A molecule of an ideal gas has mass m and is contained in a cubic box of side length L. The molecule is moving with velocity u towards the face of the box that is shaded in Fig. 3.1. The molecule collides elastically with the shaded face and the face opposite to it alternately. Deduce expressions, in terms of m, u and L, for: [Figure 3.1]

1. (a)(i)State what is meant by an elastic collision.[1]
2. (a)(ii)State two other assumptions of the kinetic theory of gases.[2]
3. (b)(i)the magnitude of the change in momentum of the molecule on colliding with a face[1]
4. (b)(ii)the time between consecutive collisions of the molecule with the shaded face[1]
5. (b)(iii)the average force exerted by the molecule on the shaded face[1]
6. (b)(iv)the pressure on the shaded face if the force in (iii) is exerted over the whole area of the face.[1]
7. (c)When the model described in (b) is extended to three dimensions, and to a gas containing N molecules, each of mass m, travelling with mean-square speed (<c²>), it can be shown that pV = ⅓ Nm<c²> where p is the pressure exerted by the gas and V is the volume of the gas. Use this expression, together with the equation of state of an ideal gas, to show that the average translational kinetic energy EK of a molecule of an ideal gas is given by EK = 3/2 kT where T is the thermodynamic temperature of the gas and k is the Boltzmann constant.[2]
8. (d)The mass of a hydrogen molecule is 3.34 × 10-27 kg. Use the expression for EK in (c) to determine the root-mean-square (r.m.s.) speed of a molecule of hydrogen gas at 25°C.[2]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.