Physics

An electrochemical reaction can be described by the equation: 2Fe3++Cl−↔2Fex+Cl2 What is the value of x ?

+2

A wool sweater and two balloons are all electrically neutral. The two balloons are rubbed on the wool sweater, after which each balloon has a net charge of -3 n C. What is the final net charge of the sweater?

+6 Nc

As shown in the figure, three charges are at corners of a rectangle. The charge Q in the bottom right corner is a test charge; the other two charges are source charges. What is the magnitude of the net electric field at the test charge's location due to the source charges? (1 nC = 1 x 10-9 C)

--

An athlete doing push-ups performs 650 kJ of work and loses 425 kJ of heat. What is the change in the internal energy of the athlete?

-1075 kJ

A monatomic ideal gas undergoes an expansion at a constant temperature of 300 K, as the volume increased from to The final pressure is What is the change in the thermal energy of the gas during this process? (R = 8.31 J/mol ∙ K)

0.0 kJ

If V = 20 V and the battery is ideal, what is the current through R3 in the figure?

0.20 A

A mass m oscillates on a horizontal spring without any resistive (damping) or driving forces. The period of the oscillation is 0.25 s and the spring constant is K. If the spring constant is decreased to K/4, and the amplitude of the oscillation is doubled, what will be the new period of oscillation?

0.5 s

If the temperature of a gas is increased from 20°C to 100°C, by what factor does the rms speed of an ideal molecule change?

1.1

A piece of plastic has a net charge of +2.00 μC. How many more protons than electrons does this piece of plastic have? (e = 1.60 × 10-19 C)

1.25 × 10^13

A system has 1000 microstates. Through some process, the system changes to 3000 microstates. What is the change in entropy for this process?

1.5e-23 J/K

Consider two equal-volume flasks of gas at the same temperature and pressure. One gas, oxygen, has a molecular mass of 32. The other gas, nitrogen, has a molecular mass of 28. What is the ratio of the number of oxygen molecules to the number of nitrogen molecules in these flasks?

1/1

If the length and diameter of a wire of circular cross section are both tripled, the resistance will be

1/3 of what it originally was.

A sound of 40 decibels is

100 times as intense as a sound of 20 decibels.

The potential difference between the plates of an ideal air-filled parallel-plate capacitor with a plate separation of 6.0 cm is 60 V. What is the strength of the electric field between the plates of this capacitor?

1000 V/m

A standing wave on a string has the form shown in the picture below. If the distance between A and B is 6 m and the velocity of the counter-propagating waves composing the standing wave is 240 m/s, what is the frequency of the standing wave?

20 Hz

There are two speakers, A and B. Speaker A is initially positioned at x = 0 and speaker B is fixed in place at x = 48 m. You are standing some distance away from the speakers along the x-axis (your exact position is not important). The speakers are both emitting identical sound waves. Speaker A is moved gradually in the +x direction. When speaker A is at position x= 24 m you hear the greatest constructive interference of the sound waves. Which wavelength could the sound waves possibly have? (If there is more than one, you must select all of them.)

24 m 6 m 3 m 12 m

Two tiny particles having charges +20.0 μC and -8.00 μC are separated by a distance of 20.0 cm. What are the magnitude and direction of electric field midway between these two charges? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)

25.2 × 10^5 N/C directed towards the negative charge

Two ideal parallel-plate capacitors are identical in every respect except that one has twice the plate area of the other. If the smaller capacitor has capacitance C, the larger one has capacitance

2C

A conducting wire has a resistance R, length L, and a rectangular cross-sectional are A. A current I flows through the wire when it is connected to a battery with a constant potential difference. What would be the current flow and resistance of the wire if it had a length of L/2 and a cross-sectional area of A/4? Resistance = 2R Current = I/2

2R I/2

Suppose there are 3 identical atoms each with energy levels 0, 1E, 2E, 3E, and 4E. If the total energy of the 3-atom system is 3E, What is the number of microstates of the system? (Since the atoms are identical, we can't distinguish between the first, second, and third atom.)

3

If the temperature of an ideal gas is increased from 20°C to 40°C, by what percent does the speed of the molecules increase?

3%

A current of 5.0 A flows through an electrical device for 10 seconds. How many electrons flow through this device during this time? (e = 1.60 × 10-19 C)

3.1 x 10^20

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

300 J

A 6 Ohm resistor is connected to a battery with a constant potential difference V. The power dissipated in the resistor is 16 W. The battery is disconnected from the resistor, and a new battery with potential difference V/2 is connected to the resistor. What is the power dissipated in the resistor after connecting the new battery?

4 W

The electric potential at a distance of 4 m from a certain point charge is 200 V relative to infinity. What is the potential (relative to infinity) at a distance of 2 m from the same charge?

400 V

In a region where the electric field is uniform and points in the +xdirection, the electric potential is -2000 V at x = 8 m and is +400 V at x = 2 m. What is the magnitude of the electric field?

400 V/m

An ideal air-filled parallel-plate capacitor with horizontal plates has a plate separation of 5.0 cm. If the potential difference between the plates is 2000 V, with the top plate at the higher potential, what are the magnitude and direction of the electric field between the plates?

40000 N/C downward

A cylinder contains 1.50 moles of an ideal monatomic gas that is initially at a temperature of 317 K. If the gas gains 2730 J of heat and performs 780 J of work, what is its final temperature? (R = 8.31 J/mol ∙ K)

421 K

During a constant temperature process, 5.0 J of heat is removed from an ideal gas. What is the work for the process, and does the volume of the gas increase or decrease?

5.0 J, decrease

Imagine you have 2 packets of energy to distribute to 8 boxes (representing atoms). 4 boxes belong to system A and 4 boxes to system B. How many ways are there to distribute the two energy packets across the 4 boxes of system A (and none in B) ?

6

There are two infinite plates with surface charges +4sigma and +sigma arranged as shown. What is the electric field, magnitude, and direction, at point P?

6(pi)(kc)(sigma)

A proton is placed in an electric field of intensity 800 N/C. What are the magnitude and direction of the acceleration of the proton due to this field? (e= 1.60 × 10-19 C, mproton = 1.67 × 10-27 kg)

7.66 × 10¹⁰ m/s² in the direction of the electric field

Imagine you have 4 packets of energy to distribute to 16 boxes (representing atoms). 8 boxes belong to system A and 8 boxes to system B. How many ways are there to distribute the four energy packets across the 8 boxes of system A (and none in B) ?

70

Two isolated copper plates, each of area 0.40 m2, carry opposite charges of magnitude 7.08 × 10-10 C. They are placed opposite each other in parallel alignment, with a spacing of 4.0 cm between them. What is the potential difference between the plates? (ε0 = 8.85 × 10-12 C2/N ∙ m2)

8.0 V

Consider a uniform horizontal electric field of 50 N/C directed toward the east. If the electric potential at a given point in the field is 80 V, what is the potential at a point 1.0 m directly south of that point?

80 V

An air-filled 20-μF capacitor has a charge of 60 μC on its plates. How much energy is stored in this capacitor?

90 uj

Which one of the arrows shown in the figure best represents the direction of the electric field between the two uniformly charged metal plates?

A

Suppose a certain chemical reaction 𝐴+𝐵→𝐶+𝐷is known to have positive changes in both enthalpy and entropy, and the reaction does not occur spontaneously at a temperature 𝑇0. What can you say about whether the reaction will occur at a different 𝑇?

A) It could occur spontaneously at 𝑇>𝑇0

Let us compare two situations for a reaction A⇋B : Situation 1: A has an energy that is 3kBT higher than B. In between the two states there is an energy barrier of height 1kBT. Situation 2: A has an energy that is 2kBT higher than B. The energy barrier has height 3kBT. In both cases, all molecules are initially in state A. Which of the following is correct?

B

Three equal charges +Q are at three of the corners of a square of side d. A fourth charge +Q of equal magnitude is at the center of the square as shown in the figure. Which one of the arrows shown represents the net force acting on the charge at the center of the square?

B

Plants make glucose (𝐶6𝐻12𝑂6) by reacting carbon dioxide (𝐶𝑂2) and water (𝐻2𝑂) through the reaction 6𝐶𝑂2+6𝐻2𝑂→𝐶6𝐻12𝑂6+6𝑂2. Using the Gibbs free energies of formation in the table, this reaction is:

B) Endergonic

A hot object with temperature 𝑇ℎ is in contact with a cold object with temperature 𝑇𝑐. They are isolated from their surroundings. Heat transfers energy from the hot object to the cold object. How does the amount of heat leaving the hot object, 𝑄ℎ, compare to the amount of heat entering the cold object, 𝑄𝑐?

B) 𝑄ℎ=𝑄𝑐

A parallel-plate capacitor consists of a set of two parallel plates of area Aseparated by a distance d. This capacitor is connected to a battery that maintains a constant potential difference across the plates. A slab of a dielectric material is inserted in the region between the plates and completely fills it. What changes would you observe as the dielectric is inserted? (There could be more than one correct choice.)

Both the charge on the plates of the capacitor and its capacitance would change.

A hot object with temperature 𝑇ℎ is in contact with a cold object with temperature 𝑇𝑐. They are isolated from their surroundings. Heat transfers energy from the hot object to the cold object. How does the change in entropy of the hot object, Δ𝑆ℎ, compare to the change in entropy of the cold object, Δ𝑆𝑐?

C) Δ𝑆ℎ<Δ𝑆𝑐

A gas initially contained in a volume 𝑉is allowed to expand into a volume 2𝑉by the removal of a barrier. The gas is surrounded by an environment at constant temperature 𝑇(a "reservoir"). What happens to the internal energy 𝑈𝑖𝑛𝑡, the entropy 𝑆, and the Helmholtz free energy 𝐹of the gas?

C) 𝑈𝑖𝑛𝑡stays the same, 𝑆increases, and 𝐹decreases

In the circuits shown below, all the capacitors, resistors and batteries are identical. In which circuit does the circled resistor have the largest current flow when CA and CB are uncharged and CC is completely charged? (If two or more circuits are tied for the largest, you must select all of them.)

Circuit A and B

A series of equipotential lines are shown here with their corresponding values of electric potential. What are the directions of the electric field E and the electric force on a negative charge?

E points left and F points right.

Three Boltzmann probability functions P corresponding to energies E1 , E2 , and E3 are shown in the graph as functions of temperature, T . What is the correct ranking of the energies of these probability functions?

E1<E2<E3

In the three cases below, point charges are arranged as shown in the figures. What is the correct ranking for the electric field magnitude at point P in each of the three cases. For example, E1 > E2 = E3 means the electric field magnitude at point P is greater in case 1 than in case 2, and case 3 is equal to case 2.

E3>E1>E2

Three identical charges (Q,q1,andq2 ) are lined up in a row. If we compare the electric force QQ exerts on charge q1(F⃗ Q→1)q1(F→Q→1) to the force QQ exerts on charge q2(F⃗ Q→2)q2(F→Q→2)

F→Q→2 is less than half as big as F→Q→1

In the Boltzmann probability function, c⋅e−E/(kBT)c⋅e−E/(kBT), the dependence on the temperature TT indicates that

Higher-energy states become more probable as the temperature increases

Assume that the relative probability of a system having two different free energies is a number much greater than 1: P(G2)P(G1)≫1 This means that the reaction going from the state with G1 to the state with G2 is

Highly Spontaneous

When a certain capacitor carries charges of ±10 µC on its plates, the potential difference cross the plates is 25 V. Which of the following statements about this capacitor are true? (There could be more than one correct choice.)

If we double the charges on the plates to ±20 µC, the potential difference across the plates will also double. If we double the charges on the plates to ±20 µC, the capacitance of the capacitor will not change.

A battery charges a parallel-plate capacitor fully and then is removed. The plates are then slowly pulled apart. What happens to the potential difference between the plates as they are being separated?

It increases.

Imagine you have 2 packets of energy to distribute to 8 boxes (representing atoms). 4 boxes belong to system A and 4 boxes to system B. How many ways are there to distribute the two energy packets such that each system gets one of them?

More than 12

Imagine you have 4 packets of energy to distribute to 16 boxes (representing atoms). 8 boxes belong to system A and 8 boxes to system B. How many ways are there to distribute the four energy packets such that each system gets two?

More than 70

Two systems A and B can be in 6 or 8 microstates, respectively. What is the entropy of the combined system A+B and what are the number of microstates of the combined system?

More than one of the above

In the circuit shown in the figure, R1 = 10 Ω, R2 = 12 Ω, R3 = 20 Ω, V1 = 1.0 V, V2 = 7.0 V, and the batteries are both ideal. What is the current through R1?

NOT 0.18 A

Three point charges, -2.00 μC, +4.00 μC, and +6.00 μC, are located along the x-axis as shown in the figure. What is the electric potential (relative to infinity) at point P due to these charges? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

NOT 154 kV

A portion of a circuit is shown in the figure, and the batteries are ideal. What is the potential difference VA - VB if I = 5.0 A?

NOT 45 V

When different resistors are connected in parallel across an ideal battery, we can be certain that

NOT the same current flows in each one.

A +5.0 x 10-6 C point charge is placed at the 0 cm mark of a meter stick, and a -4.0 x 10-6 C point charge is placed at the 50 cm mark. What is the net electric field at the 30 cm mark?

No idea

5 J of energy is transferred from system 1 to system 2 without changing their temperatures. What can we say about their entropies S?

None of the above

The charge Q is negative. What direction is the electric field vector at point P?

Up

Four waves are described by the following equations, where distances are measured in meters and times in seconds. I. y = 0.21 cos(2x +10t) II. y = 0.5 sin(10x + 5t) III. y = -0.32 cos(4x + 20t) IV. y = 1.64 sin(x - 5t)

Wave II has the smallest wavelength. Waves I and IV move at the same speed but in opoosite directions.

Oxygen molecules are 16 times more massive than hydrogen molecules. At a given temperature, how do their average molecular speeds compare? The oxygen molecules are moving

at 1/4 the speed of the hydrogen molecules.

As a proton moves in a direction perpendicular to the electric field lines

both its electric potential and electric potential energy remain constant.

An ideal gas undergoes a spontaneous expansion at constant temperature. During this process, its entropy

increases.

The plates of a parallel-plate capacitor are maintained with constant voltage by a battery as they are pulled apart. What happens to the strength of the electric field between the plates during this process?

it decreases

As a proton moves in the direction of the electric field lines

it is moving from high potential to low potential and losing electric potential energy.

Suppose an isolated and thermally insulated 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, how does the new entropy of the gas compare to the entropy of the original system?

larger

Hydrogen atoms in the atmosphere of the sun can exist in different energy states. The difference between the lowest energy state (the ground state) and the second to lowest energy state (the first excited state) is about 10 eV. The temperature of the sun's atmosphere is about 5800 K (so kBT≈0.5 eV). What will be the ratio of the number of atoms in the first excited state divided by the number of atoms in the ground state?

much much smaller than 1

Four tiny charged particles (two having a charge +Q and two having a charge -Q) are distributed on the x- and y-axes as shown in the figure. Each charge is equidistant from the origin. In which direction is the net electric field at the point P on the y-axis?

net field is zero, there is no direction

When a 1.0-m length of metal wire is connected to a battery, a current of flows through it. What is the diameter of the wire? The resistivity of the metal is 2.24 × 10-8 Ω ∙ m.

not 6.0

You have a perfectly ordinary coin. When you flip the coin twice, there are three possible outcomes: both heads, both tails, or one heads and one tails (in any order). Which of these outcomes has a higher entropy?

one head and one tail

There are two quantum oscillators. The graphs here show the energy levels of the oscillators. (The graphs have the same vertical scale.) Which oscillator has a shorter period?

oscillator 2

The absolute temperature of an ideal gas is directly proportional to which of the following quantities?

the average kinetic energy of its molecules

When unequal resistors are connected in parallel in a circuit,

the potential drop is always the same across each resistor.

If the electric potential at a point in space is zero, then the electric field at that point must be

uniform?

The charge Q is negative. Point Y is twice as far from Q as point X. What is the relationship between the magnitude of the electric field at point X, |E→X|, and the magnitude of the electric field at point Y, |E→Y|?

|E→X|=4|E→Y|

Suppose a certain chemical reaction 𝐴+𝐵→𝐶+𝐷does not occur spontaneously at a temperature 𝑇0. What can you say about the Gibbs free energy change Δ𝐺at 𝑇0for this reaction?

Δ𝐺>0

Three Boltzmann probability functions P corresponding to temperatures T1, T2, and T3 are shown in the graph as functions of energy, E . What is the correct ranking of the temperatures of these probability functions?

T1<T2<T3

A graph of a Boltzmann probability function as a function of energy is shown here. Two possible energies, E1 and E2, are indicated. How do the temperatures of these energy states compare?

T1=T2

The figure shows conventional current passing through a resistor. The arrow shows the direction in which this conventional current is flowing. Which of the following statements are correct? (There could be more than one correct choice.)

The current at point b is the same as the current at point a. The electric potential is lower at point b than at point a.

A 9-V battery is hooked up to two resistors in series using wires of negligible resistance. One has a resistance of 5 Ω, and the other has a resistance of 10 Ω. Several locations along the circuit are marked with letters, as shown in the figure. Which statements about this circuit are true? (There could be more than one correct choice.)

The current is exactly the same at points A, B, C, and D. The potential at B is equal to the potential at C.

Charge q is a test charge used to measure the electric field created by a source charge Q. To determine the electric field, we use E→=F→e/q . What happens to the electric field created by charge Q if q is doubled?

The electric field doesn't change

A hot object with temperature 𝑇ℎ is in contact with a cold object with temperature 𝑇𝑐. They are isolated from their surroundings. Heat transfers energy from the hot object to the cold object. What is true about the entropy in each object?

The entropy of the hot object is decreasing and the entropy of the cold object is increasing

Charge q is a test charge used to measure the electric field created by a source charge Q. What happens to the electric force on these charges if q is doubled?

The force on both 𝑄 and 𝑞 doubles

There are two containers, A and B, each with 2 mol of gas. The molecules of gas in A have twice the mass of the molecules in B. The temperature of the gas in B is twice the temperature of A. Which statement is true?

The gas in container A has a smaller rms speed and a smaller thermal energy than the gas in B.

A fixed container holds oxygen and helium gases at the same temperature. Which of the following statements are correct? (There could be more than one correct choice.)

The helium molecules have the same average kinetic energy as the oxygen molecules. The helium molecules have the greater speed.

A 10-L flask and a 1-L flask each contain two moles of ideal diatomic gas (but not the same gas) at 25°C. Which of the following statements about these gases must be true? There could be more than one correct choice.

The molecules in the smaller flask have the same average kinetic energy per molecule as those in the larger flask. The thermal energy of the gas in both flasks is the same.

A graph of a Boltzmann probability function as a function of energy is shown here. According to this graph, which statement is true?

The most likely value of the energy is 0

Suppose an isolated and thermally insulated 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, how does the new internal energy of the gas compare to the internal energy of the original system?

The new internal energy is the same

A region of space contains a uniform electric field, directed toward the right, as shown in the figure. Which statement about this situation is correct?

The potential at points A and B are equal, and the potential at point C is lower than the potential at point A.

Two uniformly charged spheres are firmly fastened to and electrically insulated from frictionless pucks on an air table. The charge on sphere 2 is three times the charge on sphere 1. Which force diagram correctly shows the magnitude and direction of the electric forces on the spheres?

D

A chemical reaction proceeds spontaneously at some temperature T, even though the change of enthalpy is + 200 kJ. What can we say about this reaction? (select all that apply)

The reaction would likely be non-spontaneous if we decreased the temperature. The entropy change is positive. The reaction is endothermic

A wave pulse is traveling in the +x direction at a speed of 1 m/s. A snapshot graph corresponding to t = 2 s is shown here. What is the correct history graph corresponding to the position x = 3 m?

complete reflection (graph 2)

As more resistors are added in series to a constant voltage source, the power supplied by the source

decreases.

If the electric field between the plates of a given air-filled capacitor is weakened by removing charge from the plates, the capacitance of that capacitor

does not change

The internal energy of an object increases while its volume changes, but pressure is held constant. Which of the following are true? (i) Heat must have been added to the system regardless of how the volume changed (ii) If the volume increased then the system must have transferred energy to the environment as work (iii) Since pressure is constant, enthalpy is conserved (iv) If the volume increased then the environment must have transferred energy into the system as heat

ii and iv