# Physics 9702 Doubts | Help Page 236

__Question 1103: [Ideal gas]__
An ideal gas occupies a container of
volume 4.5 × 10

^{3}cm^{3}at a pressure of 2.5 × 10^{5}Pa and a temperature of 290 K.**(a)**Show that the number of atoms of gas in the container is 2.8 × 10

^{23}.

**(b)**Atoms of a real gas each have a diameter of 1.2 × 10

^{–10}m.

(i) Estimate the volume occupied by
2.8 × 10

^{23}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 × 10

^{3}cm^{3}= 4.5 × 10^{3}× 10^{-6 }m^{3}}
(2.5 × 10

^{5}) × (4.5 × 10^{3}× 10^{-6}) = N × (1.38 × 10^{-23}) × 290
N = 2.8 × 10

^{23}**(b)**

(i)

{The atoms of a real gas
are assumed to be spherical. Volume of a sphere of radius r = (4/3) πr

^{3}. 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 × 10^{23}OR (4/3) πr^{3}× 2.8 × 10^{23}
Volume = 4.8 × 10

^{-7}m^{3}2.53 × 10^{-7}m^{3}
(ii)

EITHER {volume
of container} 4.5 × 10

^{3}cm^{3}>> {volume of atoms of real gas} 0.48 cm^{3}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]