IB Physics SL B.3 Gas laws Questions

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Practise IB Physics SL B.3 by modelling pressure, volume, amount and absolute temperature with ideal-gas equations and molecular explanations.

77 questions in this syllabus scope, with question parts counted together.

Exam points & syllabus

Exam points

Choose the actual contact area and perpendicular force for pressure; use a pressure difference for net loading from two sides.
Connect molecular wall collisions to momentum change, average force and pressure; use Newton third law explicitly when requested.
Distinguish wall-impact strength from collision rate: isothermal volume changes preserve mean thermal speed but change momentum transfer per time.
Use the mean-square-speed or mean-energy pressure relation consistently: P = ρ⟨v²⟩/3 = 2N⟨Ek⟩/(3V).
Specify the counted entity before using n = N/Nₐ and n = m/M; compare sample particle counts through m/M rather than mass alone.
For single-atom estimates, use M/Nₐ for mass and divide the matching bulk volume by the atom count for volume per atom.
State precise ideal-model assumptions and valid real-gas contrasts; elastic collisions do not imply equal speeds or fixed energy for each particle.
Use low pressure, low density and sufficiently high temperature as approximation conditions; explain extreme-compression failures through the model assumptions.
Test ideal behaviour with numerical graph evidence, retaining the controlled temperature, amount or volume and the actual axis scales.
Choose the particle or molar state equation for the requested quantity and retain kelvin, pressure and volume conversions.
For fixed amount, compare pV/T between states and identify the fixed variable; convert Celsius before taking a ratio.
Use column height as a volume proxy only with fixed cross-section, and retain the pressure condition or mercury-load orientation in the state balance.
Retain variable particle amount in open-system comparisons and distinguish the final total from the quantity added or removed.
For connected same-gas vessels, use common pressure with each vessel’s V/T; for isothermal valve mixing, conserve total amount over combined volume.
Read graph gradients by rearranging the state equation; convert the slope to the requested volume, amount or particle number.
Combine gas-state count with particle or molar mass for sample mass, and distinguish density changes from pressure changes at equal N,V,T.
Translate a production rate into the amount over the requested interval, then use the supplied gas-state conditions for the resulting volume.
Define internal energy through total random particle kinetic energy, separate it from bulk motion, and retain the monatomic 3/2 factor where applicable.
Use U = 3nRT/2 = 3pV/2 for monatomic states; compare particle amounts as well as temperature and subtract state values for an energy change.
Use the actual temperature convention on an energy graph: a point at 27°C means 300 K before applying n = 2U/(3RT).
For model evaluation, connect an unexpected force or a stated cooling expansion to the relevant assumptions and physical energy or momentum transfer.

Covered syllabus points

B.3.1—Pressure B.3.2—Amount of substance B.3.3—Ideal gas model B.3.4—Empirical gas laws B.3.5—Ideal gas equations B.3.6—Molecular pressure model B.3.7—Ideal gas internal energy B.3.8—Ideal gas approximation limits

Exam points

Derive pressure from perpendicular force and actual contact area: for a solid cylinder, weight ρAhg divided by A gives p = ρgh.
For a thin cylindrical rim, use contact area approximately 2πRx, giving pressure W/(2πRx); the full circular face is not in contact.
Use pressure difference across a surface for net normal force, F = AΔp, rather than multiplying area by one side’s absolute pressure.
When asked to comment on an unexpectedly large force, connect its size to a limitation of the pressure model or a mechanism reducing the force.

[Maximum number: 2]

A solid cylinder of height h and density $\rho$ rests on a flat surface.

Show that the pressure $p_{\mathrm{C}}$ exerted by the cylinder on the surface is given by $p_{\mathrm{C}}=\rho g h$ .

weight of cylinder $=A h g \rho$ $\text { pressure }=\frac{F}{A}=\frac{A h g \rho}{A}$

Marking guidance:

Allow use of $A=\pi r^{2}$ in MP1.

Exam points

Relate amount of substance to a specified entity count using n = N/Nₐ; one mole contains Avogadro’s number of those entities.
Convert sample mass to amount with n = m/M, then use N = nNₐ; keep sample and molar-mass units consistent, including in order-of-magnitude estimates.
Compare particle counts with ratios of m/M; distinguish atoms from molecules and avoid inserting an extra atomicity factor for the wrong entity.
Find a single-atom mass from M/Nₐ, converting g mol⁻¹ to kg mol⁻¹; an appropriate atomic-mass-unit conversion is an alternative.
For volume per atom, divide bulk volume m/ρ by the matching atom count; use the same sample mass in both quantities.
At the question’s stated precision, use the numerical conversion between u in grams and Nₐ; distinguish approximate numerical values from units.

[Maximum number: 1]

This question is in two parts. Part 1 is about ideal gases and specific heat capacity. Part 2 is about simple harmonic motion and waves.
Part 1 Ideal gases and specific heat capacity

Argon behaves as an ideal gas for a large range of temperatures and pressures. One mole of argon is confined in a cylinder by a freely moving piston.

Define what is meant by the term one mole of argon.

One mole of argon is the molecular weight of argon in grams, or $6.02\times10^{23}$ argon atoms, or the same number of particles as in 12 g of carbon-12.

Allow atoms or molecules for particles.

1\ \mathrm{mol}=6.02\times10^{23}\ \text{particles}

Exam points

State distinct ideal-gas assumptions precisely: negligible particle volume, random motion, negligible forces except during collisions and elastic collisions.
Do not assume identical particle speeds or constant kinetic energy for one molecule; elastic collisions can redistribute energy between molecules.
Contrast real gases with ideal point particles through finite molecular size, intermolecular forces or possible liquefaction.
Test ideal behaviour at fixed temperature and amount with at least two numerical pV products from the graph, then draw the conclusion.
Recognise molecular kinetic theory as a model explaining the ideal-gas equation of state from particle behaviour.

[Maximum number: 2]

This question is in two parts. Part 1 is about ideal gases and specific heat capacity. Part 2 is about simple harmonic motion and waves.
Part 1 Ideal gases and specific heat capacity

State two assumptions of the kinetic model of an ideal gas.

Exam points

For fixed gas amount, use pV/T = constant with kelvin temperature; identify which variable remains fixed before simplifying the relation.
Convert each Celsius temperature to kelvin before scaling, then convert back only if requested; doubling volume at constant pressure does not double °C.
In a constant-area tube, replace volume ratios with gas-column height ratios only after establishing the applicable pressure or temperature condition.
Read the stated stages independently: an isothermal stage preserves T, and a following isobaric stage gives T₂/T₁ = V₂/V₁.
Test p ∝ T at fixed volume with two numerical graph points, keeping temperature in kelvin and checking a consistent p/T ratio.
For a pV graph against Celsius temperature, require a linear trend with the −273°C intercept, or verify equal pV/T values using kelvin.

[Maximum number: 2]

The equipment shown in the diagram was used by a student to investigate the variation with volume, of the pressure p of air, at constant temperature. The air was trapped in a tube of constant cross-sectional area above a column of oil.

The pump forces oil to move up the tube decreasing the volume of the trapped air.

Outline how the results of this experiment are consistent with the ideal gas law at constant temperature.

$V \propto H$ thus ideal gas law gives $p \propto \frac{1}{H}$

so graph should be «a straight line through origin,» as observed

Exam points

Choose pV = nRT for moles or pV = NkBT for particles; keep N = nNₐ and R = NₐkB consistent.
Rearrange for the requested state variable, use kelvin and convert pressure/volume scales before substituting.
For fixed particle amount, compare pV/T between states; convert Celsius first and convert back only after the ratio calculation.
If particles enter or leave, retain the changing N in pV = NkBT; distinguish final total particles or mass from the amount added or removed.
For constant pressure and volume, particle count is inversely proportional to kelvin temperature; compute percentage change relative to the initial count.
Connected containers of the same gas share pressure: compare their masses through V/T even when their temperatures differ.
For isothermal mixing after a valve opens, conserve total gas amount over the combined volume: P(V₁ + V₂) = P₁V₁ + P₂V₂.
Combine equation-of-state particle or mole count with molecular or molar mass to infer sample mass, keeping the requested gram or kilogram unit.
At the same p, V and T, gases have equal particle counts; molecular mass changes sample mass and density rather than the ideal-gas pressure.
For the same gas species, pressure scales as particle number density × T, or mass density × T; compare all changing factors.
Interpret graph gradients through the equation: slope of V against T is NkB/p, slope of p against T is nR/V, and slope of p against 1/V is nRT.
From a constant-area gas-column experiment, use V = AH; a p against 1/H gradient b gives n = bA/(RT).
Use the actual graph scales and temperature convention when finding gas states or predicting p–T graphs; doubling N doubles the gradient at fixed V.
Use absolute gas pressure in the state equation, adding or subtracting a mercury-column load according to the inspected tube orientation.
Combine pV = NkBT with the actual cylinder geometry and F = pA; state whether the requested force is gas force or a net two-sided force.
Translate a molar production rate into the amount produced over the requested time, then calculate gas volume at the supplied pressure and temperature.
When mean random kinetic energy is used instead of temperature, apply its proportionality to kelvin T before using the fixed-pressure volume relation.

[Maximum number: 2]

The pump forces oil to move up the tube decreasing the volume of the trapped air.

The cross-sectional area of the tube is $1.3 \times 10^{-3} \mathrm{~m}^{2}$ and the temperature of air is 300 K . Estimate the number of moles of air in the tube.

$n=\frac{b A}{R T} OR$ correct substitution of one point from the graph

$n=\frac{5 \times 10^{4} \times 1.3 \times 10^{-3}}{8.31 \times 300}=0.026 \approx 0.03$

Answer must be to 1 or 2 SF. Allow ECF from (b).

Exam points

Explain pressure through particle momentum change at wall collisions, the force on the particles and the equal opposite force on the wall.
For isothermal expansion, keep mean kinetic energy or speed unchanged and link fewer wall collisions per unit time to a smaller momentum-transfer rate.
For heating at fixed volume, link greater mean particle speed to stronger or more frequent wall impacts, then greater force on the same wall area.
Distinguish a single collision from repeated-impact force: isothermal compression increases total wall force through collision rate, not a higher thermal speed.
Use P = 2N⟨Ek⟩/(3V), keeping ⟨Ek⟩ as the mean translational energy per particle and N/V as particle number density.

[Maximum number: 1]

A solid cylinder of height h and density $\rho$ rests on a flat surface.

A tube of constant circular cross-section, sealed at one end, contains an ideal gas trapped by a cylinder of mercury of length 0.035 m . The whole arrangement is in the Earth's atmosphere. The density of mercury is $1.36 \times 10^{4} \mathrm{~kg} \mathrm{~m}^{-3}$ .

When the mercury is above the gas column the length of the gas column is 0.190 m .

Outline why the gas particles in the tube hit the mercury surface less often after the tube has been rotated.

Exam points

Define ideal-gas internal energy as total random molecular kinetic energy, with negligible intermolecular potential energy; distinguish total from mean.
For a monatomic ideal gas, use U = 3NkBT/2 = 3nRT/2 = 3pV/2; multiply single-particle mean energy by the full particle count.
Find a state-to-state monatomic internal-energy change from ΔU = 3Δ(pV)/2; at fixed pressure this becomes 3pΔV/2.
In a fixed-amount isothermal ideal-gas change, conclude that internal energy remains constant and explicitly link this to unchanged mean kinetic energy.
Keep bulk translational motion separate from random thermal motion; the idealised uniformly moving container has unchanged internal energy and temperature.
At the same temperature, total monatomic internal energy scales with particle count; equal sample mass does not imply equal internal energy.
When reading U against Celsius temperature, convert the labelled temperature to kelvin before using n = 2U/(3RT).
For the stated cooling expansion, explain energy transfer from molecules to the piston and the resulting fall in mean kinetic energy and temperature.

[Maximum number: 3]

This question is in two parts. Part 1 is about ideal gases and specific heat capacity. Part 2 is about simple harmonic motion and waves.
Part 1 Ideal gases and specific heat capacity

At the temperature of 350 K , the piston in (b) is now freed and the argon expands until its temperature reaches 300 K .
Explain, in terms of the molecular model of an ideal gas, why the temperature of argon decreases on expansion.

Exam points

Identify low pressure, low density and sufficiently high temperature as conditions favouring the ideal-gas approximation.
For extreme compression, connect large 1/H to small gas volume and high pressure, then explain why ideal-model assumptions may fail.

[Maximum number: 2]

The pump forces oil to move up the tube decreasing the volume of the trapped air.

The equation of the line of best fit is:

p=a+\frac{b}{H}

The equation above may be used to predict the pressure of the air at extremely large values of $\frac{1}{H}$ . Suggest why this will be an unreliable estimate of the pressure.

very large $\frac{1}{H}$ means very small volumes / very high pressures

at very small volumes the ideal gas does not apply

OR

at very small volumes some of the assumptions of the kinetic theory of gases do not hold

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