O-LevelPhysicsForces5054/21 · Oct/Nov 2022 · Q38 Marks

A curved, glass tube is open at one end and sealed at the other. A dense liquid is poured into the tube. The liquid traps air in the sealed end. Fig. 3.1 shows the tube, the liquid and the trapped air.

(a)The difference between the liquid levels is h. At room temperature, h is 0.57 m. The density of the liquid is 1.4 × 10⁴kg/m³. The gravitational field strength g is 10N/kg and the atmospheric pressure is 1.0 × 10⁵ Pa. Calculate the pressure of the trapped air.[3]
(b)(i)The height of the trapped air in the tube is x. Explain, in terms of molecules, why x changes when the air is heated.[3]
(b)(ii)The trapped air reaches a constant temperature that is greater than its initial temperature. Describe and explain the change in h in terms of the pressures involved.[2]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

[1] (Dp =) hrg or 0.57 × 1.4 × 10⁴ × 10
[1] 8.0 × 10⁴ or 7.98 × 10⁴ or 1.0 × 10⁵ + (0.57 × 1.4 × 10⁵ × 10)
[1] 1.8 x 10⁵ Pa
[1] (air molecules) speed up
[1] (they) hit the liquid surface harder or hit the liquid surface more often
[1] (increased / extra) force on (surface of liquid) or air pressure increases
[1] (as the liquid moves / as air volume increases) difference between liquid levels / h increases
[1] (eventually) pressures balance / become equal / stay balanced

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