A-LevelPhysicsIdeal gases9702/42 · Feb/Mar 2020 · Q210 Marks
A large container of volume 85m³ is filled with 110kg of an ideal gas. The pressure of the gas is 1.0 × 10⁵ Pa at temperature T. The mass of 1.0 mol of the gas is 32 g.
- (a)Show that the temperature T of the gas is approximately 300K.[3]
- (b)The temperature of the gas is increased to 350K at constant volume. The specific heat capacity of the gas for this change is 0.66 Jkg⁻¹K⁻¹. Calculate the energy supplied to the gas by heating. energy = ................................................................ J [2][2]
- (c)Explain how movement of the gas molecules causes pressure in the container.[3]
- (d)The temperature of a gas depends on the root-mean-square (r.m.s.) speed of its molecules. Calculate the ratio: r.m.s. speed of gas molecules at 350 K r.m.s. speed of gas molecules at 300 K ratio = ........................................................................ [2][2]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2020). The mark or mark type is shown in brackets.
- [1] n = 110/0.032 or 110000/32 or 3440
- [1] pV = nRT
- [1] T = (1.0 × 10⁵ × 85) / (8.31 × (110 / 0.032)) = 300 K
- [1] E = mcΔθ
- [1] = 110 x 0.66 × 50 = 3600 J
- [1] molecule collides with wall
- [1] momentum of molecule changes during collision (with wall)
- [1] force on molecule so force on wall
- [1] many forces act over surface area of container exerting a pressure
- [1] KE ∝ T
- [1] v ∝ √T
- [1] ratio = √(350/300) = 1.1
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