NEB Class 11 • Physics • Worked Practice

Ideal Gas Practice Set: NEB 11 Physics

Move from conversions and controlled-variable laws to two-state changes, molecular explanations, process graphs and experimental judgement. Show the model before the arithmetic.

Twenty graded questions with worked solutions
State tables, ratios, PV=nRT and kinetic theory
Timed challenge, error analysis and FAQs

Pressure, volume, temperature and amount belong to one gas state.

Practice boundary

What this set tests

The problems follow the CDC Physics Grade 11 context and the state-equation treatment in OpenStax Ideal Gas Law. Review the concept guide or study guide before an unfamiliar level.

Level 1

Units, scales and direct meaning

1. Temperature conversion

Convert 27°C and 127°C. Solution: approximately 300 K and 400 K. Their ratio is 4/3, not 127/27.

2. Volume conversion

2.50 L = 2.50×10⁻³ m³. Multiply litres by 10⁻³.

3. Absolute pressure

Gauge pressure is 150 kPa with atmospheric pressure 100 kPa. Solution: absolute P=250 kPa.

4. Amount and molecules

0.50 mol contains N=0.50×6.02×10²³≈3.01×10²³ molecules.

Level 2

Controlled-variable gas laws

5. Isothermal compression

120 kPa gas at 3.0 L is compressed to 1.2 L. P₂=120×3.0/1.2=300 kPa.

6. Constant pressure heating

Volume is 2.0 L at 300 K and temperature reaches 450 K. V₂=3.0 L.

7. Rigid tank

Absolute pressure is 200 kPa at 250 K. At 375 K, P₂=200×375/250=300 kPa.

8. Ratio challenge

At fixed n, volume halves and kelvin temperature doubles. Since P∝T/V, pressure becomes four times larger.

Level 3

PV=nRT and two-state changes

9. Find moles

P=1.0×10⁵ Pa, V=0.050 m³, T=300 K. n=PV/(RT)=5000/2493≈2.01 mol.

10. Find volume

n=0.25 mol, T=320 K, P=2.0×10⁵ Pa. V=nRT/P≈3.32×10⁻³ m³ or 3.32 L.

11. General two-state problem

Fixed gas: P₁=100 kPa, V₁=4.0 L, T₁=300 K; V₂=2.5 L, T₂=375 K. P₂=100×4×375/(300×2.5)=200 kPa.

12. Leak diagnosis

A rigid tank returns to the same temperature but its absolute pressure falls 10%. From PV=nRT with fixed V,T, n also falls 10%, suggesting gas loss.

Level 4

Kinetic-theory explanations

13. Pressure from collisions

Molecules change momentum at walls. Force is the rate of momentum transfer; pressure is force per area.

14. Temperature doubles

Average translational kinetic energy 3k_BT/2 doubles, while rms speed rises by √2.

15. Compare gases

At equal T, helium and oxygen molecules have equal average translational kinetic energy. Helium molecules have higher rms speed because of lower mass.

16. Constant-volume heating

Faster molecules collide more often and transfer more momentum per collision, so pressure rises.

Check the OpenStax kinetic-theory derivation after completing explanations unaided.

Level 5

Graphs and experiment

17. Linearise Boyle’s law

Plot P against 1/V. For fixed n,T, gradient is nRT and the ideal line passes through the origin.

18. Celsius extrapolation

At constant pressure, V versus Celsius temperature may extrapolate toward −273.15°C. This is an ideal extrapolation; a real gas changes phase first.

19. Rapid compression error

Rapid compression warms the gas, so a Boyle-law P reading can be larger than the isothermal prediction. Compress slowly and wait for equilibrium.

20. Dead volume

Air in tubing adds to syringe volume. Ignoring it especially distorts small-volume data; include a fitted or measured dead volume.

Twenty-minute mixed challenge

Questions without method labels

Convert 37°C to kelvins.
A fixed gas halves V at constant T. Find P ratio.
Use PV=nRT to find n from a stated SI state.
Explain pressure rise in a rigid heated tank.
Compare rms speeds when T quadruples.
Sketch P against V and P against 1/V.
Explain one real-gas limitation.
Evaluate a Boyle-law experiment.

Checks: 310 K approximately; pressure ratio 2; rms-speed ratio 2. State assumptions and absolute variables.

Use PhET Gas Properties after writing predictions. Record one incorrect prediction and the collision model that corrected it.

Error analysis

Common Ideal Gas failures

Scale

Celsius or gauge values used in proportional laws.

Boundary

Combined law used even though gas amount changes.

Process

A fixed variable assumed but not stated.

Meaning

Equal temperature mistaken for equal molecular speed.

Review Physical Quantities for conversions. For online or physical NEB tuition, call 9846662070.

Frequently asked questions

Questions about the Ideal Gas practice set

How should I mark a solution?

Credit the state table, absolute conversions, fixed variables, symbolic relation, substitution, unit and physical direction check.

Why must amount be checked?

The combined gas law cancels n only when the same fixed gas sample is compared.

Can I use litres in ratio problems?

Yes when the same volume unit cancels; convert to cubic metres when using SI R in PV=nRT.

What is the best graph for Boyle’s law?

P against 1/V should be linear for a fixed ideal gas at constant temperature.

What score shows readiness?

Aim for at least 80% on a fresh mixed set with no repeated scale, boundary or fixed-variable error.

Where can I get NEB Ideal Gas help?

For current online or physical tuition options, call 9846662070 and confirm timetable, class mode, teacher availability and fees.

References and next steps

Sources and related study guides

Continue with Reflection at Curved Mirrors as Geometrical Optics begins. Curriculum scope and sources were checked on 2 August 2026; follow current CDC, NEB and college instructions if requirements change.

Level 6

Multi-step and model-limit problems

21. Density change

For fixed molar mass at constant pressure, ρ=PM/(RT), so warming from 300 K to 360 K changes density by 300/360=5/6.

22. Mixed sample

If two ideal gases share the same container and temperature, total pressure is associated with total molecule number in PV=NkT. State that chemical reaction and non-ideal interaction are excluded.

23. Model boundary

A gas is compressed toward liquefaction. PV=nRT may no longer match closely because molecular size and attraction matter; do not extrapolate the ideal curve without qualification.

Extended practice

Seven more worked Ideal Gas problems

24. Two connected vessels

A 2.0 L gas sample at 300 kPa expands isothermally into a total rigid volume of 5.0 L. With fixed amount and temperature, P₂=300×2/5=120 kPa.

25. Molar mass from density

An ideal gas has density 1.20 kg m⁻³ at 100 kPa and 300 K. M=ρRT/P=1.20×8.31×300/100000≈0.0299 kg mol⁻¹.

26. Molecule count from state

For P=2.0×10⁵ Pa, V=1.0×10⁻³ m³ and T=300 K, N=PV/(k_BT)≈4.83×10²².

27. rms-speed ratio

For the same gas at 200 K and 800 K, v_rms,2/v_rms,1=√(800/200)=2.

28. Different molecular masses

At equal temperature, a molecule four times heavier has half the rms speed because v_rms∝1/√m.

29. Gradient of a linearised graph

A P versus 1/V graph for fixed n,T has gradient nRT. If T doubles without changing n, the gradient doubles.

30. Identify non-ideal risk

Near liquefaction at high density, molecular attractions and finite size matter. State that PV=nRT is an approximation rather than forcing an exact answer.

Marking grid

A complete numerical answer earns evidence for state boundary, absolute-unit conversions, fixed-variable choice, symbolic relation, substitution, units and physical direction. A correct number reached with Celsius ratios or a leaking fixed-n assumption should not be treated as complete understanding.

Run two timed rounds: questions 1–15 in 25 minutes, then 16–30 in 35 minutes after a one-day delay. Redo only the first decision that failed before repeating full arithmetic.

Reasoning extension

Five conceptual explanations to write in full

Why can rapid compression produce a higher pressure than an isothermal Boyle-law prediction?
Why do equal-temperature gases have equal average translational kinetic energy but different rms speeds?
Why is absolute pressure required even when a gauge reading is convenient?
Why does a P-versus-1/V graph help test Boyle’s law?
Why can a real gas near condensation depart from PV=nRT?

Answer frame: rapid compression can raise gas temperature before energy transfers to surroundings; molecular kinetic energy is proportional to absolute temperature while speed also depends on molecular mass; gauge zero is atmospheric pressure rather than physical zero; reciprocal volume linearises the inverse relation; and finite molecular volume plus attractions matter at high density and near phase change.

Create two additional questions by changing an assumption rather than a number. Make one sample leak and make another process non-isothermal. Write which cancellation in the combined law becomes invalid and what extra information would be needed. This is stronger practice than repeating the same substitution with new digits. End the session by ranking your three least certain questions and explaining the first model choice aloud before looking at any worked solution.

Final score: count a problem complete only when the state boundary, absolute variables, fixed conditions, equation, unit and molecular or limiting-case check all agree physically and mathematically.

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