Download Physics 132 Prof. Buehrle 2/11/14

Quiz 2 Info
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2/20/2014
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Physics 132
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1. (3 pts) The internal energy of an object at
atmospheric pressure is observed to increase. At the
same time its volume changes, but pressure is held
constant. Which of the following is true?
A.
B.
C.
D.
E.
Heat must have been added to the system.
If the volume increased the system did positive work on
its surroundings.
Since pressure is constant, enthalpy is conserved.
If the volume increased heat must have been added to
the system.
If the enthalpy is constant, the volume must have
decreased.
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Physics 132
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2. (2 pts) In a certain process, 400 J of heat is added
to a system and the system simultaneously does
100 J of work. The change in internal energy of the
system is
A.
B.
C.
D.
E.
F.
G.
500 J
400 J
300 J
0J
100 J
−300 J
The change in internal energy depends on how the heat
was added and the work was done
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3. (2 pts) Suppose we have two identical boxes
of matter, A and B, that are in thermal contact
but cannot exchange materials. They come to
thermal equilibrium. System 1 consists of box A
alone, while system 2 consists of both boxes A
and B. What can you say about the entropy of
the two systems?
A.
B.
C.
D.
E.
The entropy of system 2 is twice as high as that of
system 1.
The entropy of system 2 is a lot more than twice as
high compared to system 1.
The number of microstates of system 2 is twice as high
as those of system 1.
The number of microstates of system 2 is a lot more
than twice as high as those of system 1.
You can’t tell anything about the comparative entropy
of the two systems without more information.
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4. (3 pts) Two rooms of a cabin are kept at
different temperatures, as shown. If 5 J of
energy pass through the interior wall from
room 2 to room 1, the exchange is too small to
change the temperature of either room by a
measurable amount. S1 and S2 are the
entropies of the two rooms. If only this
exchange occurs
A.
B.
C.
D.
E.
S1 and S2 decrease by equal amounts.
S1 and S2 decrease by unequal amounts.
S1 increases, but S2 decreases by more.
S1 increases and S2 decreases by equal
amounts.
None of the above exchanges occur.
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Your Questions
Are you saying that the energy of the whole universe stays constant, but that the entropy is
constantly increasing as systems lose heat to their environment? Yes
What other types of free energy is there besides Gibbs? And what does it mean?
It’s a matter of what you is being held constant in the process you are examining. Gibbs is
often used when holding pressure and temperature constant (common for bio and chem).
Helmholtz free energy is often used when the temperature and volume are held constant.
How can lower energy levels equate to a higher entropy? Goes back to what higher entropy
means… a greater number of possibilities for states with that energy level. The most
probable configuration of states winds up having the lowest overall energy.
What is the probability the distribution addresses? The probability of what? Finding the system
in that particular state
Can you quickly work out the example provided towards the end of this section? I have tried to
use the numbers given but I can not seem to get the answer.**
Why would there only be one packet of energy in object A while there would be 2 packets of
energy in object B when there are 3 packets in total?
Josiah Willard Gibbs: 1839 -1903
http://en.wikipedia.org/wiki/Josiah_Willard_Gibbs
Tidbits from Wikipedia:
"In 1863, Yale awarded Gibbs the first American doctorate
in engineering."
"... for a thesis entitled "On the Form of the Teeth of Wheels
in Spur Gearing", in which he used geometrical techniques
to investigate the optimum design for gears."
" ... was praised by Albert Einstein as "the greatest mind in
American history"."
“ Gibbs, who had independent means and had yet to publish
anything, was assigned to teach graduate students
exclusively and was hired without salary.”
Known for
Statistical mechanics
Statistical ensemble
Gibbs entropy
Phase space
Gibbs free energy
Phase rule
Gibbs paradox
Vector calculus
Cross product
Gibbs phenomenon
Gibbs–Helmholtz equation
Gibbs–Duhem equation
Gibbs algorithm
Gibbs measure
Gibbs state
Gibbs–Thomson effect
Gibbs isotherm
Gibbs–Donnan effect
Gibbs–Marangoni effect
Gibbs lemma
Gibbs' inequality
Gibbs Energy: Can a change happen?
External Environment: P and T fixed.
Entropy goes up
Internal System:
Entropy changes:
∆Sint,
Volume changes: ∆V
Heat transferred to
environment: -Q
W= P∆V
Q
Change can happen if T(∆Sint + ∆Sext ) > 0
But, T ∆Sext = -Q = -∆H
External Environment: P and T fixed.
Loses heat Q
Internal System:
Entropy changes:
∆Sint,
Volume changes: ∆V
Heat transferred from
environment: Q
W= P∆V
Q
Change can happen if T(∆Sint + ∆Sext ) ≥ 0
But, T ∆Sext = -Q = -∆H
T∆Sint -∆H > 0 or ∆G = ∆(H-TS) < 0
Foothold ideas:
Energy changes in a process




Internal energy:
thermal and chemical
Enthalpy:
internal plus amount needed
to make space at constant p
Gibbs free energy:
enthalpy minus amount associated with
raising entropy of the rest of the universe due
to energy dumped
A process will go spontaneously if ΔG < 0.
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Physics 132
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How does ΔG affect the rate
of a given reaction?
33%
33%
C
C.
33%
B
B.
Reaction rate is directly
proportional to ΔG
ΔG has no effect on
reaction rate
Reaction rate is
inversely proportional
to ΔG
A
A.
That’s why we need catalysts/inhibitors for certain
reactions!
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External Environment: V and T fixed.
Loses heat Q
Internal System:
Entropy changes:
∆Sint,
Volume changes: ∆V
Heat transferred from
environment: Q
W= P∆V=0
Q
Change can happen if T(∆Sint + ∆Sext ) ≥ 0
But, T ∆Sext = -Q = -∆U
What≥if0Volume
T∆Sint -∆U
or ∆Fis=fixed?
∆(U-TS) < 0
Whiteboard,
TA & LA
Foothold ideas:
Energy distribution



Due to the randomness of thermal collisions,
even in (local) thermal equilibrium a range of
energy is found in each degree of freedom.
The probability of finding an energy E is
proportional to the Boltzmann factor
At 300 K,
kBT ~ 1/40 eV
NAkBT = RT ~ 2.4 kJ/mol
Physics 132
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1.
2.
3.
4.
5.
6.
17%
5
17%
6
17%
4
17%
3
17%
2
1
In the Boltzmann
factor,
,
the "T" means:
17%
Higher-energy states are only possible above a certain
temperature
Higher-energy states are only possible below a certain
temperature
Higher-energy states become more probable as the temperature
increases
Higher-energy states become more probable as the temperature
decreases
More than one of these
None of these
2/20/2014
Physics 132
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The molecules in liquid water are connected
by hydrogen bonds whose energy is about
23 kJ/mol. (This is what is responsible
for the heat of vaporization of water.)
What is the probability that
the thermal motion of the water
molecules at STP will result in
breaking one of those
hydrogen bonds?
To get probability of about .8
probability, need 1 eV/molecule ~
100 kJ/mole.
Physics 132
17%
17%
E
F
17%
D
17%
C
A
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17%
B
A gas of molecules at room temperature
interacts with the potential shown below. Each
molecule can be in the state E1 or E2. If the gas
is at STP and E1 – E2 = 25 meV, then at
equilibrium, the number of molecules found in
the state E1 divided by the number of
molecules found in the state E2 will be
A. About 1
B. About 1/3
C. About 3
D. Much, much larger than 1
E. Much, much smaller than 1
F. Cannot be determined from the
information given
17%
16
The energy of a C-C single bond is about
350 kJ/mol. What is the probability that
thermal motion will result in breaking this
bond?
What if it were a double C=C bond? (Energy
about 615 kJ/mol)
If we assume that the atmosphere is in thermal
equilibrium and at a uniform temperature
(not really a great assumption!), then we expect
the density of a given molecule in the atmosphere
(say oxygen) to fall off with height by the Boltzmann
factor:
(this defines h0).
Find h0, given that at STP,
kBT ≈ 1/40 eV or RT ≈ 2.4 kJ/mole
and
1 eV/molecule ~ 100 kJ/mole.
Foothold ideas:
Using Boltzmann & Gibbs Energy


Gibbs free energy combines the
effects of energy (here, that's the
original Boltzmann factor) and of
entropy (the number of possible
arrangements)
For systems at constant pressure and
temperature, the Gibbs free energy is
what really tells us which states are
more probable, and therefore what a
system is actually going to do. That's
why Gibbs free energy gets so much
attention in chemistry and biology.
1/23/13
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Week 4
Outline
 Review electric
Forces
 Review electric Potential
Electric charges are key
to life!
 Phosphate group is
charged and has electric
field


Simulation based on
F=ma (Newton’s laws)
– What are the forces?
Pastor Biophys J 2006
Model: Charge
A hidden property of matter




Matter is made up of two kinds of electric charges
(positive and negative) that have equal magnitude
and that cancel when they are together and hide
matter’s electrical nature.
Like charges repel, unlike charges attract.
The net charge (postive minus negative charges) is a
constant
Matter with an equal balance is called neutral.
22
Foothold idea:
Coulomb’s Law
r→
kC qQ
Fq →Q = 2 rˆq →Q
rqQ
23
Making Sense of Coulomb’s Law

Changing the test charge

Changing the source charge

Changing the distance

Specifying the direction

Use Subscripts!
10/12/12
r→
kC qQ
ˆ
FQ →q =
r
Q →q
2
R
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What does r̂ mean?
2.
3.
4.
5.
2/20/2014
Vector length 1,
dimension length
Scalar length 1,
dimension length
Vector length 1,
dimensionless
Scalar length 1,
dimensionless
Don’t know
Physics 132
20% 20% 20% 20% 20%
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1.
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MOVEMENT OF CHARGES
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Can Charges Move?

Insulators
– Charges are bound and cannot move around freely.
– Excess charge tends to just sit there.

Conductors
– Charges can move around throughout the object.
– Excess charge redistributes itself or flows off
 Solid: Electrons move
 Fluid: Charged atoms move

Unbalanced charges attract neutral matter
(polarization)
27
When two objects with the same sign of
charge but different magnitudes are put
together, they accelerate _____
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Physics 132
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C.
25% 25% 25% 25%
th
e
B.
with the same acceleration.
With different acceleration Larger charge has higher
acceleration.
With different acceleration –
Smaller charge has higher
acceleration.
Not enough information
w
ith
A.
28
A.
B.
C.
D.
E.
16F
4F
F
F/4
other
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20%
ot
he
r
20%
F/
4
20%
F
20%
4F
20%
16
F
Two small objects each with a net charge of
Q (positive) exert a force of magnitude F on
each other. We replace one of the objects
with another whose net charge is 4Q. The
original magnitude of the force on the Q
charge was F; what is the magnitude of the
force on the Q now?
20%
20%
20%
20%
20%
A.
B.
C.
D.
E.
16F
4F
F
F/4
other
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ot
he
r
F/
4
F
4F
16
F
What is the magnitude of the force
on the 4Q charge?
ADDITION OF FORCES
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20%
te
ll
20%
ca
n’
t
E.
20%
Yo
u
D.
20%
D
C.
20%
B
B.
A
B
C
D
You can’t
tell
A
A.
C
In the figure are shown four arrangements of charge. Each
charge has the same magnitude, but some are + and some
are -. All distances are to the same scale. In which
arrangement would the magnitude of the force felt by a
positive test charge placed at P be the largest?
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Compare the magnitude and direction of the
net force exerted on Q
+q
A
+q
B
d
1/23/13
Physics 132
ite
d.
m
..
ag
ni
tu
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20% 20% 20% 20% 20%
m
ag
ni
C.
-
e
B.
Same magnitude
+q
+
Same direction
Same magnitude and
direction
Same magnitude,
opposite direction
Neither same
magnitude nor same
direction
Sa
m
A.
d
33
-q
1.
2.
3.
4.
→
𝐹𝐹
𝐶𝐶
→
No 𝐹𝐹
t e 𝐵𝐵
+
no
ug 𝑞𝑞
→
h
in 𝐹𝐹 𝐶𝐶
fo
rm
at
io
n
to
te
+
𝐵𝐵
𝑞𝑞
→
𝐹𝐹
𝐴𝐴
+
→
ll
25% 25% 25% 25%
𝐹𝐹
𝐴𝐴
𝑞𝑞
→
𝐹𝐹
A test charge (labeled q) is placed in a situation in
which it feels the electrical force from three other
charges (of opposite sign to it) labeled A, B, and C.
(The charges are on a uniform grid as shown and
the positions are to scale.) Which of
the following combinations of
forces has the greatest magnitude?
𝐹𝐹⃗𝐴𝐴→𝑞𝑞
𝐹𝐹⃗𝐵𝐵→𝑞𝑞 + 𝐹𝐹⃗𝐶𝐶→𝑞𝑞
𝐹𝐹⃗𝐴𝐴→𝑞𝑞 +𝐹𝐹⃗𝐵𝐵→𝑞𝑞 +𝐹𝐹⃗𝐶𝐶→𝑞𝑞
Not enough
information to tell
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ELECTRIC FIELDS
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Foothold idea:
Electric Forces and Fields
When we focus our attention on the electric force on a particular
object with charge q0 (a “test charge”) we see the force it feels
depends on q0.
Define quantity that does not depend on charge of test object
“test” charge -> Electric Field E
E is defined everywhere in space not just in places where
charges are present
Foothold ideas:
Fields



A field is a concept we use to describe anything that exists at
all points in space, even if no object is present.
A field can have a different in magnitude at different points
in space. (and if it’s a vector field, direction). Examples:
temperature, wind speed, wind direction
A gravitational, electric, or magnetic field is a force field.
Fields allow us to predicts the force that a test object would
experience. The field does not depend on what test object
is used.
𝑔𝑔⃗ 𝑟𝑟⃗ =
10/17/12
𝐸𝐸 𝑟𝑟⃗ =
⃗
𝐹𝐹⃗ acting on 𝑚𝑚 (𝑟𝑟)
𝑚𝑚
⃗
𝐹𝐹⃗acting on 𝑞𝑞 (𝑟𝑟)
𝑞𝑞
Physics 131
Field is the value at a position
in space “ r “ assuming that
the force is measured by
placing the object at r .
37
See the system below. A B and C are positive charges, q is
a negative charge. How many interactions do we need to
add to compute the force exerted on a test charge?
Test Charge
38
See the system below. A B and C are positive charges, q is
a negative charge. How many terms do we need to add to
compute the electric field?
39
The electric field at a particular
point in space
B.
C.
D.
E.
Depends only on the
magnitude of the test charge
used to measure it.
Depends only on the sign of
the test charge used to
measure it.
Depends on both the sign and
magnitude of the test charge
used to measure it.
Does not depend on the test
charge used to measure it.
None of the above
1/23/13
20% 20% 20% 20% 20%
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...
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Physics 132
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POTENTIAL ENERGY
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Foothold ideas:
Energies between charge clusters
Atoms and molecules are made up of charges.
 The potential energy between two charges is


The potential energy between many charges
is
2/15/13
Physics 132
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A positive charge might be placed
at one of three spots in a region. It feels the
same force (pointing to the left) in each of the
spots.
How does the electric potential energy, Uelec,
on the charge at positions 1, 2, and 3
compare?
A. U is greatest at 1
B. U is greatest at 2
C. U is greatest at 3
D. U = 0 at all three spots
E. U ≠ 0 but same at all
three spots
F. Not enough information
1/23/13
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Does the potential energy of the system change
when I add a test charge?
Test Charge
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