Topic questions Particle model of matter Kinetic theory of gases
12 questions · 131 marks · about 2.5 hours
Also involves Newton's laws of motion · Momentum
*14
Air molecules are trapped in a container by a piston, as shown.
The position of the piston is adjusted so that the volume available to the air molecules is reduced. The temperature of the air stays constant.
Explain how the pressure exerted by the air changes. You should refer to the motion of the air molecules.
*6 Air at room temperature was sealed in a closed container. The container was placed in an ice bath and the temperature of the air decreased. The volume of the container remained constant.
Explain what happened to the pressure exerted by the air. In your response you should refer to the momentum of the air molecules.
A hot air balloon consists of a fabric envelope, heaters and a basket, as shown.
When the balloon is set up, the envelope is partly filled with air at 20°C. The air is then heated to 120°C and expands to fill the envelope and becomes less dense.
The air pressure inside the envelope is always equal to the air pressure outside the envelope because the envelope is open at the bottom.
The balloon takes off when the upthrust is more than the total weight of the balloon, the air in the envelope and the passengers.
Deduce whether the balloon can take off.
volume of air at 120°C in inflated envelope = 2800 m3 density of air at 20°C = 1.2 kg m–3 mass of balloon = 380 kg mass of passengers = 340 kg upthrust when the envelope is full = 33 000 N
State one assumption of the kinetic theory of gases.
Derive an equation to show that, for a gas at temperature T, the mean kinetic energy of the molecules = 
kT
Calculate the root-mean-square speed of nitrogen molecules at a temperature of 120°C.
mass of nitrogen molecule = 28 u
The fuel used in a camping stove is butane, which is stored in a canister as shown.
Some of the butane in the canister is in a liquid state, and some is a gas.
When the stove uses the butane gas, some of the liquid butane evaporates.
Explain why the temperature of the canister decreases when the stove is used.
The pressure inside the canister is 220 kPa and the temperature of the gas is 21
C.
The canister is in the shape of a cylinder of length 0.23 m and radius 0.11 m.
Calculate the number of molecules of butane gas in the canister.
Assume the volume of liquid butane inside the canister is negligible.
Calculate the r.m.s. speed of the molecules of butane gas.
mass of butane molecule = 9.6×10–26kg
Air is trapped in a glass tube. When the air is forced into a smaller volume at a constant temperature, the pressure increases.
Which of the following statements about air molecules is a reason why the pressure the trapped air exerts on the tube increases?
Also involves Particle motion and pressure in gases
The photographs show a wooden pop gun before and after the cork is popped.
The diagram shows a cross-section through the pop gun.
Initially the piston is at the right-hand end of the cylinder, as shown. Then the cork is pushed into the other end of the cylinder.
When the handle is pushed in, the pressure of the air in the cylinder increases. This exerts an additional force on the cork.
Once the additional force is sufficient to overcome the frictional force between the cork and the cylinder, the cork is pushed out.
Show that the pressure of the air in the cylinder must be about 2 
105Pa in order to push the cork out.
maximum frictional force = 8.8 N cross-sectional area of cork = 9.2 
10−5m2 atmospheric pressure = 1.0 
105Pa
Calculate the temperature of the gas in the cylinder at the instant the cork is expelled.
volume of air in the cylinder with the handle pulled out = 1.1 
10−5m3 volume of air in the cylinder at the moment the cork is pushed out = 6.7 
10−6m3 atmospheric pressure = 1.0 
105Pa initial temperature of air = 19 °C
The formulae sheet for this paper includes the equation
Calculate the root mean square speed of the molecules of air in the cylinder before the handle is pushed in.
average mass of molecule of air = 4.8 10−26kg temperature of air = 19 °C
At the Culham Centre for Fusion Energy (CCFE) experiments are carried out to investigate nuclear fusion and the properties of plasmas. A plasma consists of ionised gas, containing positive ions and electrons.
In a fusion experiment at CCFE, ions of two isotopes of hydrogen fuse to produce helium ions and fast-moving neutrons.
Show that a single fusion reaction releases about 3 
10−12J of energy.
mass of12H = 2.013553 u mass of13H = 3.015501 u mass of42He = 4.001506 u mass of01n = 1.008665 u
Fusion occurs naturally in the core of stars.
Explain why very high densities of matter and very high temperatures are needed to bring about and maintain nuclear fusion in stars.
In a plasma experiment 5.0 mg of deuterium, an isotope of hydrogen, occupies a volume of 98 m3. The temperature of deuterium is raised to 1.3 
108K. In this experiment, the deuterium behaves as an ideal gas.
Calculate the pressure due to the deuterium ions.
mass of deuterium ion = 3.3 
10−27kg
Calculate the root mean square speed of the deuterium ions at this temperature.
The temperature of the plasma is monitored using the Doppler effect. Light from a laser is directed into the plasma and the wavelength of the light reflected is measured.
The Doppler shift observed when light is reflected by a deuterium ion is twice the Doppler shift that would be observed for a source of light moving at the same speed as the deuterium ion.
Calculate the maximum wavelength of light that would be detected after reflection from a deuterium ion moving at 1.5 × 106m s−1.
wavelength of laser light = 1064 nm
At the Culham Centre for Fusion Energy (CCFE) experiments are carried out to investigate nuclear fusion and the properties of plasmas. A plasma consists of ionised gas, containing positive ions and electrons.
Fusion occurs naturally in the core of stars.
Explain why very high densities of matter and very high temperatures are needed to bring about and maintain nuclear fusion in stars.
In a plasma experiment 5.0 mg of deuterium, an isotope of hydrogen, occupies a volume of 98 m3. The temperature of deuterium is raised to 1.3 108K. In this experiment, the deuterium behaves as an ideal gas.
Calculate the pressure due to the deuterium ions.
mass of deuterium ion = 3.3 10−27kg
Calculate the root mean square speed of the deuterium ions at this temperature.
The temperature of the plasma is monitored using the Doppler effect. Light from a laser is directed into the plasma and the wavelength of the light reflected is measured.
The Doppler shift observed when light is reflected by a deuterium ion is twice the Doppler shift that would be observed for a source of light moving at the same speed as the deuterium ion.
Calculate the maximum wavelength of light that would be detected after reflection from a deuterium ion moving at 1.5 × 106m s−1.
wavelength of laser light = 1064 nm
A student investigated how the volume of a fixed mass of air varies with the temperature of the air. She used the apparatus shown.
A glass tube was sealed at one end. A plug of oil trapped a length l of air in the tube. The water in the beaker was heated to a temperature 
. The corresponding value of l was measured. This was repeated for a range of temperatures.
The thermometer had a resolution of 0.5 °C. The scale had mm divisions.
The student’s results are shown in the table.
 / °C | l / cm |
| 24 | 8.8 |
| 60 | 9.8 |
| 78.5 | 10.3 |
| 95.5 | 10.9 |
Criticise the student’s results.
Explain two possible sources of error in this investigation.
Describe two improvements that would increase the accuracy of measurements obtained in this investigation.
The student plotted a graph of l against θ as shown.
Explain the significance of the intercept on the x-axis.
The student wrote a report of the investigation in her lab book. In the conclusion she wrote:
“In this investigation uncertainties were minimised by selecting measuring instruments with a high resolution. The points lie on a perfect straight line, indicating that the investigation is accurate.”
Discuss the student’s conclusion.
Also involves Conservation and dissipation of energy
Our understanding of the atom has developed over time, from early models in which atoms were considered to be hard incompressible spheres, through to the nuclear model of the atom and the ladder model in which electrons exist in a discrete number of allowed energy states.
*(a) The model of atoms as hard incompressible spheres, moving rapidly and randomly, can be used to explain why gases exert a pressure.
Explain, using ideas of momentum, why the pressure exerted by a gas increases as the temperature of the gas increases.
The nuclear model of the atom was established following a series of experiments in which alpha particles were directed at thin gold foil.
An alpha particle approaching a gold nucleus,19779Au, head-on will be brought to rest and returned along its original path.
Calculate the minimum distance between the alpha particle and the nucleus for alpha particles of energy of 5.5 MeV.
It is observed that electrons, with energy of 5.5 keV, are diffracted as they pass through the thin gold foil.
Explain a conclusion about the electrons that can be made from this observation.
In the energy ladder model of the atom, electrons exist in a discrete number of allowed energy states. The collision of electrons with gold atoms may lead to the production of high frequency electromagnetic radiation.
Explain how high frequency electromagnetic radiation may be produced when electrons collide with atoms in a metal.
Barnard’s star is a red dwarf star in the vicinity of the Sun. The wavelength of a line in the spectrum of light emitted from Barnard’s star is measured to be 656.0 nm. The same light produced by a source in a laboratory has a wavelength of 656.2 nm.
Calculate the velocity of Barnard’s star relative to the Earth.
A diffraction grating can be used to analyse the radiation emitted by a variety of sources.
A diffraction grating of known grating spacing is used in a school laboratory to analyse the light emitted by a laser.
Describe how the diffraction grating is used and the measurements that should be taken.
A diffraction grating with grating spacing of 2.2 × 10−6 m is used to determine the difference in wavelength for the spectral line emitted by Barnard’s star.
Comment on the suitability of using a diffraction grating with this spacing. You should include appropriate calculations.
Visible light from the star originates from the photosphere. In the photosphere of Barnard’s star, hydrogen and helium atoms are at a temperature of 3100 K.
Calculate the mean kinetic energy of an atom in the photosphere at a temperature of 3100 K.
Describe how these atoms emit visible light.
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