Ideal gases and kinetic theoryEdexcel A-Level Physics: Subtopic test

1. 1
   A rigid steel cylinder of volume 0.020 m³ contains 4.8 × 10²⁴ atoms of helium at a temperature of 300 K. The helium behaves as an ideal gas.

   (a)

   Which statement is an assumption of the kinetic model of an ideal gas?

   [1 mark]

   • AMolecules attract one another with weak forces between collisions
   • BCollisions between molecules, and with the walls, are perfectly elastic
   • CThe volume of the molecules is a significant fraction of the volume of the container
   • DAll of the molecules travel at the same speed

   (b)

   Calculate the pressure of the helium in the cylinder.

   [1 mark]

   • A4.0 × 10² Pa
   • B3.3 × 10⁵ Pa
   • C1.5 × 10⁶ Pa
   • D9.9 × 10⁵ Pa

   (c)

   The cylinder is heated until the temperature of the helium is 600 K. Explain, using the kinetic model, why the pressure of the gas increases.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A laboratory at 27 °C contains argon and helium, each behaving as an ideal gas. An argon atom has mass 6.63 × 10⁻²⁶ kg and a helium atom has mass 6.6 × 10⁻²⁷ kg.

   (a)

   Calculate the mean kinetic energy of an argon atom in the laboratory.

   [1 mark]

   • A5.6 × 10⁻²² J
   • B4.1 × 10⁻²¹ J
   • C6.2 × 10⁻²¹ J
   • D1.2 × 10⁻²⁰ J

   (b)

   Calculate the root mean square speed of the argon atoms.

   [1 mark]

   • A433 m s⁻¹
   • B353 m s⁻¹
   • C1.9 × 10⁵ m s⁻¹
   • D216 m s⁻¹

   (c)

   Compare the mean kinetic energy and the root mean square speed of the helium atoms with those of the argon atoms in the laboratory.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A student investigates how the volume of a fixed mass of air varies with its pressure. The air is trapped above oil in a uniform vertical glass tube that is sealed at the top and has cross-sectional area 1.5 × 10⁻⁴ m². A foot pump raises the pressure on the oil, which is read from a Bourdon gauge, and the length of the trapped air column is read from a scale. The laboratory temperature is 293 K. At a pressure of 1.00 × 10⁵ Pa the air column is 12.0 cm long, and at 2.00 × 10⁵ Pa it is 6.0 cm long.

   (a)

   Describe how the student could use a full set of readings of pressure $p$ and column length $l$ to show that $p$ is inversely proportional to the volume $V$ of the air.

   [3 marks]

   (b)

   (i) Calculate the number of air molecules in the tube. (ii) State, with a reason, the number of molecules in the tube when the pressure is 2.00 × 10⁵ Pa.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A sealed cubic box of side $l$ contains $N$ molecules of an ideal gas, each of mass $m$, moving randomly at thermodynamic temperature $T$. All collisions between molecules and with the walls are perfectly elastic.

   (a)

   Derive the equation $pV = \frac{1}{3}Nm\langle c^2\rangle$ for the pressure exerted by the gas.

   [6 marks]

   (b)

   Use $pV = \frac{1}{3}Nm\langle c^2\rangle$ and $pV = NkT$ to show that the mean kinetic energy of a molecule is $\frac{3}{2}kT$. Hence calculate the temperature at which the root mean square speed of hydrogen molecules (mass 3.35 × 10⁻²⁷ kg) would equal the escape speed from the Earth, 1.12 × 10⁴ m s⁻¹.

   [6 marks]

   Total for question 4: 12 marks

End of questions