LQs and Quizzes for Exam 1
When a positive test charge is released from rest near a (fixed) positive source charge, what happens to the electric potential of the positive test charge? - It will increase because the charge will move in the direction of the electric field - It will decrease because the charge will move in the direction opposite to the electric field - It will increase because the charge will move in the direction opposite to the electric field - It will decrease because the charge will move in the direction of the electric field - It will remain constant because the electric field is uniform - It will remain constant because the charge remains at rest - Something else
- It will decrease because the charge will move in the direction of the electric field
When a negative test charge is released from rest near a (fixed) positive source charge, what happens to the electric potential of the negative test charge? - It will increase because the charge will move in the direction of the electric field - It will decrease because the charge will move in the direction opposite to the electric field - It will increase because the charge will move in the direction opposite to the electric field - It will decrease because the charge will move in the direction of the electric field - It will remain constant because the electric field is uniform - It will remain constant because the charge remains at rest - Something else
- It will increase because the charge will move in the direction opposite to the electric field.
In the Boltzmann factor e − Δ E k B The "T" means -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
-Higher energy states become more probable as the temperature increases
A 5000 kg coaster is released 20 meters above the ground on a frictionless track. What is its approximate speed at 10 meters high (point B )?
14 m/s
A 5000 kg coaster is released 20 meters above the ground on a frictionless track. What is the approximate speed at ground level (point A)? -20 m/s -14 m/s -10 m/s -7 m/s -None of these is correct
20 m/s
Suppose I have a block of matter with 8 two-state "Degrees of Freedom" (bins in which to place energy that can only hold 1 energy packet).I have 2 packets of thermal energy. How many ways are there to distribute 2 packets? (i.e., How many microstates are there?)
28
Suppose I have a block of that has 8 open "Degrees of Freedom" (bins in which to place energy that can only hold any number of energy packets).I have 2 packets of thermal energy. How many ways are there to distribute 2 packets? (i.e., How many microstates are there?)
36
Suppose we have a box containing a weakly interacting monatomic gas of N particles. Treat the atoms as if they had no internal degrees of freedom. (They cannot hide any energy inside them.)The gas contains ____ degrees of freedom and the total energy of the gas at thermal equilibrium would be ____ (use k for Boltzmann's constant).
3N, 1.5NkT
What is the magnitude of the force on the 4Q charge? - 16F - 4F - F - F/4 - other
4F
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? - 16F - 4F - F - F/4 - other
4F Force is the product of both charges.
What is the magnitude of the change in the chemical energy for the reaction 2H2O → 2H2+O2(per reaction) in eV? O-H: -4.77eV H-H: -4.52eV O--O (double bond): -5.03eV (Number only and two digits after the decimal point please!)
5.01 (Between 4.75 and 5.26)
Now treat the molecules as if they were ball-and-stick dimers. (We will still assume that the atoms cannot hide any energy inside them.) The gas contains ____ degrees of freedom and the total energy of the gas at thermal equilibrium would be ____ (use k for Boltzmann's constant).
5N, 2.5NkT
Consider a solid composed of N atoms in a structure that looks like the picture below. How many degrees of freedom does each atom have?
6 (with margin: 0) For each spatial dimension, we have springs (PE) and movement (KE) possible. That makes 2 d.o.f for each dimension, for a total of 6 d.o.f
Now treat the molecules as if the "stick" could vibrate - was a spring, not a rigid stick. (We will still assume that the atoms cannot hide any energy inside them.) The gas contains ____ degrees of freedom and the total energy of the gas at thermal equilibrium would be ____ (use k for Boltzmann's constant).
7N, 3.5NkT
Suppose a small amount of heat Q flows from a system A at low temperature (250K) to a system B at high temperature (350K). Which of the following must be true regarding the entropy of the rest of the universe during this process? A. It increases by an amount greater than | Δ S A | − | Δ S B |. B. It increases by an amount smaller than | Δ S A | − | Δ S B |. C. It decreases D. It stays the same E. It cannot be determined from the given information.
A
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 - About 1 - About 1/3 - About 3 - Much, much larger than 1 - Much, much smaller than 1 - Cannot be determined from information given
About 1/3
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 -About 1 -About 1/3 -About 3 -Much, much larger than 1 -Much, much smaller than 1 -Cannot be determined from the information given
About 1/3
This train has two cars. It costs $2 to ride in the first car and $10 to ride in the second car. Also, everyone riding is a billionaire. Where do you expect there will be more passengers? - First car - Second car - About the same in both
About the same in both
This train has two cars. Where do you expect there will be more passengers? - First car - Second car - About the same in both
About the same in both
A small amount of heat flows out of a hot system A (350 K) into a cold system B (250 K). Which of the following correctly describes the entropy changes that result? (The systems are thermally isolated from the rest of the universe) A. | Δ S A | > | Δ S B | B. | Δ S A | < | Δ S B | C. I Δ S A I = I Δ S B I
B
If a membrane could change its value of E, what change would it make to open more ion channels? A. Increase the magnitude of E B. Decreasing the magnitude of E C. Changing the magnitude of E would not have any open effect on how many ion channels were open
B
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? A. +++P B. ++P- C. ++P+ D. +-P+
B
Suppose an isolated box of volume 2V is divided into two equal compartments. An ideal gas occupies half of the container and the other half is empty. When the partition separating the two halves of the box is removed and the system reaches equilibrium again, how does the new (Helmholtz) free energy of the gas compare to the free energy of the original system? (Use internal energy rather than enthalpy in the FE equation since pressure is not constant.) - The free energy increases - The free energy decreases - The free energy stays the same - There is not enough information to determine the answer
The free energy decreases
These two atoms can exist in a stable bound state. How is this represented visually in the PE diagram? -The potential energy approaches zero as r gets large -The PE curve is close to horizontal as r gets large -The PE curve is close to vertical as r gets small -The potential energy has a minimum -More than one of these -The PE diagram doesn't demonstrate this information
The potential energy has a minimum
Suppose an isolated box of volume 2V is divided into two equal compartments. An ideal gas occupies half of the container and the other half is empty. When the partition separating the two halves of the box is removed and the system reaches equilibrium again, how does the new pressure of the gas compare to the pressure of the original system? -The pressure increases -The pressure decreases -The pressure stays the same -There is not enough information to determine the answer
The pressure decreases
What is the direction of the net force acting on the skater (assume no friction)? -Up -Down -Left -Right -There is no net force on the skater -There is not enough info to decide
There is no net force on the skater
Minimum, how many forces are acting on the skater? (no friction) -None -One -Two -More than two
Two
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?
U is greatest at 2, Objects move from higher potential energy to lower potential energy. The charge that is farthest "uphill" or against the field has largest potential energy
A massive object might be placed at one of three spots in a region where there is a uniform gravitational field.How do the gravitational potentials, V = gh, on the masses at positions 1, 2, and 3 compare?
V is greatest at 2, Objects move from higher potential to lower potential. The mass that is highest or against the field has the largest potential
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, V on the charge at positions 1, 2, and 3 compare?
V is greatest at 2, Positive charges move from higher potential to lower potential. The charge that is farthest "uphill" or against the field has the largest potential
What does r ^ mean? - Vector, magnitude 1, length dimension - Scalar, magnitude 1, length dimension - Vector, magnitude 1, dimensionless - Scaler, magnitude 1, dimensionless - Something else
Vector, magnitude 1, dimensionless
Suppose an isolated box of volume 2V is divided into two equal compartments. An ideal gas occupies half of the container and the other half is empty.When the partition separating the two halves of the box is removed and the system reaches equilibrium again, how does the new internal energy of the gas compare to the internal energy of the original system? -The energy increases -The energy decreases -The energy stays the same -There is not enough information to determine the answer
The energy stays the same
What would be a general way to describe the direction of the net force here? -Always uphill -Always downhill -Sometimes uphill and sometimes downhill -Downhill everywhere but one spot -No way to tell
Downhill everywhere but one spot
Consider the electric field near a long line of uniform charge, where lambda id the charge per unit length. Which of these has the right dimensions ([lambda]= Q/L])
E = 2klambda/d
You put an ice cube at 0°C inside a large metal box at 70°C. The ice melts and the entropy of the ice increases. Which statement is correct? - Entropy of the metal box is unchanged; total entropy increases - None of the statements is correct - Entropy of the metal box decreases; total entropy decreases - Entropy of the metal box decreases; total entropy is unchanged - Entropy of the metal box decreases; total entropy increases
Entropy of the metal box decreases; total entropy increases
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?
F A->q (A is closer)
This train has two cars. It costs $2 to ride in the first car and $10 to ride in the second car. Where do you expect there will be more passengers? - First car - Second car - About the same in both
First car
Consider the points A and B on the p-V plane shown. An ideal monatomic gas is carried from a state of thermal equilibrium at A to one at B over a path not specified. If one knows the pressure, volume, and temperature at both A and B, it is then possible to calculate the (check all that apply) -Work done on the gas as it expands -Gain or loss of the internal energy of the gas -Heat transferred to or from the gas -Molecular mass of the gas -Number of grams of the gas -None of these
Gain or loss of the internal energy of the gas
In the Boltzmann factor e^-Δ E/k B T, the "T" means - Higher-energy states are the 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
Higher-energy states become more probable as the temperature increases
Suppose an isolated box of volume 2V is divided into two equal compartments. An ideal gas occupies half of the container and the other half is empty. When the partition separating the two halves of the box is removed and the system reaches equilibrium again, how does the new entropy of the gas compare to the entropy of the original system? - It increases - It decrease - It remains the same - There is not enough information to determine the answer
It in creases
Suppose an isolated box of volume 2V is divided into two equal compartments. An ideal gas occupies half of the container and the other half is empty. When the partition separating the two halves of the box is removed and the system reaches equilibrium again, how does the new internal energy of the gas compare to the internal energy of the original system? - There is not enough information to determine the answer - It remains the same - It decreases - It increases
It remains the same. Isolated means no heat exchange and there is no work done to expand or compress a wall. First law of thermodynamics indicates no change in internal energy.
In a fixed volume V containing 1 mole of NO2 at pressure p0, suppose a reaction takes place that decomposed all of the NO2 by the reaction2NO2 (g) →N2 (g) + 2O2 (g)If T remains the same (thanks to a heat sink), what would happen to the pressure p? -It would remain the same -It would be 1.5 times as big -It would double -It would decrease by a factor of 2 -It would decrease but not by a factor of 2 -It would increase by some other factor
It would be 1.5 times as big
What might happen to the charge on the man when he touches the doorknob? (has neg charges) - Most electrons will go into the knob and down to the earth - Some electrons will go from the earth through the knob and into the man
Most electrons will go into the knob and down to the earth. The charges will flow through the conductor to reach the ground -- space where they can maximize their separation from one another
What is the sign of the change in the chemical energy for the reaction C+O2 → CO2? Product bond energy: 2(-8.24 eV) = -16.48 eV Reactant bond energy: -5.03 eV - Positive - It cannot be determined - It is zero so it doesn't have a sign - Negative
Negative (More energy in the product than reactant... change in chemical energy is negative)
Compare the magnitude and direction of the net force exerted on Q - Same magnitude - Same direction - Same magnitude and direction - Same magnitude, opposite direction - Neither same magnitude nor same direction
Neither same magnitude nor same direction (Remember, these are vector quantities. Add them like vectors)
A large -20°C ice cube is dropped into a super-insulated container holding a small amount of 5°C water, then the container is sealed. Ten minutes later, is it possible that the temperature of the ice cube will be colder than -20°C? -Yes -No -Maybe. It depends on other factors.
No
When two objects with the same sign of charge but different magnitudes are put together, they accelerate _____ - with the same acceleration - with different acceleration - larger charge has higher acceleration - with different acceleration - larger charge has higher acceleration - Not enough information
Not enough information, While N3 gives an excellent way to say they both experience the same force, we do not know the masses of these charges... therefore we cannot determine how much they will accelerate
If a mixture of carbon and oxygen gas undergoes the reaction in a closed vessel, what is the sign of the change in the thermal energy of the gas in the container as a result of this reaction taking place? -Positive -Negative -There is not enough information to decide
Positive
If we pull the pins holding the piston in place, the gases would expand until the pressures are equal. The new volume is 1.5 times as big as the original volume. The work done by the gas on the piston is -Positive -Negative -Unable to be determined from the given information
Positive
For the reaction 2H2O→2H2+O2, ΔH = -572 kJ/mol. What is the sign of pΔV? - Positive - Negative - Zero
Positive. (The number of particles increases, so there must be an increase in volume... positive pdV)
What happens when I change the sign of the test charge? - Potential energy graph changes - Electrostatic potential graph changes - Both change - Neither graph changes
Potential energy graph changes
When the balloon is rubbed on the sweater, what might happen? - Some positive charges in the sweater will move onto the balloon - Some negative charges in the sweater will move onto the balloon
Some negative charges in the sweater will move onto the balloon
What do you think will happen when the balloon is moved closer to the wall? - Some positive charges in the wall will move towards the balloon - Some negative charges in the wall will move towards the balloon - Some positive charges in the wall will go onto the balloon - Some negative charges on the balloon will go to the wall
Some positive charges in the wall will move towards the balloon. The negatively-charged balloon will polarize the wall -- negatively charged electrons will orient farther from the balloon leaving positive charges closer
You know that two atoms that are far apart are barely interacting. How is this represented visually in the PE diagram? -The potential energy approaches zero as r gets large -The PE curve is close to horizontal as r gets large -The PE curve is close to vertical as r gets small -The potential energy has a minimum -More than one of these -The PE diagram doesn't demonstrate this information
The PE curve is close to horizontal as r gets large.
Two negatively charged balloons. What do you think the balloons will do? - The balloons move towards each other - The balloons move away from each toher - The balloons will not move
The balloons will move away from each other. The negatively-charged balloons will repel one another more and more as they are moved closer together
The two curves show the probabilities of finding an ion channel either open or closed as a function of E/kBT = (E1-E2)/kBT. Think about the way accessible energy states, probability, and temperature work together, examine the figure, and identify the true statements in the list: A. The top curve is the probability of finding the ion channel open B. The top curve is the probability of finding the ion channel closed C. The curves show that the probability of finding the ion channel open is greater at low temperature D. The curves show that the probability of finding the ion channel open is greater at high temperature E. If (E1-E2) is much less than kBT, the relative probability R is approximately 1
B. As the excitation energy gets large at a fixed T, the probability of its being open drops (it's harder to get enough energy thermally to open the channel). Which means that as epsilon grows, the probability of finding the channel closed increases.D. High T means low 1/T so the red curve gets smaller (probability of being closed) at T gets larger.E. The relative probability is just e-ε/kBT, so if epsilon is small, we approximately get e0 = 1.
If we pull the pins holding the piston in place, the gases would expand until the pressures are equal. What would the new volume be? A. V 0 B, 2 /3 V 0 C. 3/ 2 V 0 D. Between A and B E. Between A and C F. Something else G. It cannot be determined from the information given.
C
Suppose a certain chemical reaction , taking place at constant temperature and pressure, is known to have a positive enthalpy change, and the reaction does not spontaneously take place at a temperature . What can you say about the free energy change at ? A. Δ G ≤ 0 B. Δ G = 0 C. Δ G ≥ 0 D. You cannot say anything about Δ G from the given information.
C
If the probability of finding an ion channel open is popen and the probability of finding the ion channel closed is pclosed, which of the expressions below best represents the relative probability of open to closed, R = popen/pclosed
C. e^-e1/kBT / e^-e2/kBT: The probability of each state being open is proportional to the Boltzmann factor, e-ε/kBT, times the same normalization factor. When you take the ratio, the normalization factor cancels and you just get the ratio of the Boltzmann factors.
Which of the following sets of changes are guaranteed to produce a lower G, thereby making a process/reaction more likely to be spontaneous? A. A negative Δ H B. A positive Δ S C. A negative Δ Hand negative Δ S D. A negative Δ Hand positive Δ S E. A positive Δ Hand negative Δ S F. A positive Δ Hand positive Δ S G. None of these will suffice
D
Suppose a certain chemical reaction , taking place at constant temperature and pressure, is known to have a positive enthalpy change, and the reaction does not spontaneously take place at a temperature . What can you say about whether it will take place at any other ? A. It could take place at a higher B. It could take place at a lower C. If it doesn't take place at , it won't take place at any D. You can't say anything about other temperatures.
D (Since , if we know the change in G and H are both positive, if the change in S were positive, we could make the change in G negative by making T higher. But if we don't know the sign of we can't say anything.)
Since channels are either open or closed, it must be the case that popen + pclosed = 1. You can therefore express the absolute probability of finding the channel open as popen/ (popen + pclosed) and work out an explicit expression for it. Which of the expressions below represents the absolute probability of finding the channel open?
D. The normalization factor must be the 1 over the sum of the Boltzmann factors so that when you add up all the probabilities you get 1. Note that the expression for choice B is not the same as D, because the denominator of D is not equal to one.
Suppose a certain chemical reaction , taking place at constant temperature and pressure, is known to have a positive enthalpy change, and the reaction does not spontaneously take place at a temperature . What can you say about the free energy change at ? - Delta G = 0 - You cant tell anything about Delta G from the given information - Delta G < 0 - Delta G > 0
Delta G > 0 (A positive change in Gibbs free energy indicates a non-spontaneous process)
The electric field at a particular point in space - 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
Does not depend on the test charge used to measure it. (The electric field depends on only the source charge(s).)
What is the direction of the net force acting on the skater (assume no friction)? -Uphill -Downhill -There is no net force on the skater -There is not enough information to decide
Downhill
The figure shows the interaction potential between two molecules (along a particular orientation of the two molecules). The units of the horizontal axis are in nm. Two possible states of the molecule are shown: one is labeled E12, the other E2. We are interested in understanding the forces between the molecules, and how stable the binding between the molecules is (i.e. how much energy it takes to completely separate the two molecules). Which of the following statements are correct? (Pick up to 2) -When the molecules are in the state E2, they are more stable than when they are in state E1 -When the molecules are separated by a distance of 7 nm, the force b/t them is attractive -When the molecules are in the state E1, they are more stable than when they are in the state E2 -When the molecules are separated by a distance of 5 nm, the force b/t them is attractive -When the molecules are separated by a distance of 2 nm, the force b/t them is attractive
When the molecules are in the state E2, they are more stable than when they are in the state E1 and When the molecules are separated by a distance of 7nm, the force between them is attractive
Two test charges are brought separately into the vicinity of a charge +Q. First, test charge +q is brought to point A a distance r from +Q.Next, +q is removed and a test charge +2q is brought to point B a distance 2r from +Q.Compared with the electrostatic potential of the charge at A, that of the charge at B is - greater - smaller - the same - you can't tell from the given information
smaller. Electric potential depends on the source charge and distance from the source charge... it has nothing to do with the amount of test charge.
Two test charges are brought separately into the vicinity of a charge +Q. First, test charge +q is brought to point A a distance r from +Q.Next, +q is removed and a test charge +2q is brought to point B a distance 2r from +Q.Compared with the electrostatic potential energy of the charge at A, that of the charge at B is - greater - smaller - the same - you can't tell from the given information
the same. (Electric potential energy depends on both charges and the distance between the charges)
A 200 g block of copper at a temperature of 55oC is put into an insulated beaker of water at 20oC. The two come to thermal equilibrium at a temperature of about 30oC - much closer to the original temperature of the water than of the copper. (From the macroscopic point of view, the specific heat of water is about 1.0 J/g-oC while the specific heat of copper is only about 0.4 J/g-oC.) However, from the microscopic point of view, you can conclude, - The information given doesn't tell you anything about the number of degrees of freedom in the matter - there are about the same number of degrees of freedom in 200 g of copper as there are in 200 g of water - there are more degrees of freedom in 200 g of copper than in 200 g of water - there are fewer degrees of freedom in 200 g of copper than in 200 g of water
there are fewer degrees of freedom in 200 g of copper than in 200 g of water. (Each degree of freedom is a "bin" for energy. The more degrees of freedom, the more energy is required to raise the temperature (a measure of the average amount of energy per d.o.f.))
How does ΔG affect the rate of a given reaction? - Reaction rate is inversely proportional to ΔG - ΔG has no effect on reaction rate Reaction rate is directly proportional to ΔG
ΔG has no effect on reaction rate (The change in Gibbs free energy indicates whether a process will take place (spontaneity) and how much energy is "free" to do work if it is. It does not affect not indicate how quickly the process will occur.)
