Ideal gasesAQA A-Level Physics: Subtopic test

1. 1
   A rigid sealed cylinder of volume 2.0 × 10⁻² m³ contains 0.80 mol of an ideal gas at a temperature of 300 K (27 °C). The molar gas constant is 8.31 J mol⁻¹ K⁻¹ and the Avogadro constant is 6.02 × 10²³ mol⁻¹.

   (a)

   What is the pressure of the gas?

   [1 mark]

   • A1.0 × 10² Pa
   • B2.0 × 10⁵ Pa
   • C5.0 × 10⁴ Pa
   • D1.0 × 10⁵ Pa

   (b)

   The cylinder is heated to 327 °C. The volume of the cylinder is unchanged. How does the pressure of the gas change?

   [1 mark]

   • AIt increases by a factor of 12
   • BIt doubles
   • CIt is unchanged
   • DIt halves

   (c)

   Calculate the number of molecules of gas in the cylinder.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A student investigates a fixed mass of dry air trapped in a glass tube by a short thread of oil. In the first experiment the pressure on the air is varied using a pump while the temperature is kept constant. In the second experiment the tube is heated in a water bath at atmospheric pressure.

   (a)

   In the first experiment, which graph of the results would be a straight line through the origin if Boyle's law is obeyed?

   [1 mark]

   • APressure against 1/volume
   • BPressure against volume
   • CPressure × volume against pressure
   • DVolume against pressure

   (b)

   In the second experiment, the volume of the air is plotted against temperature in °C and the straight line is extrapolated to zero volume. At what temperature does the line cross the temperature axis?

   [1 mark]

   • A0 °C
   • B100 °C
   • C−273 °C
   • D+273 °C

   (c)

   In the first experiment, the student waits for a short time after changing the pressure before each reading of the volume. Explain why.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A gas is trapped in a cylinder by a frictionless piston and kept at a constant pressure of 1.0 × 10⁵ Pa. Its initial volume is 2.0 × 10⁻³ m³ at a temperature of 290 K. The gas is heated slowly until its volume is 5.0 × 10⁻³ m³. Treat the gas as ideal, with $R$ = 8.31 J mol⁻¹ K⁻¹.

   (a)

   Calculate the work done by the gas as it expands.

   [3 marks]

   (b)

   Calculate the number of moles of gas in the cylinder and the final temperature of the gas.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A school technician uses a cylinder of helium of volume 0.0100 m³ at a pressure of 1.50 × 10⁷ Pa and a temperature of 290 K. Helium has a molar mass of 4.00 g mol⁻¹. Treat helium as an ideal gas with $R$ = 8.31 J mol⁻¹ K⁻¹ and $N_A$ = 6.02 × 10²³ mol⁻¹. In part (a) the technician calculates properties of the gas in the cylinder. In part (b) students use air to investigate Charles's law.

   (a)

   Calculate the number of moles of helium in the cylinder, the mass of helium in the cylinder, and the number of helium atoms in the cylinder.

   [6 marks]

   (b)

   Describe how the students could use air to investigate Charles's law, and explain how their results lead to a value for absolute zero.

   [6 marks]

   Total for question 4: 12 marks

End of questions