Ideal gases: A Level Physics questions with answers
Free Ideal gases questions for A Level Physics (9702), part of Thermal & modern physics. Each question has the answer and the marking points an examiner would look for.
A container of volume 5.0 × 10−3 m3 holds an ideal gas at a pressure of 1.5 × 105 Pa and a temperature of 310 K.
(a)
Calculate the number of molecules of gas.
[2]
(b)
Calculate the mean translational kinetic energy of a molecule.
[2]
(c)
Half of the gas leaks out at constant temperature. State and explain the change in pressure using the kinetic theory.
[3]
(d)
The temperature of the remaining gas is raised to 620 K. Calculate the ratio of the new r.m.s. speed to the original.
[1]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
1.75 × 1023
pV = NkT C1 1.75 × 1023A1
2
(b)
6.42 × 10−21 J
3/2 kT C1 6.42 × 10−21A1
2
(c)
pressure halves: half as many molecules so half the rate of collisions with walls; mean speed unchanged
pressure halves B1 fewer collisions per unit time B1 same mean speed (constant T) B1
3
(d)
√2 = 1.41
1.41 B1
1
Question 2Structured · 7 marksA* challenge
The kinetic theory of gases gives pV = ⅓Nm<c2>.
(a)
State three assumptions of the kinetic theory of gases.
[3]
(b)
Explain how the molecules exert a pressure on the walls of the container.
[2]
(c)
Use pV = ⅓Nm<c2> and pV = NkT to show that the mean kinetic energy of a molecule is 3/2 kT.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
negligible volume; elastic collisions; no forces; random
Any 3 of: any three of: molecules have negligible volume compared with the container; collisions are elastic; no intermolecular forces except during collisions; random motion; time of collision negligible B3
3
(b)
momentum change gives force
molecules collide with the walls and their momentum changes B1 force = rate of change of momentum, and pressure = force per unit area B1
2
(c)
shown
⅓Nm<c2> = NkT M1 ½m<c2> = 3/2 kT A1
2
Question 3Structured · 8 marks
An ideal gas at 1.0 × 105 Pa and 300 K occupies 3.0 × 10−3 m3. It is compressed to 1.2 × 10−3 m3, when its pressure is 2.5 × 105 Pa.
(a)
Define an ideal gas.
[1]
(b)
Calculate the final temperature of the gas.
[2]
(c)
Calculate the increase in the total translational kinetic energy of the molecules.
[3]
(d)
Explain, using the first law of thermodynamics, how the internal energy can increase during a rapid compression.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
obeys pV = nRT at all T, p, V
a gas that obeys pV ∝ T (pV = nRT) for all values of pressure, volume and temperature B1
1
(b)
300 K
p₁V₁/T₁ = p₂V₂/T₂ C1 300 K A1
2
(c)
0 J
n = pV/RT = 0.12 mol C1 ΔU = 32nRΔT C1 0 J A1
3
(d)
work done on gas; little heat lost in short time, so ΔU positive
work is done on the gas (W positive) B1 in a rapid compression there is little time for thermal energy to escape (q ≈ 0), so ΔU increases B1
2
Question 4Structured · 10 marks
A cylinder contains 2.0 × 10−3 m3 of an ideal gas at a pressure of 1.5 × 105 Pa and a temperature of 300 K.
(a)
State two assumptions of the kinetic theory of gases.
[2]
(b)
Calculate the number of moles of gas.
[2]
(c)
Use your answer to (b) to calculate the number of molecules.
[1]
(d)
Calculate the mean translational kinetic energy of a molecule.
[2]
(e)
The molar mass of the gas is 0.004 kg mol−1. Calculate the root-mean-square speed of the molecules.
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
negligible molecular volume; no intermolecular forces except in collisions; elastic collisions; random motion
Any 2 of: any two: volume of molecules negligible compared with the gas volume; no forces between molecules except during collisions; collisions are elastic; time of collision negligible; random motion B2
2
(b)
0.12 mol
pV = nRT C1 n = 0.12 mol A1
2
(c)
7.24 × 1022
N = nNA = 7.24 × 1022B1
1
(d)
6.21 × 10−21 J
E = 32kT C1 6.21 × 10−21 J A1
2
(e)
1370 m s−1
½m⟨c2⟩ = 32kT with m = M/NAC1 ⟨c2⟩ = 3RT/M C1 crms = 1370 m s−1A1
3
Question 5Structured · 2 marks
An ideal gas at a pressure of 131 kPa occupies 7.9 × 10−3 m3 at 334 K. Calculate the amount of gas in moles.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
0.373 mol
pV = nRT C1 0.373 A1
2
Question 6Structured · 6 marks
A container of volume 2.0 × 10−3 m3 holds an ideal gas at 1.0 × 105 Pa and 300 K.
(a)
Calculate the number of molecules.
[2]
(b)
Calculate the mean translational kinetic energy of a molecule.
[2]
(c)
State two assumptions of the kinetic theory of gases.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
4.83 × 1022
n = pV/RT C1 × NA = 4.83 × 1022A1
2
(b)
6.21 × 10−21 J
(3/2)kT C1 6.21 × 10−21 J A1
2
(c)
elastic collisions; negligible volume; no intermolecular forces
Any 2 of: any two: collisions elastic; molecules of negligible volume; no intermolecular forces except during collisions; random motion; time of collision negligible B2
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Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in