• Physics 9702 Doubts | Help Page 236

Question 1103: [Ideal gas]

An ideal gas occupies a container of volume 4.5 × 10³ cm³ at a pressure of 2.5 × 10⁵ Pa and a temperature of 290 K.

(a) Show that the number of atoms of gas in the container is 2.8 × 10²³.

(b) Atoms of a real gas each have a diameter of 1.2 × 10^–10 m.

(i) Estimate the volume occupied by 2.8 × 10²³ atoms of this gas.

(ii) By reference to your answer in (i), suggest whether the real gas does approximate to an ideal gas.

Reference: Past Exam Paper – November 2009 Paper 41 Q2

Solution 1103:

(a)

EITHER pV = NkT                OR pV = nRT and n = N / N_A

clear correct substitution e.g.

{4.5 × 10³ cm³ = 4.5 × 10³ × 10^-6 m³}

(2.5 × 10⁵) × (4.5 × 10³ × 10^-6) = N × (1.38 × 10^-23) × 290

N = 2.8 × 10²³

(b)

(i)

{The atoms of a real gas are assumed to be spherical. Volume of a sphere of radius r = (4/3) πr³. For an estimate, (4/3) π can be neglected as it is a constant not depending on the atom. Else, the complete formula can also be used. We need to find the volume of N atoms, as calculated previously.}

Volume = (1.2 × 10^-10)³ × 2.8 × 10²³               OR (4/3) πr³ × 2.8 × 10²³

Volume = 4.8 × 10^-7 m³                                   2.53 × 10^-7 m³ 

(ii)

EITHER {volume of container} 4.5 × 10³ cm³ >> {volume of atoms of real gas} 0.48 cm³                        OR ratio of volumes is about 10^-4

It is justified because the volume of molecules is negligible

{We need to make a comparison between the volume occupied by the atoms and the volume of the containing vessel.}

Question 1104: [Kinematics > Projectile motion]

A projectile is fired at an angle α to the horizontal at a speed u, as shown.

What are the vertical and horizontal components of its velocity after a time t ?

Assume that air resistance is negligible. The acceleration of free fall is g.

vertical component                  horizontal component

A         u sin α                                      u cos α

B         u sin α – gt                              u cos α – gt

C         u sin α – gt                              u cos α

D         u cos α                                     u sin α – gt

Reference: Past Exam Paper – June 2003 Paper 1 Q7 & November 2006 Paper 1 Q9

Solution 1104:

Answer: C.

From trigonometry,

Horizontal component = u cosα

Vertical component = u sinα

u is a velocity while g is an acceleration. Quantities need to be of the same dimension (units). Here, we need the units of velocity.

The force of gravity acts vertically downwards (towards the surface). It does not affect the horizontal component of velocity.

The acceleration of free fall opposes the vertical component of motion which is upwards. At a time t, the vertical component of velocity: u sinα – gt

Question 1105: [Waves > Stationary waves]

The diagram represents the pattern of stationary waves formed by the superposition of sound waves from a loudspeaker and their reflection from a metal sheet (not shown).

W, X, Y and Z are four points on the line through the centre of these waves.

Which statement about these stationary waves is correct?

A An antinode is formed at the surface of the metal sheet.

B A node is a quarter of a wavelength from an adjacent antinode.

C The oscillations at X are in phase with those at Y.

D The stationary waves oscillate at right angles to the line WZ.

Reference: Past Exam Paper – June 2009 Paper 1 Q24

Solution 1105:

Answer: B.

A nodes is a point with zero displacement and an antinode is a point with maximum displacement.

At the surface of the metal sheet, a node is formed. [A is incorrect]

The distance between 2 successive nodes is half the wavelength and there is an antinode at the middle of 2 successive nodes. Thus, a node is a quarter of a wavelength from an adjacent antinode. [B is correct]

For a stationary wave, the points in a loop are in phase with other and the points in adjacent loops are out of phase. [C is incorrect]

The stationary waves formed does not oscillate. [D is incorrect]