Energy in Thermal Processes
AP Physics B
Lecture Notes
Energy in Thermal Processes
Topics
11-01 Heat and Internal Energy
11-02
11-03
11-04
11-05
Specific Heat
Calorimetry
Latent Heat and Phase Change
Energy Transfer
Heat and Internal Energy
Heat is random thermal Energy
Unit of heat: calorie (cal)
1 cal is the amount of heat necessary to raise the
temperature of 1 g of water by 1 Celsius degree.
1 kcal is the amount of heat necessary to raise the
temperature of 1 kg of water by 1 Celsius degree.
Heat and Internal Energy
Heat is a form of energy and can be equated to
mechanical energy.
The apparatus below is used to determine the
mechanical equivalent of heat:
4.186 J  1 cal
4186 J  1 kcal
Heat and Internal Energy
Definition of heat:
Heat is thermal energy transferred from one
object to another because of a difference in
temperature.
The sum total of all the energy of all the molecules in a
substance is its internal (or thermal) energy.
Temperature: measures molecules’ average kinetic energy
Internal energy: total energy of all molecules
Heat: transfer of energy due to difference in temperature
Energy in Thermal Processes 11-01
The amount of heat necessary to raise the temperature
of 1 gram of water by 1°C is referred to as the
(A) calorie.
(B) kilocalorie.
(C) British thermal unit.
(D) joule.
Heat and Internal Energy
Internal energy of an ideal
(monatomic) gas:
2
U  N 1 mv2
kinetic energy in terms
of the temperature
1
m v 2  3 kT
2
2
NkT  nRT
U  3 NkT
2
U  3 nRT
2

Energy in Thermal Processes 11-02
The measure of the average kinetic energy of individual
molecules is referred to as
(A) internal energy.
(B) thermal energy.
(C) temperature.
(D) heat.
Energy in Thermal Processes 11-03
The internal energy of an ideal gas depends on
(A) its volume.
(B) its pressure.
(C) its temperature.
(D) all of the above
Energy in Thermal Processes 11-04
An ideal gas with internal energy U at 200°C is heated
to 400°C. Its internal energy then will be
(A) still U.
(B) 2 U.
(C) 1.4 U.
(D) 1.2 U.
Specific Heat
(c) Specific heat
of the material
(Q) Thermal
energy added
Q  mc T
(m) Mass of
the object
m
(T) Change in
temperature
Specific Heat
Energy in Thermal Processes 11-05
Water has a higher specific heat capacity than iron. Now,
consider equal masses of water and iron that are initially in
thermal equilibrium. The same amount of heat, 30 calories, is
added to each. Which statement is true?
(A) They remain in thermal equilibrium.
(B) They are no longer in thermal equilibrium; the iron is warmer.
(C) They are no longer in thermal equilibrium; the water is warmer.
(D) It is impossible to say without knowing the exact mass
involved and the exact specific heat capacities.
Problem
A 50 g piece of cadmium is at 20 oC. If 400 J of heat
is added to the cadmium, what is its final temperature
ccadmium  230
Q  mcT
T 
Q

mc
400 J
0.050 kg  230
 34.8 Co
J
kg  Co
Tf  To  T
Tf  20.0 oC  34.8 Co
o
 54.8 C
J
kg  Co
Problem
A 100 g lead bullet traveling at 300 m/s is stopped by a large
tree. Half the kinetic energy of the bullet is transformed into
heat energy and remains with the the bullet while the other
half is transmitted to the tree. What is the increase in
temperature of the bullet?
J
Q bullet   
mcT 
mv
c lead  130
ΔK bullet 
2
2
4
T 
v
2
4c

300 m/s 2
4  130
J
kg  Co
 173 Co
kg  Co
Problem
A 3.0 kg block of iron is dropped from rest from the top
of a cliff. When the block hits the ground it is observed
that its temperature increases by 0.50 oC. Assume that
all the potential energy is used to heat the block. How
high is the cliff?
J
c iron  450
 U block   Qblock 
mgh  mcT
h
cT
g
450

J
kg  C

0.50o C 
o
9.8 m/s 2
 23 m
kg  Co
Problem
A 1.5 kg copper block is given an initial speed of 30 m/s on
a rough horizontal surface Because of friction, the block
finally comes to rest. If the block absorbs 85% of its initial
kinetic energy in the form of heat, Calculate its increase in
temperature?
J
ccopper  390
Q block   0.85 K block 
mcT  0.85 
T  0.85 
v
mv
2
2c
kg  Co
2
2
 0.85 
30 m/s 2
2  390
J
kg  Co
o
 1.0 C
Calorimetry
m1
m2

TH
Q loss 
TL
Q gain 
Conservation of thermal energy:
Qgain   Qloss
m 2c 2ΔT2  m1c1ΔT1
m 2c 2 Tf  TL   m1c1 TH  Tf 
Final Temperature:
Tf 
m1c1TH  m 2c 2TL
m1c1  m 2c 2
Calorimetry (Problem)
A 0.40 kg iron horseshoe that is initially at 500 oC is
dropped into a bucket containing 20 kg of water at 22 oC.
What is the final equilibrium temperature?
Neglect any heat transfer to for from the surroundings.
c iron  450
Qgain   Qloss
m Wc W ΔTW  m I cI ΔTI
20 4186 Tf
 22  0.4 450 500  Tf 
83720Tf  1841840  90000  180Tf
o
Tf  23 C
J
kg  Co
J
c water  4186
kg  Co
Calorimetry (Problem)
A 200 g block of copper at a temperature
of 90 oC is dropped into 400 g of water at
27 oC. The water is contained in a 300 g
glass container. What is the final
temperature of the mixture
ccopper  390
c water  4186
c glass  840
Qgain   Qloss
m Wc W ΔTW  mG cG ΔTG  mCcCΔTC
0.4 4186 Tf
 27   0.3 840 Tf  27   0.2 390 90  Tf 
1674.4Tf  45208  252Tf  6804  7020  78Tf
Tf  29.5 oC
J
kg  Co
J
kg  Co
J
kg  Co
Latent Heat and Phase Change
Energy is required for a material
to change phase, even though its
temperature is not changing.
(m) Mass of
the object
Q  mL
(Q) Thermal
energy added
(L) Latent heat
of the fusion or
vaporization
Latent Heat and Phase Change
Heat of fusion, Lf: heat required to change 1.0 kg
of material from solid to liquid
Heat of vaporization, Lv: heat required to change 1.0 kg
of material from liquid to vapor
Latent Heat and Phase Change
1 kg
Ice
-50 oC
Q2= mLf
Q4= mLv
3.33 x 105 J
22.6 x 105 J
150
100
50
0
50
Q1= mcIt
1.05 x 105 J
Q3= mcWt
Q5= mcSt
4.19 x 105 J
1.01 x 105 J
Latent Heat and Phase Change
Heat required to convert 1 kg of ice
at -50 oC to steam at 150 oC
Q1 = 1.05 x 105 J
Q2 = 3.33 x 105 J
Q3 = 4.19 x 105 J
Q4 = 22.6 x 105 J
Q5 = 1.01 x 105 J
3.22 x 106 J
Latent Heat and Phase Change (Problem)
A large block of ice at 0 oC has a hole chipped in it, and
400 g of aluminum pellets at a temperature of 30 oC are
poured into the hole. How much of the ice melts?
Q( gain )  Q loss 
caluminum  900
mI Lf  m Ac A TA
L f water   333
mI  
m A c A TA
Lf
0.4 kg  900
mI  
J
kg  C

0  30 Co
o
3.33 x 105
J
kg
 0.032 kg
J
kg  Co
kJ
kg  Co
Energy Transfer
Heat conduction can be visualized as occurring through
molecular collisions.
x
The heat flow per unit time is given by:
Q
t

kAT1  T2 
x
Energy in Thermal Processes 11-06
Equal masses of water at 20°C and 80°C are mixed.
What is the final temperature of the mixture?
(A) 40°C
(B) 50°C
(C) 60°C
(D) 70°C
Energy Transfer
The constant k is called the thermal
conductivity.
Materials with large k are called
conductors; those with small k are
called insulators.
Energy Transfer (Problem)
Problem:
A window has a glass surface of 1.6 x 103 cm2 and a
thickness of 3.0 mm. Find the rate of heat transfer by
conduction through this pane when the temperature of
the inside surface of the glass is 20 oC and the outside
temperature is 40 oC.
J
Q
t

k glass  0.84
kAT
x



W 

 1m 
3
2
 0.84
 1.6 x 10 cm 

o
 100 cm 

m C
3.0 x 10  3 m
ΔQ
Δt
 896 J / s
2
20 oC
s  m  Co
Energy Transfer (Problem)
Problem:
A glass window pane has an area of 3.0 m2 and a
thickness of 0.60 cm. If the temperature difference
between its faces is 25 oC, how much heat flows
through the window per hour?
Q
t

Q 
k glass  0.84
kAT
x
kAT t
x
ΔQ  3.78 x 107 J



J
s  m  Co
W 

 0.84
 3 m 2 25 Co 3600 s 

m  Co 

0.006 m
Energy Transfer
Building materials are measured using R−values rather than
thermal conductivity:
R
x
k
Where, x is the thickness of the material.
Energy in Thermal Processes 11-07
The heat required to change a substance from the solid to
the liquid state is referred to as the
(A) heat of fusion.
(B) heat of vaporization.
(C) heat of melting.
(D) heat of freezing.
Energy in Thermal Processes 11-08
When a liquid freezes
(A) the temperature of the substance increases.
(B) the temperature of the substance decreases.
(C) heat energy leaves the substance.
(D) heat energy enters the substance.
Energy in Thermal Processes 11-09
Phase changes occur
(A) as the temperature decreases.
(B) as the temperature increases.
(C) as the temperature remains the same.
(D) all of the above
Energy in Thermal Processes 11-10
By what primary heat transfer mechanism does one end
of an iron bar become hot when the other end is placed
in a flame?
(A) natural convection
(B) conduction
(C) radiation
(D) forced convection
Energy in Thermal Processes 11-11
If you double the thickness of a wall built from a
homogeneous material, the rate of heat loss for a given
temperature difference across the thickness will
(A) become one-half its original value.
(B) also double.
(C) become one-fourth its original value.
(D) none of the above
Energy Transfer Summary
Internal energy U refers to the total energy of all molecules
in an object. For an ideal monatomic gas,
U  3 NkT  3 nRT
2
2
Heat is the transfer of energy from one object to another
due to a temperature difference. Heat can be measured in
joules or in calories.
Q  mcΔT
Specific heat of a substance is the energy required to change
the temperature of a fixed amount of matter by 1° C.
Energy Transfer Summary
In an isolated system, heat gained by one part of the
system must be lost by another.
Calorimetry measures heat exchange quantitatively.
Energy in involved in phase changes even though the
temperature does not change.
Heat of fusion: amount of energy required to melt 1
kg of material.
Heat of vaporization: amount of energy required to
change 1 kg of material from liquid to vapor.
Q  mL
Energy Transfer Summary
Heat transfer takes place by conduction, convection, and
radiation.
In conduction, energy is transferred through the
collisions of molecules in the substance.
Q
t

kAT
x