q
heat capacity =
ΔT
ΔT
• Specific heat takes into account the size (mass) of
y
the system
Q
specific
ifi h
heatt = c =
m ΔT
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Specific Heat
• Heat adds energy to object/system
• IF system
t
d
does NO workk then:
th
– Heat increases internal energy: Q = ΔU
– Heat
H t iincreases ttemperature:
t
Q = C ΔT
T
• Q = c m ΔT
– Heat required to increase temperature
depends on amount of material (m) and type
of material (c)
• Q = cmΔT : “Cause” = “inertia” x “effect” (just like F=ma)
–
–
–
–
cause = Q
effect
ff t = ΔT
inertia = cm (mass x specific heat capacity)
c … specific heat
• ΔT = Q/cm (just like a = F/m)
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Exercise
After a grueling work out, you drink a liter of cold
water (0 C). How many Calories does it take for
your body to raise the water up to body
e pe a u e o
of 36 C
C?
temperature
A) 36
B) 360
C) 3,600
3 600
D) 36,000
36 000
1 liter
li
= 1
1,000
000 grams of
f H20
1000 g x 1 calorie/(gram degree) x (36 degree) = 36,000 calories
36,000 calories = 36 Calories!
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Question
Suppose you have equal masses of aluminum and
copper at the same initial temperature.
temperature You add 1000 J
of heat to each of them. Which one ends up at the
higher final temperature
A) aluminum
B) copper
C)) the same
Substance
aluminum
copper
iron
lead
h
human
body
b d
water
ice
c in J/(kg-C)
900
387
452
128
3500
4186
2000
ΔT = Q/cm
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ILQ
Two insulated buckets contain the same amount of water at
room temperature. Two blocks of metal of the same mass,
both at the same temperature, are warmer than the water in
the buckets. One block is made of aluminum (c=0.9) and one
is made of copper
copper. You put the aluminum block into one
bucket of water, and the copper (c=0.385) block into the other.
After waiting a while you measure the temperature of the
water in both buckets. Which is warmer?
A) The water in the bucket containing the aluminum block
B) The water in the bucket containing the copper block
C) The water in both buckets will be at the same temperature
Since aluminum has a higher specific heat than copper, you are
adding more heat to the water when you dump the aluminum in the
bucket (Q=mcΔT).
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Specific Heat for Ideal Gas
• Monatomic Gas (single atom)
–
–
–
–
Translational kinetic energy only
At constant Volume work = 0
Q = ΔU = 3/2 nRΔT
CV = 3/2 R = 12.5 J/(K
( mole))
• Diatomic Gas (two atoms)
– Can also rotate
– CV = 5/2 R = 20.8 J/(K mole)
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Latent Heat
• As you add heat to water, the temperature increases
f a while,
for
hil th
then it remains
i constant,
t t d
despite
it th
the
additional heat!
steam
T
Substance
water
Lf (J/kg)
33.5 x 104
f=fusion
100oC
Lv (J/kg)
22.6 x 105
water
t
temp
rises
v=vaporization
water
changes
to steam
(boils)
temp
rises
Latent Heat
Q added to water
• Latent Heat L [J/kg] is heat which must be added (or
removed) for material to change phase (liquid-gas).
• |Q| = m L
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Phases of Matter
• There
Th
are three
th
states
t t off matter:
tt
– Solid
– Liquid
– Gas
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Solids
• The atoms in many solids are arranged in an orderly
and repeating pattern called a crystalline lattice
– Each atom is held in place by the forces exerted by
neighboring atoms
– These forces are a result of chemical bonds within the
solid
– The atoms actually vibrate about their positions as simple
harmonic oscillators
• An amorphous solid has atoms arranged without the
repeating structure found in a crystal
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Liquids
• The atoms in a liquid are not held in fixed locations
by the forces of neighboring atoms
• The atoms are able to move about
• The atoms adjacent to a particular atom are not
likely to be adjacent a short time later
• This motion helps liquids to flow
• Although the bonds between neighboring atoms do
not persist, there is still potential energy associated
with the forces between the molecules
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Gases
• In some ways, a gas is similar to a liquid
• The molecules are able to move over long distances
• The density of a gas is generally much lower than
that of a liquid
• The spacing
p
g between the molecules of a g
gas is
larger
• The magnitude of the intermolecular force
force, and
therefore potential energy, is much smaller
• Most of the mechanical energy in a gas is found in
the kinetic energies of its molecules
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Internal Energy
• The mechanical energy of the molecules in a system
is called the internal energy of the system
– Denoted by U
• The internal energy of a system is the sum of all
potential energies associated with all the
intermolecular bond plus the kinetic energies of all
the molecules
• The value of U increases as we go from solid to
liquid to gas
• In general, the internal energy of all systems
p
is increased
increases as the temperature
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Phase Transitions
• A phase transition occurs whenever a material is changed
from one phase
phase, such as the solid phase
phase, to another phase
phase,
such as the liquid phase.
– Phase transitions occur at constant temperature.
– The latent heat of vaporization LV is the heat per unit mass that must
flow to change the phase from liquid to gas or from gas to liquid.
• F
Fusion
i occurs when
h a liliquid
id tturns iinto
t a solid.
lid
• Evaporation occurs when a liquid turns into a gas.
• Sublimation
S bli ti occurs when
h a solid
lid changes
h
di
directly
tl tto a gas
without going into a liquid form.
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Phase Changes
• The transformation of a solid
to a liquid, a liquid to a gas,
etc. is called a phase
change
• Phase changes
g can be
produced by changing the
p
or by
y changing
g g
temperature
the pressure of the system
• A phase diagram shows the
phases found at different
temperatures and pressures
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Phase Changes, cont.
• Phase diagrams show the phase changes a system
can experience
• The line that separates liquid and gas ends at the
critical
i i l point
i
• The triple point is where solid, liquid, and gas phase
regions all meet
– For water, this is 273.16 K
– This was actually used in the definition of the Kelvin scale
• Table 14.3 lists the melting and evaporation
temperatures of some common substances
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Phase Diagram
H2O
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Phase Diagram
CO2
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Ice ILQ
Which can absorb more energy from your soda, a
cooler filled with water at 0 C
C, or a cooler filled
“cooler”
with ice at 0 C.
A) W
Water
t
B) Ab
Aboutt S
Same
C) IIce
Latent Heat L [J/kg] is heat which must be added
((or removed)
m
)f
for m
material to change
ng p
phase ((liquidqu
water
ice
gas).
ice
T
Substance
water
Lecture 25
Lf (J/kg)
33 5 x 104
33.5
0oC
Lv (J/kg)
22 6 x 105
22.6
temp
rises
Purdue University, Physics 220
changes
to water
(melts)
temp
rises
Latent Heat
Q added to water
27
Exercise
During
g a tough
g work out, yyour body
y sweats ((and evaporates)
p
)
1 liter of water to keep cool (37 C). How much cold water
would you need to drink (at 2 C) to achieve the same thermal
cooling?
li ? ((recallll CV = 4.2
4 2 J/
J/g ffor water,
t Lv=2.2x10
2 2 103 J/g)
J/ )
A) 0.15 liters
B) 1.0 liters
C) 15 liters
D) 150 liters
Qevaporative = L m = 2.2x103 kJ/kg x 1kg
Qc = c m Δt = 4.2kJ/kgK x 35K x m
m = 2.2x10
2 2 103 / 147 = 15kg
15k or 15 liters!
lit !
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Boiling Point
Going from Lafayette to Denver the
temperature at which water boils:
A) Increases
Lecture 25
B) Decreases
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C) Same
29
Boiling ILQ
What happens to the boiling point when
beaker is placed in ice-water?
A) Increases
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B) Decreases
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C) Same
30
Cooling ILQ
What happens to the pressure in the beaker
when placed in ice-water?
A) Increases
B) Decreases C) Same
PV = nRT
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ILQ
What will happen to the water in the container
when I pour ice water over the container
A) cool down
Lecture 25
B) Boil
C) Both D) Neither
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Exercise
How much ice (at 0 C) do you need to add to 0.5 liters of a
water
ate at 25
5 C, to cool
coo itt do
down to 10
0C
C?
(L = 80 cal/g, c = 1 cal/g C)
Qwater = mcΔT
= (0.5kg )(1cal / gC )(15C )
= (7,500
(7 500 calories)
Qice = mL + mcΔT
Qice
∴ m=
L + cΔT
7,500cal
=
= 83.3 grams
80cal / g + (1cal / gC )(10)
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Exercise
Ice cube trays are filled with 0.5 kg of water at 20 C and
placed
p
aced into
to tthe
e freezer.
ee e How
o much
uc e
energy
e gy must
ust be
removed from the water to turn it into ice cubes at -5 C?
(L = 80 cal/g, cwater = 1 cal/g C, cice = 0.5 cal/g C)
Water going from 20 C to 0 C:
Q1 = mcwater ΔT1
= 500 ×1× (−20) = −10000 (cal )
Water turning into ice at 0 C:
Q2 = −mL
= −500 × 80 = −40000 (cal )
Ice going from 0 C to -5 C:
Q3 = mcice ΔT2
= 500 × 0.5 × (−5) = −1250 (cal )
∴ Q = Q1 + Q2 + Q3 = −51250 (cal )
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Summary of Concepts
• Heat is FLOW of energy
– Flow
Fl
off energy may increase
i
ttemperature
t
• Specific Heat
– ΔT = Q / ((c m))
– Monatomic IDEAL Gas CV = 3/2 R
– Diatomic IDEAL Gas CV = 5/2 R
• Latent Heat
– Heat associated with change in phase
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