Transcript Physics 7A -- Lecture 2 Winter 2008

Physics 7A -- Lecture 2
Winter 2009
Prof. Robin D. Erbacher
343 Phy/Geo Bldg
[email protected]
This course has two instructors:
 Prof. Robin Erbacher (me) rderbacher @ucdavis
 Ruggero Tacchi (Lead DL Instructor) rtacchi @ucdavis
You are enrolled in one of two 7A classes.
 7A-C/D has lectures on Tuesdays.
 We are independent courses but cover the same material, so you
can attend any review session.
 We have a common final exam.
The final exam is Friday March 20th, 6:00 pm-8:00 pm
 If you know you cannot make the final, you should take 7A in
a different quarter. There are no make-up exams.
• Join this Class Session with your PRS clicker!
(Practice run today, credit begins next time.)
• Quiz today! Lecture 1, DLM 1 + FNTs.
Must take it in correct lecture time slot.
• Check Physics 7 website frequently for calendar &
announcements. DL Instructors have PTA numbers
for adding this class. No Lecture next week!
• Turn off cell phones and pagers during lecture.
• Three-phase model of matter
• Energy-interaction model
• Mass-spring oscillator
We started with
these two…
• Particle model of matter
 Particle model of bond energy
 Particle model of thermal energy
• Thermodynamics
• Ideal gas model
• Statistical model of thermodynamics
We introduce
this one next
(chapter 2)
3-Phase Model
Revisited
Example H2O
• Solid: Keeps its shape without a container.
• Liquid: Takes the shape of the (bottom of) the
container. Keeps its volume the same.
• Gas: Takes the shape and volume of the
container.
Tbp
Tmp
• Tbp: Temperature at which a pure substance changes phase
from liquid to gas (boiling point).
• Tmp: Temperature at which a pure substance changes phase
from solid to liquid (melting point).
You take ice out of the freezer at -300C and place it in a
sealed container and slowly heat it on the stove. You
would find:
• the temperature of the ice rises,
• remains fixed at 00C for an extended time while it is a
mixture of ice and water,
• the temperature rises again after it all melted,
• remains fixed at 1000C for an extended time while it
is a mixture of liquid and gas,
• the temperature rises again after it is all gas (steam).
Example H2O
Q How do we change the phase of matter?
How do we change the temperature of matter?
A
By adding or removing energy. In some cases this
energy is transferred from, or to, the substance as heat, “Q”.
Thermal Equilibrium
and Heat
Ice-cube
Water
00 C
00 C
An ice-cube sits in a bath of water.
Water and ice can exchange heat with each other
but not with the environment.
What is the direction of heat transfer?
A. From ice-cube to water
B. From water to ice-cube
C. Neither of above
D. Impossible to tell
Starting definition of heat (to be revised much later):
Heat (Q) is the transfer of energy from a hot object to a
cold object because the objects are at different temps.
Low temp
Q
High temp
Corollary: If the two objects are at the same temperature, no Q
(heat) flows between them.
Energy leaves hot objects in the form of heat.
Energy enters cold objects in the form of heat.
The Zeroth law of thermodynamics says:
If objects A and B are separately in thermal
equilibrium with a third object C, then A and B
are in thermal equilibrium with each other
Since they are in thermal equilibrium with each
other, there is no net energy exchanged
among them.
If the two objects are at the same temperature, no heat flows between them.
A system in thermal equilibrium
is a system whose temperature is not changing in time.
Low temp
Tfinal
High temp
Energy leaves hot objects in the form of heat
Energy enters cold objects in the form of heat
The Zeroth law of thermodynamics example:
• Let the third object C be the thermometer.
• If the two readings are the same, then A and B are
also in thermal equilibrium.
• Energy (heat) will not flow between A and B if put
together.
A cup of hot coffee
left in a room…
A thermometer
Cold beer
It can take some time for things to reach thermal equilibrium with its
environment. ~ what is happening at microscopic level? => more to
come when we cover Particle models of thermal energy
Coffee cup:
ceramic
material
Beer glass:
glass
A thermometer
Tip: metal
Body: glass, plastic

Q
C=
T
[C] = J/K
Heat capacity [C] of substances:
A measure of the amount of energy required to
increase the temperature of the substance a
certain amount
Q
C=
T
[C] = J/K

Heat capacity of substances:
A measure of the amount of energy required to
increase the temperature of the substance a
certain amount
Heat capacity C is an extensive property:
2kg of water will have twice the heat capacity of 1kg water
Porcelain
1.1kJ/kgK
Glass
0.84kJ/kgK
Tip:metal
(Silver:
0.24kJ/kgK)
Body: plastic
~ 1.2kJ/kgK
Specific heat capacity Cp of substances:
the amount of energy per unit mass/unit mole required to
increase the temperature of the substance
by one degree Kelvin
[Cp] = kJ/kgK
= kJ/moleK
Specific heat capacity Cp is an intensive property:
Specific heat capacity only depends on the substance
The scientific "calorie" is
spelled with a lower-case "c".
One "calorie" = 4.184 Joules
The "dieter's" calorie is
spelled with an upper-case "C".
One "Calorie" = 1000 calories
You heat 1 L of water and raise its
temperature by 100 C. (Water~1g/ml)
Question: If you add the same quantity of
heat to 2 L of water, how much will the
temperature rise?
a) Not enough information is given.
b) Twice as much.
c) Half as much.
You heat 1 L of water and raise its
temperature by 100 C. (Water~1g/ml)
Question: If you add the same quantity of
heat to 5 L of water, how much will the
temperature rise?
a) Not enough information is given.
b) 20 C.
c) 500 C.
Heat capacity C – sort of the slope here of A, C, E
Q
C =
T

E
Heat of fusion
Heat of vaporization
in the Three-phase
Model of Matter
Temperature (K)
Q
C=
T
gas
[C] = J/K
liquid
∆T 
solid
∆E
Energy added (J)
in the Three-phase
Model of Matter
Temperature (K)
Q
C=
T
gas
[C] = J/K
Tb

liquid
solid
∆E
Energy added (J)
“Heat” of vaporization : ∆H
Temperature (K)
the amount of energy per unit mass/unit mole
required for a substance to change its phase
from liquid to gas or vice versa
gas
Tb
liquid
solid
∆E
Energy added (J)
“Heat” of fusion (melting) : ∆H
Temperature (K)
the amount of energy per unit mass/unit mole
required for a substance to change its phase
from solid to liquid or vice versa
gas
liquid
Tm
solid
∆E
Energy added (J)
Typically,
∆Hv >> ∆Hm
e.g. It takes 6 times more energy to vaporize 1kg of water
than to melt the same amount of ice
Temperature (K)
gas
Tb
liquid
Tm
solid
∆E
∆E
Energy added (J)
In our notation, we always have E = Efinal - Einitial .
E negative: Energy is released from the system. (“Neg. energy added.”)
E positive: Energy is put into the system.
 Be sure to select the correct sign for all energy transfers!
=> Note also: T is always Tf - Ti .
Heat capacity - Extensive
-How much energy it takes to change the temperature of this
amount of pure substance (see parts A, C and E in graph).
Specific heat capacity (or specific heat) - Intrinsic
-How much energy it takes to change the temperature per
unit of pure substance (mass/mole) (parts A, C and E).
Heat of fusion - Intrinsic
-How much energy it takes to melt all of the ice to water (see
isothermal part B of graph).
Heat of vaporization - Intrinsic
- How much energy it takes to boil all the water to steam (see
isothermal part D of graph).
You put a red hot iron 1.0 kg mass into
1.0 L of cool water.
1) The increase in the water
temperature is equal to the
decrease in the iron’s
temperature. True or False?
You put a red hot iron 1.0 kg mass into
1.0 L of cool water.
1) The increase in the water
temperature is equal to the decrease
in the iron’s temperature. True or
False?
2) The iron and the water will both
reach the same temperature.
True or False?
Conservation of Energy
and the
Energy Interaction
Model
• Energy is a thing (quantity). You & I contain energy, as do the
chairs you sit on and the air we breathe.
• We cannot see it, but we can measure the transformation of
energy (or change, E) through measuring a process.
Conservation of Energy
Energy cannot be created nor destroyed, simply
converted from one form to another.
• If the energy of an object increases, something else must have
given that object its energy.
• If it decreases, it has given its energy to something else.
• A transfer of energy is when one object gives energy to another.
There are 2 types of energy transfers E -- Heat and Work.
Conservation of Energy
Energy cannot be created nor destroyed, simply
converted from one form to another.
x
x
Fermilab
E=Mc2 !
Protons + anti-protons  New particles!
There are many different types of energies called energy syste
Emovement
(KE)
Etherma
Esprin
Ebond
g
l
Eelectri
Egravit
c
y
........
For each energy system, there is an indicator that tells us
how that energy system can change:
Ethermal: indicator is temperature
Ebond: indicator is the mass of the initial and final phas
•Ethermal = C T, Temperature is the indicator.
• Between phase changes, only thermal
energy changes.
Etherma
l
• Ebond = |m H|, m is the indicator.
Ebond
• At a physical phase change, only the bond-energy
system changes. H is the heat of the particular
phase change. m is the amount that changed phase.
• In a chemical reaction, there are several bond energy changes
corresponding to diff. molecular species (reactants or products).
Here H is the heat of formation for a particular species.
Ea
Eb
Ec
Conservation of Energy
The total energy of a closed physical system must remain
constant. So, the change of the energies of all energy systems
associated with the physical system must sum to zero.
Change in closed system energy = ∆Ea + ∆ Eb + ∆ Ec = 0
Energy added
Ea
Energy removed
Eb
Ec
Conservation of Energy
The change of the energies of all systems associated with an
open physical system must sum to the net energy added or
removed. Energy is added or removed as Heat or Work.
Change in open system energy = ∆Ea + ∆ Eb + ∆ Ec
= (Energy added) - (Energy removed) = Q + W.
Energy added = + 100 J
Clicker!
Ea
Suppose we have a system where 100J of heat comes in from
the outside. Joe claims that the only energy system that
changes is Ea and that Ea is negative (Ea decreases).
Can Joe be correct?
1) Yes, its possible that he is correct.
2) Yes, Joe is definitely correct.
3) No way is Joe’s description correct.
Temperature
Example: Melting Ice
Ti= 0°C  Tf = room temperature
Final
gas
Initial
l-g coexist
TBP
s-l coexist
liquid
TMP
solid
Energy of substance
Temperature
Example: Melting Ice
Process 1: Ice at T=0ºC  Water at T=0ºC
Process 2: Water at T=0ºC  Water at room temperature
Process 1
Final /
Process 2
Process 1 Initial
Initial
gas
l-g coexist
TBP
liquid
TMP
s-l coexist
solid
Process 2
Final
Energy of substance
Example: Melting Ice
Process 1: Ice at T=0ºC  Water at T=0ºC
Ice
Etherm
Ebond
al
∆T = 0
∆Eth = mCpT = 0
Initial phase Solid, Final phase Liquid
Example: Melting Ice
Process 1: Ice at T=0ºC  Water at T=0ºC
Ice
Heat
Etherm
Ebond
al
∆T=0
∆Eth = mCpT =0
Initial phase Solid, Final phase Liquid
Example: Melting Ice
Process 1: Ice at T=0ºC  Water at T=0ºC
Ice
Heat
Etherm
al
Ebond
Mw
Initial phase Solid, Final phase Liquid
∆T=0
∆Eth + ∆Ebond= Q+W
∆Eth = mCpT =0
∆Ebond= ±|m||H| = Q
Example: Melting Ice
Process 2: Water at T=0ºC  Water at room temperature
Ice
Etherm
Ebond
al
Initial phase Liquid, Final phase Liquid
Example: Melting Ice
Process 2: Water at T=0ºC  Water at room temperature
Ice
Heat
Etherm
Ebond
al
T
∆Eth + ∆Ebond= Q+W
Initial phase Liquid, Final phase Liquid
∆Eth= mCpT = Q
∆Ebond= ±|m||H| = 0
Example: Melting Ice
Freezing
(Water at T=0°C  Ice at
T=0°C)
Ice
Etherm
Ebond
al
Mw
Heat
∆T=0
Initial phase Liquid, Final phase Solid
∆Eth= mCpT= 0
NOTE: Heat is released when
bonds are formed!
(In general E is negative)
• For a closed system:
E total  E1  E 2  E 3  ...  0
(Is it clear why there’s no Q or W for a closed system?)
• For an open system:
E total  E1  E 2  E 3  ...  Q + W
(Q and W can be positive or negative, as can Es.)
Next Time:
Two New Energy
Systems
Backup
Information:
•
•
•
Kelvin: the standard for scientific use.
Increasing the temperature by 1 K =
Increasing the temperature by 10C
Celsius/Centigrade
Same as Kelvin except 0 in a different place
Fahrenheit
Smaller unit of temperature
The heat capacity, C, of a particular substance is defined as
the amount of energy needed to raise the temperature of that
sample by 1° C.
If energy (heat, Q) produces a change of temperature, T,
then:
Q = C T
Heat capacity depends on the amount of a substance we
have, since it will take more energy to change the temperature
of a larger quantity of something.
It is thus called an extensive quantity, or dependent upon the
quantity/mass of a substance (kg or mole).
The specific heat capacity, often simply called
specific heat, is a particular number for a given
substance and does not depend on quantity.
Specific heat is thus an intensive property.
The specific heat of water
is one calorie per gram
per degree Celsius.
SI units for heat capacity and specific heat:
• heat capacity
J/K
• specific heat
J/kg•K, or J/mol•K (molar specific heat)