PHYS132 Exam 1

In the Boltzmann factor e − Δ E k B Tthe "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

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 decreases -It remains the same -There is not enough information to determine the answer

-It 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 (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

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

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

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 the information given

About 1/3

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

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

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 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 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 reaction 2NO2 (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

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

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

You know that two atoms that are far apart are barely interacting. How is this represented visually in the PE diagram? -The potential energy aproaches 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

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

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

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

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 moelcules 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 moelcules 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