Container A has a sample of gas A, while container B has a sample of gas B. The atoms of both gases currently have the same average speed, but the molecules of gas B have a greater molar mass than the molecules of gas A. What can be concluded about the temperatures?

• Gas A & gas B are the same temperature

• Gas A has a greater temperature

• Gas B has a greater temperature

• Cannot be determined without knowing the number of molecules in each container

Answer explanation

Temperature is directly proportional to kinetic energy.

K = (3/2) k_BT

Whichever gas has more kinetic energy will have a greater temperature.

K = 0.5mv²

The speeds (v) is the same, but gas B has a greater mass, so it will have more kinetic energy and therefore a greater temperature.

Two capacitors are wired in series as shown. The circuit has reached steady state. A student measures the charge on the 4 μF and finds it a non-zero +Q₀.

How does Kirchhoff's loop rule apply to this circuit?

• It doesn't, it only applies to circuits with batteries

• The two capacitors will have potential differences equal in magnitude

• The voltage drop across the 2 μF will be twice that of the voltage drop across the 4 μF

• There is a voltage drop in the wire itself equal to the voltage drop in the capacitors

• Capacitors do not have voltage drops across them

Answer explanation

Kirchhoff's law applies to all circuits, whether or not they have a battery.

In in this loop, the potential differences must add up to zero. The trick here is that each capacitor will have the same magnitude of voltage drop, but in opposite directions.

At steady state, the wire will have no significant voltage drop, even if it did have some natural resistance. This is because there is no significant current flow in the wire at steady state.

Two capacitors are wired in series as shown. The circuit has reached steady state. A student measures the charge on the 4 μF and finds it a non-zero +Q₀.

What is the magnitude of charge on the 2 μF capacitor?

• 0.5Q₀

• Q₀

• 2Q₀

• 4Q₀

• 0

Answer explanation

Due to Kirchhoff's loop rule, these two capacitors have equal and opposite voltage drops.

V₄ = V₂

(Q₀ / C₄) = (Q₂ / C₂)

(Q₀ / 4 μF) = (Q₂ / 2 μF)

Q₀ = 2Q₂

Q₂ = 0.5Q₀

Another way to think of it. The 2 μF capacitor has half the "room" for electrons as compared to the 4 μF. That is essentially what capacitance is: it's a reflection on the capacitor's ability to hold electrons.

A convex mirror has a focal located 0.3 m behind it. If you place an object 0.5 m in front of the mirror, where is the image formed?

• 0.2 in front of the mirror

• 0.32 m in front of the mirror

• 0.19 m behind the mirror

• 0.45 behind the mirror

Answer explanation

For convex mirrors, the focal is located BEHIND the mirror, where light rays cannot actually go. For this reason, the focal in convex mirrors must be NEGATIVE when doing the math.

(1 / 0.5) + (1 / s_i) = (1 / −0.3)

(1 / s_i) = −0.5333

s_i = −0.1875 m

The s_i is negative, which tells us this image forms behind the mirror.

The current through resistor X is measured to be 4 A and the current through resistor Y is 1 A. What is the current through resistor Z?

• 4 A

• 3 A

• 1 A

• Cannot be determined without knowing more values

Answer explanation

The junction law says that the total current going into a junction is the amount of current coming out of the junction.

There are 4 amps before the junction. Then, one of the branches has 1 amp. So, the other branch must have 3 amps!

A, B, C, and D represent processes by which an electron drops to a lower orbit. Which process will result in the greatest frequency of photon emitted?

• A

• B

• D

• They all emit the same frequency

Answer explanation

The larger the energy drop, the greater the energy of photon released. Process D has the electron falling from E = -2 eV to E = -10 eV. This is a change of energy of -8 eV, meaning the photon released has 8 eV of energy.

Energy is directly proportional to frequency for photons (E = hf). More energy means more frequency.

Tags

NGSS.HS-PS4-3

A chef grabs a hot pan and burns his hand. By what primary process did the heat transfer into his hand?

A sealed container of gas is originally at temperature 200 K. It is taken through an isochoric process, in which the pressure triples. What is the new temperature, in Kelvin?

Mathematical Equivalence

ON

Answer explanation

PV = nRT

This is a sealed container, so the number of molecules (n) is constant.

The process is isochoric, which means volume is constant. Since P and T are the only variables changing, this results in them being linearly proportional.

P ∝ T

So if pressure triples, so does the temperature.

The blue represents a current carrying wire, while the grey represents the magnetic field around the wire. What direction is the current?

• To the right

• To the left

• The direction of current has no bearing on the magnetic field's formation

Answer explanation

Use right-hand rule to figure out the direction of the current.

Your thumb will represent the direction of the current. Your fingers will curl in the direction of the magnetic field.

Tags

NGSS.HS-PS2-5

What defines an adiabatic process?

• Q = 0

• W = 0

• ΔU = 0

• PV = 0

Answer explanation

An adiabatic process is one where heat energy, Q, does not escape the system or get added to to the system.

Only work is done to the system.

This results in a change in ΔU, since:

ΔU = Q + W

If Q = 0 and W is non-zero, then ΔU must also be non-zero. This also means the product of PV must also change.

U ∝ K

K ∝ T

T ∝ PV

Tags

NGSS.HS-PS3-1