Topic questions Particle model of matter Kinetic theory of gases
10 questions · 82 marks · about 2 hours
Plot the missing data point on the graph above and draw a line of best fit.
Describe the relationship suggested by the graph and suggest an explanation.
A flute is a musical instrument made from a long tube that is open at both ends.
A stationary sound wave in the tube produces a musical note.
The lowest frequency note that a standard flute produces in air is 262 Hz.
The speed of sound in air at a temperature of 20 °C is 340 m s–1.
Show that a standard flute has an approximate length of 0.65 m.
In an ideal gas, the speed v of sound is given by
where
is a dimensionless constant that depends on the gas
R is the molar gas constant
T is the absolute temperature
M is the molar mass of the gas.
The table below shows values of 
and M for both air and helium.
| Gas |  | M / g mol–1 |
| Air | 1.40 | 29.0 |
| Helium | 1.67 | 4.00 |
The kinetic model of an ideal gas assumes that there are a large number of particles in rapid, random motion.
State two further assumptions for the kinetic model of an ideal gas.
A standard flute is placed inside a sealed chamber.
The chamber is filled with helium at a temperature of –10 °C.
Calculate the lowest frequency that the flute could produce inside the chamber.
The Hipparcos space telescope used stellar parallax with a precision of 9.7 × 10–4 arcseconds to determine the distance to stars.
One of the stars studied was Polaris A. Data about this star is in the table below.
| Parallax angle | 7.5 × 10–3 arcseconds |
| Radius | 2.1 × 1010 m |
| Mass | 1.1 × 1031 kg |
| Surface temperature | 6000 K |
| Temperature of the atmosphere of the star | 4.0 × 106 K |
Estimate the maximum stellar distance in parsecs that could be measured using Hipparcos.
Calculate the percentage uncertainty in the calculated value of the distance to Polaris A.
A continuous stream of particles called a solar wind flows from the surface of the star into the surrounding space.
These particles include helium nuclei of mass 6.6 × 10–27 kg.
Assume that the atmosphere is modelled as an ideal gas.
Show that the typical kinetic energy of a helium nucleus in the atmosphere is about 10–16 J.
The gravitational potential energy of a helium nucleus in the outer layer of the star is –2.3 × 10–16 J.
Calculate the gravitational potential energy U at the maximum distance from the star that a helium nucleus could reach.
Calculate the distance from the centre of the star reached by this helium nucleus.
Explain why the star has a solar wind that reaches a much greater distance from the star than found in (iii).
The kinetic theory of matter is a model used to describe the behaviour of particles (atoms or molecules) in an ideal gas. There are a number of assumptions made in the kinetic model for an ideal gas.
Which one of the following assumptions is not correct?
A The collisions of particles with each other and the container walls are perfectly inelastic.
B The electrostatic forces between particles are negligible except during collisions.
C The particles occupy negligible volume compared to the volume of the gas.
D There are a large number of particles in random motion.
Your answer
A kiln used to harden ceramics is shown below.
The internal chamber is a cube. Each side of this cube has length 0.46 m. The chamber is sealed and full of argon. Argon behaves as an ideal gas.
The kiln is initially at 20 
C. The argon in the kiln has an initial pressure of 100 kPa.
Calculate the amount of argon n in the chamber in moles.
The temperature of the kiln is increased from 20 
C to 1300 C.
Calculate the pressure in kPa at 1300 
C.
The temperature of the kiln is 1300 
C. A single atom of argon is travelling horizontally towards the vertical side X of the chamber. The initial speed of this atom is 990 m s–1. After collision, it rebounds at the same speed.
Calculate the change in momentum 
p of this atom.
• mass of argon atom = 6.6 × 10–26 kg
=........ kg m s–1 
p
Assume that this atom does not collide with any other argon atoms inside the chamber. Instead, it travels horizontally, making repeated collisions with the opposite vertical walls of the chamber.
1 Show that the atom makes about 1000 collisions with side X in a time interval of 1.0 s.
2 Calculate the average force F on side X made by the atom.
Without calculation, explain how your answer to (ii)2 could be used to estimate the total pressure exerted by the atoms of the argon gas in the kiln.
This question is about the Sun and its radiation.
Use the data below to show that the luminosity of the Sun is about 4 × 1026 W. (a) (i)
• radius of Sun = 7.0 × 108 m
• surface temperature of Sun = 5800 K
Sirius, the brightest star in the night sky, has a luminosity 25 times greater than that of the Sun. It has diameter 1.7 times greater than that of the Sun.
Calculate the surface temperature T of Sirius.
Also involves Efficiency
Both the ISS and the astronauts inside it are in free fall.
Explain why this makes the astronauts feel weightless.
Calculate the value of the gravitational field strength g at the height of the ISS above the Earth.
=........ N kg–1 g
Use the information in (b)(ii) and the data below to show that the root mean square (r.m.s.) speed of the air molecules inside the ISS is approximately 15 times smaller than the orbital speed of the ISS.
• molar mass of air = 2.9 × 10–2 kg mol–1
• temperature of air inside the ISS = 20 °C
The ISS has arrays of solar cells on its wings. These solar cells charge batteries which power the ISS. The wings always face the Sun.
Use the data below and your answer to (b)(ii) to calculate the average power delivered to the batteries.
• The total area of the cells facing the solar radiation is 2500 m2.
• 7% of the energy of the sunlight incident on the cells is stored in the batteries.
• The intensity of solar radiation at the orbit of the ISS is 1.4 kW m–2 outside of the Earth’s shadow and zero inside it.
• The ISS passes through the Earth’s shadow for 35 minutes during each orbit.
Use the kinetic theory of matter to describe the solid phase (section AB) and the liquid phase (section CD) in terms of the motion and arrangement of the molecules of the substance.
Use Fig. 21 to explain how the specific heat capacity of the liquid compares with the specific heat capacity of the solid.
State what is meant by the internal energy of the substance.
Beyond the point E in Fig. 21, the substance behaves as an ideal gas.
The mass of a gas molecule is 4.8 × 10–26 kg. (i) Calculate the root mean square speed of the gas molecules at a temperature of 250 °C.
root mean square speed =........ m s–1
Calculate the internal energy of 1.3 moles of the gas at 250 °C.
A container has an ideal gas. The mean square speed of the gas molecules in the container is 3.0 × 105 m2 s−2.
Over a period of time, a third of the gas molecules escape from the container. The pressure and volume of the gas in the container remain the same.
What is the mean square speed of the molecules left in the container?
1.0 × 105 m2 s−2 A
2.0 × 105 m2 s−2 B
4.5 × 105 m2 s−2 C
9.0 × 105 m2 s−2 D
Your answer
Write an expression for the gravitational potential Vg at the surface of a planet of mass M and radius r.
The table below shows some data for Mercury and Pluto.
| Mass / kg | Radius / m | Mean distance from Sun / m | |
| Mercury | 3.30 × 1023 | 2.44 × 106 | 57.9 × 109 |
| Pluto | 0.131 × 1023 | 1.19 × 106 | 5910 × 109 |
Show that the escape velocity v of a gas molecule on the surface of Pluto is given by the equation
where M is the mass of Pluto and r is its radius.
Calculate the escape velocity v of gas molecules on the surface of Pluto.
=........ m s−1 v
Explain why Mercury has no atmosphere whilst Pluto still has a thin atmosphere. Use data from the table to support your explanation.
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