July 16, Week 7
Today: Chapter 17: Temperature and Heat
Final Homework #7 now available. Due tomorrow at 12:30.
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Heat
16th July 2015
Self Inductance
When put into a circuit, a single solenoid or solenoid-like object will
effect the circuit’s behavior.
Heat
16th July 2015
Self Inductance
When put into a circuit, a single solenoid or solenoid-like object will
effect the circuit’s behavior.
R
i
E
Heat
16th July 2015
Self Inductance
When put into a circuit, a single solenoid or solenoid-like object will
effect the circuit’s behavior.
R
i
If i is increasing:
E
Heat
16th July 2015
Self Inductance
When put into a circuit, a single solenoid or solenoid-like object will
effect the circuit’s behavior.
R
i
If i is increasing:
R
i
E
E
Heat
Eind
16th July 2015
Self Inductance
When put into a circuit, a single solenoid or solenoid-like object will
effect the circuit’s behavior.
R
i
If i is increasing:
R
i
E
E
Eind
If i is decreasing:
Heat
16th July 2015
Self Inductance
When put into a circuit, a single solenoid or solenoid-like object will
effect the circuit’s behavior.
R
i
If i is increasing:
R
i
E
E
Eind
If i is decreasing:
R
i
E
Heat
Eind
16th July 2015
Self Inductance
When put into a circuit, a single solenoid or solenoid-like object will
effect the circuit’s behavior.
R
i
If i is increasing:
R
i
E
E
If i is decreasing:
R
i
E
Heat
Eind
Eind is always opposed to the change in current
that created it, so it’s called the circuit’s back emf.
Eind
16th July 2015
Self Inductance
When put into a circuit, a single solenoid or solenoid-like object will
effect the circuit’s behavior.
R
i
If i is increasing:
R
i
E
E
If i is decreasing:
R
i
E
Eind is always opposed to the change in current
that created it, so it’s called the circuit’s back emf.
Eind
Self Inductance, L:
Heat
Eind
Eind
di
= −L
dt
16th July 2015
Inductors and Energy
Any object that has a constant self inductance is called an Inductor
Heat
16th July 2015
Inductors and Energy
Any object that has a constant self inductance is called an Inductor
R
E
Heat
I
L
16th July 2015
Inductors and Energy
Any object that has a constant self inductance is called an Inductor
2
R
N
I
For a Solenoid: L = µ0
A
ℓ
E
L
(ℓ is the solenoid’s length and A is its cross-sectional area)
Heat
16th July 2015
Inductors and Energy
Any object that has a constant self inductance is called an Inductor
2
R
N
I
For a Solenoid: L = µ0
A
ℓ
E
L
(ℓ is the solenoid’s length and A is its cross-sectional area)
1 2
Energy Stored in an Inductor: U = LI
2
Heat
16th July 2015
Inductors and Energy
Any object that has a constant self inductance is called an Inductor
2
R
N
I
For a Solenoid: L = µ0
A
ℓ
E
L
(ℓ is the solenoid’s length and A is its cross-sectional area)
1 2
Energy Stored in an Inductor: U = LI
2
1 2
B
Energy density of a magnetic field: u =
2µ0
Heat
Unit: J/m3
16th July 2015
Thermal Energy Exercise
A 10-kg mass sliding to the right, initially with speed 3 m/s, is
stopped by friction. Where does the mass’s kinetic energy go?
3 m/s
Heat
16th July 2015
Thermal Energy Exercise
A 10-kg mass sliding to the right, initially with speed 3 m/s, is
stopped by friction. Where does the mass’s kinetic energy go?
3 m/s
1
1
2
No Potential Energy ⇒ mvi + Wf = mvf2
2
2
Heat
Wf = work done by friction.
16th July 2015
Thermal Energy Exercise
A 10-kg mass sliding to the right, initially with speed 3 m/s, is
stopped by friction. Where does the mass’s kinetic energy go?
3 m/s
1
1
2
No Potential Energy ⇒ mvi + Wf = mvf2
2
2
Wf = work done by friction.
vi = 3 m/s, vf = 0 ⇒ 45 J + Wf = 0 ⇒ Wf = −45 J
Heat
16th July 2015
Thermal Energy Exercise
A 10-kg mass sliding to the right, initially with speed 3 m/s, is
stopped by friction. Where does the mass’s kinetic energy go?
3 m/s
This 45 J of energy is absorbed by
the molecules of the block, the floor,
and the surrounding air. Chapter 17
deals with the effect that this energy
has on the molecules inside each of
these substances.
1
1
2
No Potential Energy ⇒ mvi + Wf = mvf2
2
2
Wf = work done by friction.
vi = 3 m/s, vf = 0 ⇒ 45 J + Wf = 0 ⇒ Wf = −45 J
Heat
16th July 2015
Thermal Energy Exercise
A 10-kg mass sliding to the right, initially with speed 3 m/s, is
stopped by friction. Where does the mass’s kinetic energy go?
3 m/s
This 45 J of energy is absorbed by
the molecules of the block, the floor,
and the surrounding air. Chapter 17
deals with the effect that this energy
has on the molecules inside each of
these substances.
We say that Wf = −∆U
U is the
Internal Energy of the molecules.
1
1
2
No Potential Energy ⇒ mvi + Wf = mvf2
2
2
Wf = work done by friction.
vi = 3 m/s, vf = 0 ⇒ 45 J + Wf = 0 ⇒ Wf = −45 J
Heat
16th July 2015
Phases
Internal Energy, U - The total energy (both kinetic and potential) of
the molecules in a substance.
Heat
16th July 2015
Phases
Internal Energy, U - The total energy (both kinetic and potential) of
the molecules in a substance.
The types of internal energy the molecules have depends on the
phase of the substance.
Heat
16th July 2015
Phases
Internal Energy, U - The total energy (both kinetic and potential) of
the molecules in a substance.
The types of internal energy the molecules have depends on the
phase of the substance.
Phases of Matter - Solid, liquid, or gas
Heat
16th July 2015
Phases
Internal Energy, U - The total energy (both kinetic and potential) of
the molecules in a substance.
The types of internal energy the molecules have depends on the
phase of the substance.
Phases of Matter - Solid, liquid, or gas
The molecules’ “Degree of Freedom” determines whether the
object is a solid, liquid, or gas.
Heat
16th July 2015
Phases
Internal Energy, U - The total energy (both kinetic and potential) of
the molecules in a substance.
The types of internal energy the molecules have depends on the
phase of the substance.
Phases of Matter - Solid, liquid, or gas
The molecules’ “Degree of Freedom” determines whether the
object is a solid, liquid, or gas.
Solid - molecules
vibrate about a
fixed position
Heat
16th July 2015
Phases
Internal Energy, U - The total energy (both kinetic and potential) of
the molecules in a substance.
The types of internal energy the molecules have depends on the
phase of the substance.
Phases of Matter - Solid, liquid, or gas
The molecules’ “Degree of Freedom” determines whether the
object is a solid, liquid, or gas.
Solid - molecules
vibrate about a
fixed position
Heat
Liquid - molecules can
go anywhere below the
surface
16th July 2015
Phases
Internal Energy, U - The total energy (both kinetic and potential) of
the molecules in a substance.
The types of internal energy the molecules have depends on the
phase of the substance.
Phases of Matter - Solid, liquid, or gas
The molecules’ “Degree of Freedom” determines whether the
object is a solid, liquid, or gas.
Solid - molecules
vibrate about a
fixed position
Heat
Liquid - molecules can
go anywhere below the
surface
Gas - molecules
can go anywhere
16th July 2015
Internal Energy and Temperature
In all phases, the molecules have translational kinetic energy, so it
is the most important type of internal energy. (Rotational kinetic
energy, vibrational kinetic energy, and potential energy due to
interactions with other molecules can also be important.)
Heat
16th July 2015
Internal Energy and Temperature
In all phases, the molecules have translational kinetic energy, so it
is the most important type of internal energy. (Rotational kinetic
energy, vibrational kinetic energy, and potential energy due to
interactions with other molecules can also be important.)
In all phases, the molecules have random speeds. (In liquids and
gases, the molecules have random directions too.)
Heat
16th July 2015
Internal Energy and Temperature
In all phases, the molecules have translational kinetic energy, so it
is the most important type of internal energy. (Rotational kinetic
energy, vibrational kinetic energy, and potential energy due to
interactions with other molecules can also be important.)
In all phases, the molecules have random speeds. (In liquids and
gases, the molecules have random directions too.)
Temperature - A measure of the average translational kinetic
energy of the molecules
“Measure” ⇒ A number directly proportional to the average kinetic
energy
Heat
16th July 2015
Temperature Scales
In the U.S. there are currently three temperature scales used:
Heat
16th July 2015
Temperature Scales
In the U.S. there are currently three temperature scales used:
Celsius scale
Heat
16th July 2015
Temperature Scales
In the U.S. there are currently three temperature scales used:
Celsius scale - Pure water at sea level freezes at 0◦ C and boils
at 100◦ C
Heat
16th July 2015
Temperature Scales
In the U.S. there are currently three temperature scales used:
Celsius scale - Pure water at sea level freezes at 0◦ C and boils
at 100◦ C
Fahrenheit scale
Heat
16th July 2015
Temperature Scales
In the U.S. there are currently three temperature scales used:
Celsius scale - Pure water at sea level freezes at 0◦ C and boils
at 100◦ C
Fahrenheit scale - Pure water at sea level freezes at 32◦ F and
boils at 212◦ F
Heat
16th July 2015
Kelvin Scale
The Kelvin scale is based on the physical definition of temperature.
Heat
16th July 2015
Kelvin Scale
The Kelvin scale is based on the physical definition of temperature.
Lower temperature ⇒ lower kinetic energy ⇒ slower speeds
Heat
16th July 2015
Kelvin Scale
The Kelvin scale is based on the physical definition of temperature.
Lower temperature ⇒ lower kinetic energy ⇒ slower speeds
Absolute Zero - The lowest possible temperature. At absolute zero,
all molecular motion would stop.
Heat
16th July 2015
Kelvin Scale
The Kelvin scale is based on the physical definition of temperature.
Lower temperature ⇒ lower kinetic energy ⇒ slower speeds
Absolute Zero - The lowest possible temperature. At absolute zero,
all molecular motion would stop.
On the Kelvin scale, absolute zero = 0 K (No degree sign.)
Heat
16th July 2015
Kelvin Scale
The Kelvin scale is based on the physical definition of temperature.
Lower temperature ⇒ lower kinetic energy ⇒ slower speeds
Absolute Zero - The lowest possible temperature. At absolute zero,
all molecular motion would stop.
On the Kelvin scale, absolute zero = 0 K (No degree sign.)
The spacing on the Kelvin scale was chosen to be the same as the
Celsius scale
Heat
16th July 2015
Kelvin Scale
The Kelvin scale is based on the physical definition of temperature.
Lower temperature ⇒ lower kinetic energy ⇒ slower speeds
Absolute Zero - The lowest possible temperature. At absolute zero,
all molecular motion would stop.
On the Kelvin scale, absolute zero = 0 K (No degree sign.)
The spacing on the Kelvin scale was chosen to be the same as the
Celsius scale ⇒
∆T (K) = ∆T ( C)
◦
Heat
So any equation with ∆T can use either
Kelvin or Celsius
16th July 2015
Kelvin Scale
The Kelvin scale is based on the physical definition of temperature.
Lower temperature ⇒ lower kinetic energy ⇒ slower speeds
Absolute Zero - The lowest possible temperature. At absolute zero,
all molecular motion would stop.
On the Kelvin scale, absolute zero = 0 K (No degree sign.)
The spacing on the Kelvin scale was chosen to be the same as the
Celsius scale ⇒
∆T (K) = ∆T ( C)
◦
So any equation with ∆T can use either
Kelvin or Celsius
From experiment, 0 K = −273◦ C
Heat
16th July 2015
Kelvin Scale
The Kelvin scale is based on the physical definition of temperature.
Lower temperature ⇒ lower kinetic energy ⇒ slower speeds
Absolute Zero - The lowest possible temperature. At absolute zero,
all molecular motion would stop.
On the Kelvin scale, absolute zero = 0 K (No degree sign.)
The spacing on the Kelvin scale was chosen to be the same as the
Celsius scale ⇒
∆T (K) = ∆T ( C)
◦
So any equation with ∆T can use either
Kelvin or Celsius
From experiment, 0 K = −273◦ C ⇒ T (K) = T (◦ C) + 273
Heat
16th July 2015
Kelvin Scale
The Kelvin scale is based on the physical definition of temperature.
Lower temperature ⇒ lower kinetic energy ⇒ slower speeds
Absolute Zero - The lowest possible temperature. At absolute zero,
all molecular motion would stop.
On the Kelvin scale, absolute zero = 0 K (No degree sign.)
The spacing on the Kelvin scale was chosen to be the same as the
Celsius scale ⇒
∆T (K) = ∆T ( C)
◦
So any equation with ∆T can use either
Kelvin or Celsius
From experiment, 0 K = −273◦ C ⇒ T (K) = T (◦ C) + 273
5
Also, T ( C) = (T (◦ F ) − 32◦ )
9
◦
Heat
16th July 2015
Temperature Exercise
Which of the following is the correct ranking of temperatures from
coldest to hottest?
Heat
16th July 2015
Temperature Exercise
Which of the following is the correct ranking of temperatures from
coldest to hottest?
(a) 100◦ C, 100◦ F , 100 K
Heat
16th July 2015
Temperature Exercise
Which of the following is the correct ranking of temperatures from
coldest to hottest?
(a) 100◦ C, 100◦ F , 100 K
(b) 100◦ F , 100◦ C, 100 K
Heat
16th July 2015
Temperature Exercise
Which of the following is the correct ranking of temperatures from
coldest to hottest?
(a) 100◦ C, 100◦ F , 100 K
(b) 100◦ F , 100◦ C, 100 K
(c) 100 K, 100◦ C, 100◦ F
Heat
16th July 2015
Temperature Exercise
Which of the following is the correct ranking of temperatures from
coldest to hottest?
(a) 100◦ C, 100◦ F , 100 K
(b) 100◦ F , 100◦ C, 100 K
(c) 100 K, 100◦ C, 100◦ F
(d) 100 K, 100◦ F , 100◦ C
Heat
16th July 2015
Temperature Exercise
Which of the following is the correct ranking of temperatures from
coldest to hottest?
(a) 100◦ C, 100◦ F , 100 K
(b) 100◦ F , 100◦ C, 100 K
(c) 100 K, 100◦ C, 100◦ F
(d) 100 K, 100◦ F , 100◦ C
(e) 100◦ C, 100 K, 100◦ F
Heat
16th July 2015
Temperature Exercise
Which of the following is the correct ranking of temperatures from
coldest to hottest?
(a) 100◦ C, 100◦ F , 100 K
(b) 100◦ F , 100◦ C, 100 K
(c) 100 K, 100◦ C, 100◦ F
(d) 100 K, 100◦ F , 100◦ C
(e) 100◦ C, 100 K, 100◦ F
Heat
16th July 2015
Temperature Exercise
Which of the following is the correct ranking of temperatures from
coldest to hottest?
(a) 100◦ C, 100◦ F , 100 K
(b) 100◦ F , 100◦ C, 100 K
(c) 100 K, 100 C, 100 F
◦
◦
100 K = −173◦ C = −279◦ F
(d) 100 K, 100◦ F , 100◦ C
100◦ C = 212◦ F = 373 K
(e) 100◦ C, 100 K, 100◦ F
Heat
16th July 2015
Ideal Gas
In the case of an Ideal Gas, the relationship between the average
kinetic energy of the molecules and the temperature was
discovered by Ludwig Boltzmann.
Heat
16th July 2015
Ideal Gas
In the case of an Ideal Gas, the relationship between the average
kinetic energy of the molecules and the temperature was
discovered by Ludwig Boltzmann.
Ideal Gas - A gas with no interaction between
the molecules except for their random, elastic
collisions.
Heat
16th July 2015
Ideal Gas
In the case of an Ideal Gas, the relationship between the average
kinetic energy of the molecules and the temperature was
discovered by Ludwig Boltzmann.
Ideal Gas - A gas with no interaction between
the molecules except for their random, elastic
collisions.
Kav
Heat
3
= kB T
2
Average kinetic energy of a single molecule
in an ideal gas
16th July 2015
Ideal Gas
In the case of an Ideal Gas, the relationship between the average
kinetic energy of the molecules and the temperature was
discovered by Ludwig Boltzmann.
Ideal Gas - A gas with no interaction between
the molecules except for their random, elastic
collisions.
Kav
3
= kB T
2
Average kinetic energy of a single molecule
in an ideal gas
kB = 1.38 × 10−23 J/K = the Boltzmann constant
Heat
16th July 2015
Ideal Gas
In the case of an Ideal Gas, the relationship between the average
kinetic energy of the molecules and the temperature was
discovered by Ludwig Boltzmann.
Ideal Gas - A gas with no interaction between
the molecules except for their random, elastic
collisions.
Kav
3
= kB T
2
Average kinetic energy of a single molecule
in an ideal gas
kB = 1.38 × 10−23 J/K = the Boltzmann constant
3
U = N kB T
2
Heat
Internal energy of an ideal gas with N total
molecules
16th July 2015
Ideal Gas Exercise
An ideal gas has its temperature increased from 20◦ C to 50◦ C,
without gaining or losing molecules. What was the change in the
gas’s internal energy, ∆U ?
Heat
16th July 2015
Ideal Gas Exercise
An ideal gas has its temperature increased from 20◦ C to 50◦ C,
without gaining or losing molecules. What was the change in the
gas’s internal energy, ∆U ?
(a) ∆U = 0
Heat
16th July 2015
Ideal Gas Exercise
An ideal gas has its temperature increased from 20◦ C to 50◦ C,
without gaining or losing molecules. What was the change in the
gas’s internal energy, ∆U ?
(a) ∆U = 0
3
(b) ∆U = N kB (20)
2
Heat
16th July 2015
Ideal Gas Exercise
An ideal gas has its temperature increased from 20◦ C to 50◦ C,
without gaining or losing molecules. What was the change in the
gas’s internal energy, ∆U ?
(a) ∆U = 0
3
(b) ∆U = N kB (20)
2
3
(c) ∆U = N kB (30)
2
Heat
16th July 2015
Ideal Gas Exercise
An ideal gas has its temperature increased from 20◦ C to 50◦ C,
without gaining or losing molecules. What was the change in the
gas’s internal energy, ∆U ?
(a) ∆U = 0
3
(b) ∆U = N kB (20)
2
3
(c) ∆U = N kB (30)
2
3
(d) ∆U = N kB (50)
2
Heat
16th July 2015
Ideal Gas Exercise
An ideal gas has its temperature increased from 20◦ C to 50◦ C,
without gaining or losing molecules. What was the change in the
gas’s internal energy, ∆U ?
(a) ∆U = 0
3
(b) ∆U = N kB (20)
2
3
(c) ∆U = N kB (30)
2
3
(d) ∆U = N kB (50)
2
There is not enough information since I don’t have my
(e)
calculator and so can’t convert Celsius into Kelvin
Heat
16th July 2015
Ideal Gas Exercise
An ideal gas has its temperature increased from 20◦ C to 50◦ C,
without gaining or losing molecules. What was the change in the
gas’s internal energy, ∆U ?
(a) ∆U = 0
3
(b) ∆U = N kB (20)
2
3
(c) ∆U = N kB (30)
2
3
(d) ∆U = N kB (50)
2
There is not enough information since I don’t have my
(e)
calculator and so can’t convert Celsius into Kelvin
Heat
16th July 2015
Ideal Gas Exercise
An ideal gas has its temperature increased from 20◦ C to 50◦ C,
without gaining or losing molecules. What was the change in the
gas’s internal energy, ∆U ?
(a) ∆U = 0
3
(b) ∆U = N kB (20)
2
3
(c) ∆U = N kB (30)
2
3
∆U = N kB ∆T
2
∆T (K) = ∆T (◦ C)
3
(d) ∆U = N kB (50)
2
There is not enough information since I don’t have my
(e)
calculator and so can’t convert Celsius into Kelvin
Heat
16th July 2015
Heat
Heat - Transfer of energy between the molecules of two different
temperature objects that results in a change in the internal energy
of both.
Higher Temp
Heat
Lower Temp
16th July 2015
Heat
Heat - Transfer of energy between the molecules of two different
temperature objects that results in a change in the internal energy
of both.
Heat, Q
Higher Temp
Heat
Lower Temp
16th July 2015
Heat
Heat - Transfer of energy between the molecules of two different
temperature objects that results in a change in the internal energy
of both.
Heat, Q
Higher Temp
Heat
Lower Temp
The
higher
temperature
object has more energy
so conservation ⇒ heat
spontaneously flows from
higher to lower temperature
16th July 2015
Heat
Heat - Transfer of energy between the molecules of two different
temperature objects that results in a change in the internal energy
of both.
Heat, Q
Higher Temp
Lower Temp
The
higher
temperature
object has more energy
so conservation ⇒ heat
spontaneously flows from
higher to lower temperature
Thermal Equilibrium - The net heat transfer stops when two
objects reach the same temperature
Heat
16th July 2015
Heat’s Effect
Because the internal energy includes more than just kinetic energy,
heat can have more than one effect on an object.
Heat
16th July 2015
Heat’s Effect
Because the internal energy includes more than just kinetic energy,
heat can have more than one effect on an object.
Heat can cause:
Heat
16th July 2015
Heat’s Effect
Because the internal energy includes more than just kinetic energy,
heat can have more than one effect on an object.
Heat can cause:
Change in temperature.
This is quantified by the
specific heat, c of a material. Q = mc∆T
Heat
16th July 2015
Heat’s Effect
Because the internal energy includes more than just kinetic energy,
heat can have more than one effect on an object.
Heat can cause:
Change in temperature.
This is quantified by the
specific heat, c of a material. Q = mc∆T
Change in phase. This is quantified by the latent heat, L
of a material. Q = mL
Note: There is no change in
temperature during a change in phase.
Heat
16th July 2015
Heat’s Effect
Because the internal energy includes more than just kinetic energy,
heat can have more than one effect on an object.
Heat can cause:
Change in temperature.
This is quantified by the
specific heat, c of a material. Q = mc∆T
Change in phase. This is quantified by the latent heat, L
of a material. Q = mL
Note: There is no change in
temperature during a change in phase.
Thermal Expansion - Change in length due to temperature
changes. ∆ℓ = ℓα∆T
Heat
16th July 2015