Molecular kinetic theory modelAQA A-Level Physics: Subtopic test

1. 1
   A student places smoke particles in a small glass cell filled with air and observes them through a microscope, lit from the side. Each smoke particle is seen as a tiny bright speck that moves along an irregular, zigzag path.

   (a)

   Which statement best explains the motion of a smoke particle?

   [1 mark]

   • AThe smoke particles are alive and move on their own
   • BConvection currents in the air carry the particle in circles
   • CThe particle is hit unevenly by fast-moving, randomly moving air molecules
   • DThe particle is attracted by the light source

   (b)

   The air in the cell is warmed. What change would the student observe in the motion of the smoke particles?

   [1 mark]

   • AThe particles move less vigorously
   • BThe particles move more vigorously
   • CThe particles stop moving
   • DThe particles move in regular circular paths

   (c)

   Explain how this observation provides evidence for the existence of atoms and molecules.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A fixed mass of air is sealed inside a syringe. The temperature of the air can be kept constant, and the syringe can also be heated while its plunger is held fixed in position.

   (a)

   The plunger is pushed in to halve the volume of the air at constant temperature. Which statement explains why the pressure doubles?

   [1 mark]

   • AThe molecules move twice as fast
   • BThe molecules become smaller
   • CEach molecule hits the walls with twice the force
   • DThe molecules hit the walls twice as often, with the same average force per collision

   (b)

   With the plunger fixed, the syringe is heated and the pressure of the air increases. Which explanation is correct?

   [1 mark]

   • AThe molecules move faster, so they hit the walls harder and more often
   • BThe molecules expand and take up more of the volume
   • CThere are more molecules in the syringe
   • DThe molecules attract each other more strongly

   (c)

   The experiments on the syringe lead to the gas laws. Explain the difference between the gas laws and the kinetic theory model of a gas.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   An ideal gas is modelled as $N$ identical molecules, each of mass $m$, moving randomly in a cubic container of side $L$ and volume $V$. Collisions with the walls are perfectly elastic. In part (b), the container holds 2.0 × 10²² molecules of nitrogen, each of mass 4.65 × 10⁻²⁶ kg, in a volume of 1.0 × 10⁻³ m³ at a pressure of 1.00 × 10⁵ Pa.

   (a)

   A molecule of velocity component $c_x$ in the $x$ direction collides with the wall perpendicular to $x$ and rebounds along the same line. Show that the average force exerted on this wall by this molecule is $mc_x^2/L$.

   [3 marks]

   (b)

   Calculate the root mean square speed of the nitrogen molecules.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Helium (atomic mass 6.64 × 10⁻²⁷ kg per atom) is held in a sealed vessel at a temperature of 300 K and may be treated as an ideal gas. In part (b), a physics department is preparing a talk on how scientists' understanding of gases has developed.

   (a)

   Calculate the mean kinetic energy of a helium atom in the vessel, the root mean square speed of the atoms, and the internal energy of 1.00 mol of the helium.

   [6 marks]

   (b)

   Discuss how the study of Brownian motion and the kinetic theory changed scientists' understanding of gases and of matter.

   [6 marks]

   Total for question 4: 12 marks

End of questions