Transcript Slide 1

Lecture # 2
Cassandra Paul
Physics 7A
Summer Session II 2008
• Last time:
– Made Energy Diagrams
– Drew Three Phase Diagrams
• This Time:
– Lets get quantitative!
Example: two substances.
Example: 1kg of Copper at 95°C is dropped into an
insulated bucket of 1kg of water at 5°C. What is the
temperature of the water after the system comes to
equilibrium?
To set up the problem:
• Define system
• Define interval
• What indicators are changing?
• What energies are changing?
• How are they changing?
• Is this an open or closed system?
• What (if anything) is entering/leaving the system?
• Write Energy Conservation Equation
Copper
Temperature
H2O
Temperature
Initial
2839°C BP
Initial
100°C
BP
1085°C
MP
0°C MP
Energy added
(not to scale with each other)
Energy added
Example: Copper at 95 degrees C is dropped into a cup of
water at 5 degrees C. How can we model the Energy
Transfer?
System: Copper and Water
Initial: Copper at 95°C; Water at 5°C
Final: Equilibrium (same temp: 5°C<Tequl<95°C)
Copper
Water
Etherm
Etherm 
I: T=95°C
F: T=?°C
−
al
T

T

al
I: T=5°C
F: T=?°C
+
ΔEthcopper + ΔEthwater = 0
Important lines: always show these on the board and on exams.
−
+
ΔEthcopper + ΔEthwater = 0
mcΔTcopper + mcΔTwater = 0
Look up in table
(1kg)c(Tf-Ti)copper + (1kg)c(Tf-Ti)water = 0
(1kg)(0.386kJ/kgC)(Tf-95°C)copper
+ (1kg)(4.18kJ/kgC)(Tf-5°C)water = 0
Solve for Tf:
Tf = 12.6°C
Think about it: Why did the water only increase ~8°C, Temperature
when the copper decreased 82°C !????
Copper
H2O
Temperature
Initial
Fina
l
100°CBP
(2839°C)BP
Initial
Fina
l
1085°CMP
0°C MP
Energy added
(not to scale with each other)
Energy added
(Freezing point of copper: 1085°)
Why did the water only increase ~8°C,
when the copper decreased 82°C !????
A. The amount of heat leaving the copper was
greater than the amount of heat leaving the
water
B. The amount of heat leaving the water was
greater than the amount of heat leaving the
copper
C. The specific heat of the water is greater than the
copper
D. Some of the heat leaving the copper went to the
environment
E. Magic
Heat capacity
in Three-phase Model of Matter
Temperature (K)
Q
C=
T
gas
[C] = J/K
liquid
∆T 
solid
∆E
Energy added (J)
Which object has the higher heat
capacity?
B
A
∆T
∆T
∆E
∆E
Heat capacity
in Three-phase Model of Matter
Temperature (K)
Tb
Q
C=
T
0

gas
liquid
solid
∆E
Energy added (J)
Heat of vaporazation : ∆H
the amount of energy per unit mass (or unit mole) required for a
substance to change its phase from liquid to gas or vice versa
Temperature (K)
gas
Tb
liquid
solid
∆E
Energy added (J)
Heat of melting : ∆H
the amount of energy per unit mass ( or unit mole) required for a
substance to change its phase from solid to liquid or vice versa
Temperature (K)
gas
liquid
Tm
solid
∆E
Energy added (J)
Let’s try a quantitative example:
• How much energy does it take to completely
melt 2.5kg of ice initially at 0°C?
– Draw a three-phase diagram
– Draw an energy System Diagram
– Calculate!
Which Energy System?
How much energy does it take to completely melt 2.5kg of ice
initially at 0°C?
Heat
A)
B)
Ebond

Ebond
ml 

ml
Heat
C)
Ebond
ml 
Heat
D)
Ebond
ml 
Which Energy System?
How much energy does it take to completely melt 2.5kg of ice
initially at 0°C?
B)
Heat
A)
Ebond

Ebond
FREEZING!

ml
Heat
-
ml 
-
+
ΔEbond = Q
ΔEbond = Q
D)
Heat
C)
+
Ebond
IMPOSSIBLE!
m 
Ebond
IMPOSSIBLE!
ml 
l
+
-
ΔEbond = Q
+
ΔEbond = 0
B) Was the correct one, let’s solve it.
How much energy does it take to completely
melt 2.5kg of ice initially at 0°C?
+
+
Heat
Ebond
ΔEbond = Q
ml 
±lΔmΔHml = Q
Look up in table
Choose the plus!
(2.5kg)(333.5kJ/kg) = Q
833.75kJ = Q = Energy needed to melt 2.5kg of ice!
Today in Lab you will do the
DREADED…
ICED TEA PROBLEM!!!
Let’s get ready.
Let’s not talk Tea yet, let’s start easy:
Example: Lets say you have a 3kg of mercury
that you want to add 20kJ of heat to. The
substance starts in the solid phase at a
temperature of 200°K. Find the final
temperature of the mercury.
• Draw a three-phase diagram
• Draw an energy interaction diagram
Temperature (K)
Tb
Energy added (J)
Etherm
al
T
Ebond 
ml 
Etherm
al
T

Ebond
mg 
Etherm 
al
T
Temperature (K)
Q5
Q4
Tb
Q2
Q1
Q3
Energy added (J)
Etherm
al
T
ΔEth =Q1

Ebond
ml 
Etherm

al

T
ΔEbond =Q2 ΔEth =Q3
Ebond
mg 
ΔEbond =Q4
Etherm 
al
T
ΔEth =Q5
Etherm
al

T
ΔEth =Q1
Ebond

ml 
ΔEbond =Q2
Etherm
al

T
ΔEth =Q3
Ebond
mg 
ΔEbond =Q4
Example: You have exactly 20kJ of heat to add to a 3kg
block of mercury initially at 200°K. You want to know
what the final temperature will be when you have used up
all of your energy.
Melting point =234°K; Boiling Point=630°K
Specific heats: (s)=.141 kJ/kgK, (l)=.140, (g)=.103
Heat of melting: 11.3kJ/kg Heat of Vaporization: 296kJ/kg
Etherm 
al
T
ΔEth =Q5
Start with Q1
Melting point =234°K; Boiling Point=630°K
Specific heats: (s)=.141 kJ/kgK, (l)=.140,
(g)=.103
Temperature (K)
Etherm
al
T
630°K
234°K
ΔEth =Q1
Energy added (J)
mcΔT=Q1
(3)(.141kJ/kgK)(234°K-200°K)=Q1
14.4kJ=Q1
I figured out the Qs for you: Q1=14.4kJ, Q2=0.423kJ, Q3=166kJ, Q4=0.42kJ
Can you tell me what the final state is (remember we only have 20kJ)????
The mercury has enough energy to get into the liquid state but not through it!
Temperature (K)
Q5
Q4
Tb
Q1
Q2
Q3
Energy added (J)
Once we figure out the phase we can
then draw the energy system diagram…
Correct energy system diagram:
Etherm 
al
T
Ebond 
ml 
Etherm
al

T
ΔEth+ ΔEbond + ΔEth = Q
Other stuff you will see soon…
Power
• Power is a rate of energy transfer.
• Amount of energy a system receives per unit
time
• Power is measured in Watts=Joules/Second
Chemical Systems
• You will be applying energy interaction
diagrams to chemical processes
• Breaking bonds: bond energy increases
DL sections
•
•
•
•
Swapno:
11:00AM Everson Section 1
Amandeep: 11:00AM Roesller Section 2
Yi:
1:40PM Everson Section 3
Chun-Yen: 1:40PM Roesller Section 4