Essential Physics II
英語で物理学の
エッセンス II
Lecture 2: 5-10-15
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Last semester: Energy conservation
Frictionless track
Potential Energy
Potential Energy
Kinetic Energy
Total energy is unchanged
conversion
Kinetic Energy
Last semester: Energy conservation
Friction track
Potential Energy
Potential Energy
+ Thermal Energy
Kinetic Energy
+ Thermal Energy
Total energy is unchanged
conversion
Kinetic Energy
+ Thermal Energy
Thermal to mechanical energy
Most of our energy is from heat:
heat from burning fuel
conversion
mechanical energy
Thermal to mechanical energy
Most of our energy is from heat:
heat from the sun
conversion
mechanical energy
Can we convert 100% of heat energy to mechanical energy?
No!
Laws of thermodynamics
This lecture ...
... studies thermal (heat) energy
What is thermal equilibrium?
Meaning of heat and temperature
(and the difference between them)
How temperature is measured
How to use heat capacity to find equilibrium temperatures
The 3 methods of heat transfer
Thermodynamics = macroscopic
macroscopic
and
mass
kinetic energy
microscopic
mass
kinetic energy
macroscopic only
pressure
temperature
depends on motion
of all molecules
pressure
temperature
Thermodynamic equilibrium
You remove a cold drink from the refrigerator.
Its temperature :
(A)
Stays the same
(B)
Changes to room temperature
(C)
Changes to hotter than room temperature
(D)
Stays colder than room temperature
Quiz
Thermodynamic equilibrium
6 C
26 C
When drink = room temperature:
temperature stops changing
thermodynamic equilibrium
26 C
26 C
When 2 systems are placed together
and macroscopic properties do not
change
Cold
Hot
pressure
length
volume
Thermodynamic equilibrium
Quiz
2 blocks are placed together.
1 block expands (volume increase) but its pressure stays constant
Was it in thermodynamic equilibrium?
(A)
No
(B)
Yes
(C)
Can’t know
If ANY macroscopic property
changes, they were not in
thermodynamic equilibrium
Thermodynamic equilibrium
“Placed together”
object
#1
in thermal contact
object
#2
Heating object #1 changes macroscopic properties (e.g. pressure)
of object #2
Thermodynamic equilibrium
“Placed together”
object
#1
in thermal contact
object
#2
Heating object #1 changes macroscopic properties (e.g. pressure)
of object #2
Not in
thermal
contact
object #2 ‘s properties are unchanged
Thermodynamic equilibrium
A
B
C
Thermodynamic equilibrium
A
If “A” is in thermal contact
(and thermodynamic
equilibrium) with “B”
B
C
Thermodynamic equilibrium
A
If “A” is in thermal contact
(and thermodynamic
equilibrium) with “B”
B
C
And “C” is in thermal
contact (and thermodynamic
equilibrium) with “B”
Then “A” and “C” are in thermodynamic equilibrium
(but not in contact)
Thermodynamic equilibrium
The zeroth (0th) law of thermodynamics:
2 systems in equilibrium with a 3rd system are in equilibrium with
each other.
A
B
C
Thermodynamic equilibrium
The zeroth (0th) law of thermodynamics:
2 systems in equilibrium with a 3rd system are in equilibrium with
each other.
A
B
C
(If “A” is in equilibrium with “B”
Thermodynamic equilibrium
The zeroth (0th) law of thermodynamics:
2 systems in equilibrium with a 3rd system are in equilibrium with
each other.
A
B
C
(If “A” is in equilibrium with “B”
and “C” is in equilibrium with “B”
Thermodynamic equilibrium
The zeroth (0th) law of thermodynamics:
2 systems in equilibrium with a 3rd system are in equilibrium with
each other.
A
B
C
(If “A” is in equilibrium with “B”
and “C” is in equilibrium with “B”
then “A” is in equilibrium with “C” )
Thermometer
What is temperature?
2 systems have the same temperature if they are in thermodynamic
equilibrium.
A
B
thermal contact
Same temperature
measure temperature
difference
Thermodynamic equilibrium
No macroscopic changes
measure macroscopic
change…
Thermometer
A system with a macroscopic property that changes
with temperature
height of mercury (Hg)
gas pressure
electrical resistance
bending of bimetal (2 metals) strip
The gas thermometer
Constant-volume gas thermometer
The gas thermometer
Constant-volume gas thermometer
Gas reaches
thermodynamic
equilibrium with
system
Pressure
changes
P
The gas thermometer
Constant-volume gas thermometer
Gas reaches
thermodynamic
equilibrium with
system
P
tube is moved to +/-
atmospheric pressure
Pressure
changes
... so level is constant
‘h’ measures change in gas pressure and therefore, temperature
The gas thermometer
Need a temperature scale:
Define 2 points:
‘0’ temperature = gas pressure is 0
0K
Triple point for water: solid, liquid & gas
water exist together
273.16 K
(see next lecture)
Since pressure cannot be < 0,
0 K = absolute zero
can’t go lower!
kelvin (K)
SI unit
Temperature scales
Celsius
2 points:
C
T in
F
Rankine
R
0 C
Boiling point
100 C
(standard atmospheric P)
C =
TC = T
Fahrenheit
melting point of ice
T in K
273.15
in F 6= T in K
9
TF = TC + 32
5
T
T in
R =
0 R = 0K
T in F 6=
T in K
Temperature scales
Quiz
When do the temperatures in centigrade and fahrenheit agree?
(A)
Never
9
TF = TC + 32
5
(B)
At 0 degrees
TF = TC
(C)
At 100 degrees
9
T = T + 32
5
(D)
At -40 degrees
T =
(E)
At -215 degrees
40
Energy
How does a system reach thermodynamical equilibrium?
... T changes
Why?
because energy is moving.
Heat is energy moving because of a
difference in temperature ( T )
Temperature change
T
Energy change
E
Eheat
Heat increases
internal energy
Heat capacity
Heat energy transferred
Eheat = Q [J]
Q
/
=
Temperature change
T [K]
C
T
heat capacity
Q
=
mc
depends on
mass + material
T
specific heat capacity [J/kg · K]
depends on what object is made of
... not how large it is
Heat capacity
Q = mc T
Mass, m
Specific heat, c
Temperature, T
Temperature increase,
T
Add energy
E
heat
Q
Q = mc T
Heat capacity
Old units for heat
1 calorie: heat needed to raise T of 1g of water from 14.5 C to
15.5 C
= 4.184 J
Heat capacity
Quiz
The mass of an object is 199.0 g
It takes 16.0 J to raise the temperature by 10.0 C
What is the specific heat?
(A)
8.04 J/kg · K
Q = mc T
(B)
1600 J/kg · K
Q
c=
m T
(C)
0.00120 J/kg · K
(D)
3.18 ⇥ 106 J/kg · K
16.0
=
0.199 ⇥ 10
Heat capacity
Quiz
A 905 g meteor hits the Earth at a speed of 1629 m/s
If all the energy is converted to heat in the meteor, what is the
temperature rise?
specific heat of meteor: 472 J/kg · K
(A)
2810 C
(B)
2, 540, 000 C
(C) 3.10 C
(D) 11, 700 C
1
2
KE
=
mv
Initial kinetic energy:
2
1
2 = 1, 200, 773 J
= (0.905)(1629)
2
= heat energy =
1, 200, 773
T =
0.905 ⇥ 472
Q = mc T
Equilibrium Temperature
When 2 objects are in thermal contact, heat
flows from the hotter to the colder object
Eheat
If objects are thermally insulated from
the outside (no energy in or out) ....
... all energy leaving hotter object ends
up in the colder object.
m1 c1 T1 + m2 c2 T2 = 0
negative for hotter object
E
E
Equilibrium Temperature
Ex.
An aluminum frying pan of mass 1.5 kg is at 180 C.
It is dropped into 8 kg of water at 20 C.
Assuming water does not boil and no heat is lost, what is the
equilibrium temperature of pan and water?
cp = 900 J/kg · K
mp cp T + mw cw T = 0
mp cp (T
Tp ) + mw cw (T
Tw ) = 0
cw = 4184 J/kg · K
equilibrium temperature
mp cp Tp + mw cw Tw
T =
mp cp + mw cw
1.5 ⇥ 900 ⇥ 180 + 8.0 ⇥ 4184 ⇥ 20
=
1.5 ⇥ 900 + 8.0 ⇥ 4184
= 26 C
Equilibrium Temperature
Quiz
A hot rock with mass 250 g is dropped into an equal mass of
water.
Which temperature changes more?
(specific heat of water > rock)
(A) rock
(B) water
mcr Tr + mcw Tw = 0
c r Tr =
since: cr < cw
Tr >
(C) their temperature change is equal
c w Tw
Tw
Heat Transfer
Eheat
HOW is heat transferred?
3 mechanisms:
Conduction
Convection
Radiation
Heat Transfer: Conduction
Conduction: heat transfer from contact
molecules in a
hot region have
more energy
Heat Transfer: Conduction
Conduction: heat transfer from contact
molecules in a
hot region have
more energy
collide with
cold molecules
Heat Transfer: Conduction
Conduction: heat transfer from contact
molecules in a
hot region have
more energy
collide with
cold molecules
and transfer
energy
Heat Transfer: Conduction
Conduction: heat transfer from contact
How quick is the energy transfer?
Depends the material’s
thermal conductivity, k
molecules in a
hot region have
more energy
collide with
cold molecules
and transfer
energy
Heat Transfer: Conduction
metals are good
thermal conductors:
contain free
electrons that move
fast
Styrofoam is an insulator because it traps air.
Heat Transfer: Conduction
Heat flow depends on...
THot
T+
T
A
TCold
x T
thermal conductivity, k
area, A
thickness,
Eheat =
Q
x
temperature difference,
Conductive heat flow:
H=
dQ
dt
rate of heat flow [W]
T
kA
x
T
dT
dx
when area is not constant
Heat Transfer
Ex.
What is the rate of heat
conduction through the lake?
Water thermal conductivity:
k = 0.61 W/m · K
H=
T
kA
x
=
30 C 4.0 C
(0.61 W/m · K)(1.5 ⇥ 10 m )
8.0 m
=
3.0 MW
6
2
Heat Transfer
6 C
18 C
30 cm
Quiz
A solid concrete wall with area 4.0 m x 2.4 m
Thermal conductivity, k = 1.3 W/m · K
How much heat flow through the wall in 1 hour?
(A)
1.8 MJ
(B)
1.8 kJ
(C)
500 J
T
H = kA
x
6 C 18 C
= (1.3 W/m · K)(4.0 m ⇥ 2.4 m)
0.3 m
dQ
= 499.2 W =
dt
(D)
5.0 MJ
Q = 499.2 W ⇥ 3600 s = 1.8 MJ
Heat Transfer: Conduction
What if heat flows through different materials?
The heat flow rate, H, must be the same
through each material....
H
H
... or it would collect between them
Therefore...
Heat Transfer: Conduction
H=
k1 A
T2
T1
x1
x
R=
kA
Define:
=
k2 A
T3
T2
x2
Thermal resistance
[K/W]
Property of material and geometry (shape)
H=
T2
T1
R1
=
T3
T2
R2
Heat Transfer: Conduction
From:
H=
T2
T1
R1
=
So:
R1 H = T1
Adding:
(R1 + R2 )H = T1
T3
T2
R2
T2 & R2 H = T2
= T1
T2 + T2
T3
T3
T3
T1 T3
H=
R1 + R 2
Composite slab acts like a single slab with R = R1 + R2.
Heat Transfer
Quiz
3 slabs:
Same area, A, and same thickness, x.
Different thermal conductivities, k
Which has the greatest temperature difference between its faces?
(A)
T1
(B)
T2
(C)
T3
H=
T1
=
R1
T1 (k) =
T1
=
R2
T2 (3k) =
T1 = 3 T2 = 2 T3
T1
R3
T (2k)
Heat Transfer: Convection
Convection: heat transfer by fluid motion
Heated fluid
becomes less dense
and rises
It cools and sinks
Heats again and rises
Heat Transfer: Convection
Heat Transfer: Radiation
How do you feel heat from a stove? .... or the sun? .... or a lightbulb?
Electromagnetic waves or radiation
Heat Transfer: Radiation
P = ✏ AT
Stefan-Boltzmann law
4
= 5.67 ⇥ 10
object temperature
8
W/m2 · K4
emissivity:
between 0 - 1, measures ability to emit radiation
object emit radiation but....
... they also absorb radiation
Rate of absorption:
P = ✏ ATa4
4
P
=
✏
A(T
Net radiated power:
Ignore if object T >> background T :
background temperature
Ta4 )
sun = ignore
human body = important
Heat Transfer: Radiation
P = ✏ AT
P / T4
4
At high T, radiation is dominant heat loss mechanism
... at low T, radiation is less important
In a vacuum (e.g. space) : only radiation
[conduction & convection need a material
(e.g. air) to transfer heat]
Ex.
Heat Transfer: Radiation
e.g.
The Sun
A perfect emitter : ✏ = 1 blackbody
(and absorber)
T =?
R
26
The Sun radiates energy at the rate P = 3.9 ⇥ 10 W
8
and its radius is 7.0 ⇥ 10 m . What is its surface T?
✓
◆1/4
P
4
T =
P = ✏ AT
2
4⇡R
A = 4⇡R2
✏=1

26
3.9 ⇥ 10 W
=
4⇡(7.0 ⇥ 108 m)2 (5.7 ⇥ 10 8 W/m2 · K4 )
3
= 5.8 ⇥ 10 K
1/4
Heat Transfer: Radiation
Betelgeuse is a red super giant star
Radiates heat at the rate of 2.70 ⇥ 10
30
W
Surface T = 3000 K
Assuming it is a perfect emitter ( ✏ = 1 ),
what is the radius?
= 5.67 ⇥ 10
8
(A) 7.80 ⇥ 10
11
2
W/m · K
4
m
(C) 1.90 ⇥ 1011 m
(B) 8.70 ⇥ 1011 m
(D) 2.16 ⇥ 1011 m
Quiz
Quiz
Heat Transfer: Radiation
Betelgeuse is a red super giant star
Radiates heat at the rate of 2.70 ⇥ 10
30
W
Surface T = 3000 K
Assuming it is a perfect emitter ( ✏ = 1 ),
what is the radius?
P = ✏ AT 4
P
A=
T4
P
4⇡R =
T4
2
R=
s
R=
r
P
4⇡ T 4
(2.70 ⇥ 1030 W)
4⇡(5.67 ⇥ 10 8 W/m2 · K4 )(3000 K)4
= 2.16 ⇥ 10
11
m
Heat Transfer
What is the dominant (main) form of heat transfer from
a red-hot stove burner with nothing on it.
(A) conduction
(B)
convection
(C) radiation
(D) insulation
Quiz
Heat Transfer
What is the dominant (main) form of heat transfer from
a red-hot stove burner to a pot.
(A) conduction
(B)
convection
(C) radiation
(D) insulation
Quiz
Heat Transfer
What is the dominant (main) form of heat transfer from
the bottom to the top of a pot containing boiling water.
(A) conduction
(B)
convection
(C) radiation
(D) insulation
Quiz
Thermal - Energy Balance
You home is warm in winter ...
... but it is losing energy
heat loss
Heat loss Eout / Tin
/
Tout
Ein
T
House stays warm if:
Eout
Tin
Tout
heat loss rate = heat in rate
dEout
dEin
=
dt
dt
Thermal - Energy Balance
Ex.
A water heater loses heat at a rate of 120 W for each Celsius
degree difference between the water and outside.
dEout
= (120 W/ C)( T )
dt
T = Tin
Tout
It is heated by a 2.5 kW heater and the
outside T = 15 C
What is the water temperature?
dEout
dEin
Thermo-energy balance:
=
dt
dt
3
(120 W/ C)( T ) = 2.5 ⇥ 10 W
Tin = 21 C + 15 C = 36 C
T = 21 C