IB Physics HL Theme B: The particulate nature of matter questions

Question 1

Paper 2Easy7 marks

A student models the apparent brightness $b$ of a star at different distances $d$ assuming the star’s luminosity $L$ remains constant. The relationship is

b=\frac{L}{4\pi d^2}

where $b$ is measured in $\mathrm{W\,m^{-2}}$ $L$ in $\mathrm{W}$ and $d$ in $\mathrm{m}$

Figure 1 shows the modelled apparent brightness as the distance from the star is changed.

(a)

Use Figure 1 to determine the apparent brightness of the star when $d=1.0\times10^{16}\,\mathrm{m}$

[1]

(b)

Using your answer to (a), calculate the luminosity of the star.

[3]

(c)

Use Figure 1 to determine the apparent brightness when $d=2.0\times10^{16}\,\mathrm{m}$

[1]

(d)

State the factor by which the apparent brightness changes when the distance increases from $1.0\times10^{16}\,\mathrm{m}$ to $2.0\times10^{16}\,\mathrm{m}$ and explain this change using the relationship given.

[2]

Question 2

Multiple choiceMedium1 mark

During a 10.0 min interval, a sample is melting at constant temperature. A 400 W heater is on for a total of 5.0 min; assume all energy supplied while it is on enters the sample. Which row gives the energy supplied by the heater and the particle behaviour during melting?

Show answer and explanation

Answer: B. The energy supplied is $E=Pt$ using the time for which the heater is on: $E=(400\ \text{W})(5.0\times60\ \text{s})=1.2\times10^5\ \text{J}=120\ \text{kJ}$ During melting, the energy changes particle behaviour and arrangement while the average kinetic energy, and therefore the temperature, remains constant.
A: treats 5.0 min as 5.0 s, giving 2.0 kJ.
C: calculates the energy correctly but applies the temperature-rise model instead of recognizing a phase change.
D: uses the full 10.0 min interval as the heater-on time, giving 240 kJ.
Remember: energy can be transferred during a phase change without increasing the temperature.

Question 3

Multiple choiceMedium1 mark

A methane source inventory records total emissions of $1.0\times10^5\ \text{kg day}^{-1}$ Wetlands are the only natural source in the inventory and emit methane at $1.5\times10^3\ \text{kg h}^{-1}$ all other emissions are human-made. What is the mass emitted by human-made sources per day?

Show answer and explanation

Answer: B. The human-made emissions are the total emissions minus the natural emissions. Wetlands emit $1.5\times10^3\times24=3.6\times10^4\ \text{kg day}^{-1}$ so the human-made emissions are $1.0\times10^5-3.6\times10^4=6.4\times10^4\ \text{kg day}^{-1}$

A: converts the wetland rate to a daily mass but gives the natural emissions alone.
C: uses the total daily emissions without subtracting the natural contribution.
D: adds the natural contribution to the total instead of subtracting it.

Remember: convert rates to matching time units before combining emissions.

Question 4

Paper 2Medium8 marks

Satellite measurements estimate the daily-mean incident and reflected short-wave solar power per unit area for regions with the same underlying surface type. The two regions measured on day 2 were observed in the same season and had approximately matched cloud cover.

Observation	Latitude	Cloud cover	Incident solar power / W m⁻²	Reflected solar power / W m⁻²
Day 1	30°N	Low	250	50
Day 2	30°N	Extensive	250	90
Day 2	60°N	Extensive	180	81

(a)

Determine the albedo for each of the three observations.

[3]

(b)

Calculate the absorbed solar power per unit area at 30°N on day 1 and day 2.

[2]

(c)

Use your answers to (a) and (b) to explain how changing cloud cover affects the daily albedo and absorbed solar power per unit area at 30°N.

[2]

(d)

State what the comparison between the two day-2 observations suggests about the dependence of albedo on latitude.

[1]

Question 5

Multiple choiceEasy1 mark

A fixed amount of ideal gas changes between the two states shown. The labelled pressures are absolute; $p$ is a positive pressure and $V$ is a positive volume. Which expression gives $T_B/T_A$

Show answer and explanation

Answer: A. For a fixed amount of ideal gas, $PV/T=\text{constant}$ so $T_B/T_A=P_BV_B/(P_AV_A)$ Substituting the values shown gives $(3p)(2V)/[(2p)(V)]=3$ the temperature ratio is dimensionless.
B: reverses the state ratio, giving $T_A/T_B=1/3$
C: omits the volume ratio and uses pressure alone, giving $3/2$
D: omits the pressure ratio and uses volume alone, giving $2$
Remember: compare the products $PV$ when finding temperature ratios for a fixed amount of ideal gas.

Question 6

Paper 2Medium13 marks

A laboratory investigates the pressure exerted by a gas on flat panels. In each trial, a panel forms one wall of a chamber. The outer face of the panel is evacuated, and a sensor measures the force exerted by the gas perpendicular to the panel. The panel area is changed between trials. The measured forces are shown in Figure 1.

(a)

Write the equation defining pressure, P, in terms of force and area, and state what the force represents.

[2]

(b)

Use Figure 1 to determine the pressure represented by the graph, in Pa.

[3]

(c)

A further panel is exposed to gas at the pressure determined in (b). The area of the panel is 0.075 m². Determine the magnitude of the force exerted on the panel.

[2]

(d)

A panel of area 0.12 m² is exposed to gas at the pressure determined in (b). The panel is tilted. Determine the magnitude of the force exerted on it and state the force’s direction relative to the panel.

[3]

(e)

A student concludes that gas pressure increases with panel area because the force shown in Figure 1 increases. Assess this conclusion using the graph.

[3]

Question 7

Multiple choiceMedium1 mark

A real isolated system consists of parts A and B. During an irreversible change, their entropy changes are $\Delta S_A=-x$ and $\Delta S_B=+y$ where $x$ and $y$ are positive. Which relation gives the entropy change of the whole system and the resulting constraint on $x$ and $y$

Show answer and explanation

Answer: B. The changes of the two parts add: $\Delta S_{\text{whole}}=\Delta S_A+\Delta S_B=-x+y=y-x$ Since the irreversible change occurs in a real isolated system, its total entropy increases; hence $y-x>0$ so $y>x$
A: treats the decrease $-x$ as a positive contribution.
C: reverses the subtraction, giving the wrong total change and constraint.
D: counts only the increase in part B and omits part A’s entropy change.
Remember: the entropy increase applies to the isolated whole, not necessarily to each part.

Question 8

Paper 2Hard10 marks

A cyclic engine operates between two thermal reservoirs at $480\ \mathrm{K}$ and $300\ \mathrm{K}$ The engine, both reservoirs and an ideal mechanical work store form an isolated assembly. The engine returns to its initial state each cycle, and the work store’s entropy does not change.

For a reservoir at constant temperature, its entropy change is $\Delta S=Q/T$ where $Q$ is the energy received by the reservoir.

(a)

State the Clausius form and the Kelvin form of the second law of thermodynamics.

[2]

(b)

In one proposed cycle, the engine receives $1.20\ \mathrm{kJ}$ from the $480\ \mathrm{K}$ reservoir, transfers $0.50\ \mathrm{kJ}$ to the $300\ \mathrm{K}$ reservoir and delivers $0.70\ \mathrm{kJ}$ to the work store.

Assess whether this proposed cycle is consistent with energy conservation and the second law.

[4]

(c)

The engine continues to receive $1.20\ \mathrm{kJ}$ from the $480\ \mathrm{K}$ reservoir each cycle. Determine the greatest possible work delivered to the work store per cycle, consistent with the second law, and state whether the limiting cycle is reversible or irreversible.

[4]

Question 9

Multiple choiceMedium1 mark

A metal wire is connected as shown. Its temperature is held constant for the first readings, then allowed to rise as the potential difference is increased. Which row describes the first readings and the resistance trend in the later readings?

	Behaviour of first readings	Resistance during later readings
A	Ohmic	Increases
B	Ohmic	Decreases
C	Non-ohmic	Increases
D	Non-ohmic	Decreases

Show answer and explanation

Answer: A. Resistance is $R=V/I$ For the fixed-temperature readings, $1.0/0.20=5.0\ \Omega$ and $2.0/0.40=5.0\ \Omega$ so current is proportional to potential difference and the wire is ohmic. For the later readings, $3.6/0.60=6.0\ \Omega$ and $5.6/0.80=7.0\ \Omega$ so resistance increases.

B: treats the falling gradient of the current-against-potential-difference graph, $I/V$ as resistance; its decrease corresponds to increasing $V/I$

C: uses the changing gradient in the later section to classify the fixed-temperature readings, which lie on a straight line through the origin.

D: combines those errors, applying the later section’s changing gradient to the first readings and reversing resistance with $I/V$

Remember: On an $I$ -against- $V$ graph, the gradient is $I/V$ whereas resistance is $V/I$

Question 10

Paper 2Medium7 marks

A positive charge $q$ moves between the terminals of component P or component Q in the direction of conventional current. $W$ is the electrical work transferred to the component. For each component, the potential difference is constant during the measurements. Figure 1 shows measured values of $W$ for different values of $q$ Treat potential differences as magnitudes.

(a)

Explain why the gradient of a graph of $W$ against $q$ represents the potential difference across a component.

[2]

(b)

Determine the potential difference across component P using Figure 1.

[2]

(c)

A positive charge of $0.60\ \mathrm{C}$ passes through component Q. Determine the work transferred to Q. State which component transfers more energy per unit charge, and by what factor.

[3]

Question 11

Paper 2Medium9 marks

The circuits in Figure 1 are used to compare solid samples X and Y. The sources are ideal and the ammeters have negligible resistance. The samples have equal length and cross-sectional area and are each maintained at $20^\circ\mathrm{C}$

(a)

Identify which sample is an insulator.

[1]

(b)

Determine the resistance of each sample.

[3]

(c)

The voltage across X is then reduced to $1.5\ \mathrm{V}$ Its temperature remains at $20^\circ\mathrm{C}$ and its resistance is assumed unchanged. Calculate the electrical energy transferred to X in $40\ \mathrm{s}$ Show your working.

[3]

(d)

Explain, in terms of the mobility of charge carriers, why the readings in Figure 1 are consistent with X being a conductor and Y an insulator.

[2]

IB Physics HL Theme B: The particulate nature of matter questions

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