SL Paper 2
The following data are available for a natural gas power station that has a high efficiency.
| Rate of consumption of natural gas | = 14.6 kg s–1 |
| Specific energy of natural gas | = 55.5 MJ kg–1 |
| Efficiency of electrical power generation | = 59.0 % |
| Mass of CO2 generated per kg of natural gas | = 2.75 kg |
| One year | = 3.16 × 107 s |
Calculate, with a suitable unit, the electrical power output of the power station.
Calculate the mass of CO2 generated in a year assuming the power station operates continuously.
Explain, using your answer to (b), why countries are being asked to decrease their dependence on fossil fuels.
Describe, in terms of energy transfers, how thermal energy of the burning gas becomes electrical energy.
The ratio = 1.5.
Show that the intensity of solar radiation at the orbit of Mars is about 600 W m–2.
Determine, in K, the mean surface temperature of Mars. Assume that Mars acts as a black body.
The atmosphere of Mars is composed mainly of carbon dioxide and has a pressure less than 1 % of that on the Earth. Outline why the greenhouse effect is not significant on Mars.
Outline, with reference to energy changes, the operation of a pumped storage hydroelectric system.
The hydroelectric system has four 250 MW generators. The specific energy available from the water is 2.7 kJ kg–1. Determine the maximum time for which the hydroelectric system can maintain full output when a mass of 1.5 x 1010 kg of water passes through the turbines.
Not all the stored energy can be retrieved because of energy losses in the system. Explain one such loss.
At the location of the hydroelectric system, an average intensity of 180 W m–2 arrives at the Earth’s surface from the Sun. Solar photovoltaic (PV) cells convert this solar energy with an efficiency of 22 %. The solar cells are to be arranged in a square array. Determine the length of one side of the array that would be required to replace the
hydroelectric system.
A cell is connected to an ideal voltmeter, a switch S and a resistor R. The resistance of R is 4.0 Ω.
When S is open the reading on the voltmeter is 12 V. When S is closed the voltmeter reads 8.0 V.
Electricity can be generated using renewable resources.
Identify the laws of conservation that are represented by Kirchhoff’s circuit laws.
State the emf of the cell.
Deduce the internal resistance of the cell.
The voltmeter is used in another circuit that contains two secondary cells.
Cell A has an emf of 10 V and an internal resistance of 1.0 Ω. Cell B has an emf of 4.0 V and an internal resistance of 2.0 Ω.
Calculate the reading on the voltmeter.
Outline why electricity is a secondary energy source.
Some fuel sources are renewable. Outline what is meant by renewable.
A fully charged cell of emf 6.0 V delivers a constant current of 5.0 A for a time of 0.25 hour until it is completely discharged.
The cell is then re-charged by a rectangular solar panel of dimensions 0.40 m × 0.15 m at a place where the maximum intensity of sunlight is 380 W m−2.
The overall efficiency of the re-charging process is 18 %.
Calculate the minimum time required to re-charge the cell fully.
Outline why research into solar cell technology is important to society.
Two renewable energy sources are solar and wind.
An alternative generation method is the use of wind turbines.
The following data are available:
Length of turbine blade = 17 m
Density of air = 1.3 kg m–3
Average wind speed = 7.5 m s–1
Describe the difference between photovoltaic cells and solar heating panels.
A solar farm is made up of photovoltaic cells of area 25 000 m2. The average solar intensity falling on the farm is 240 W m–2 and the average power output of the farm is 1.6 MW. Calculate the efficiency of the photovoltaic cells.
Determine the minimum number of turbines needed to generate the same power as the solar farm.
Explain two reasons why the number of turbines required is likely to be greater than your answer to (c)(i).
One possible fission reaction of uranium-235 (U-235) is
Mass of one atom of U-235
Binding energy per nucleon for U-235
Binding energy per nucleon for Xe-140
Binding energy per nucleon for Sr-94
A nuclear power station uses U-235 as fuel. Assume that every fission reaction of U-235 gives rise to of energy.
A sample of waste produced by the reactor contains of strontium-94 (Sr-94). Sr-94 is radioactive and undergoes beta-minus () decay into a daughter nuclide X. The reaction for this decay is
.
The graph shows the variation with time of the mass of Sr-94 remaining in the sample.
State what is meant by binding energy of a nucleus.
Outline why quantities such as atomic mass and nuclear binding energy are often expressed in non-SI units.
Show that the energy released in the reaction is about .
Estimate, in , the specific energy of U-235.
The power station has a useful power output of and an efficiency of . Determine the mass of U-235 that undergoes fission in one day.
Write down the proton number of nuclide X.
State the half-life of Sr-94.
Calculate the mass of Sr-94 remaining in the sample after minutes.
A satellite powered by solar cells directed towards the Sun is in a polar orbit about the Earth.
The satellite is orbiting the Earth at a distance of 6600 km from the centre of the Earth.
The satellite carries an experiment that measures the peak wavelength emitted by different objects. The Sun emits radiation that has a peak wavelength λS of 509 nm. The peak wavelength λE of the radiation emitted by the Earth is 10.1 μm.
Determine the orbital period for the satellite.
Mass of Earth = 6.0 x 1024 kg
Determine the mean temperature of the Earth.
Suggest how the difference between λS and λE helps to account for the greenhouse effect.
Not all scientists agree that global warming is caused by the activities of man.
Outline how scientists try to ensure agreement on a scientific issue.
A planet orbits at a distance d from a star. The power emitted by the star is P. The total surface area of the planet is A.
Explain why the power incident on the planet is
The albedo of the planet is . The equilibrium surface temperature of the planet is T. Derive the expression
where e is the emissivity of the planet.
On average, the Moon is the same distance from the Sun as the Earth. The Moon can be assumed to have an emissivity e = 1 and an albedo = 0.13. The solar constant is 1.36 × 103 W m−2. Calculate the surface temperature of the Moon.
A photovoltaic cell is supplying energy to an external circuit. The photovoltaic cell can be modelled as a practical electrical cell with internal resistance.
The intensity of solar radiation incident on the photovoltaic cell at a particular time is at a maximum for the place where the cell is positioned.
The following data are available for this particular time:
Operating current = 0.90 A
Output potential difference to external circuit = 14.5 V
Output emf of photovoltaic cell = 21.0 V
Area of panel = 350 mm × 450 mm
Explain why the output potential difference to the external circuit and the output emf of the photovoltaic cell are different.
Calculate the internal resistance of the photovoltaic cell for the maximum intensity condition using the model for the cell.
The maximum intensity of sunlight incident on the photovoltaic cell at the place on the Earth’s surface is 680 W m−2.
A measure of the efficiency of a photovoltaic cell is the ratio
Determine the efficiency of this photovoltaic cell when the intensity incident upon it is at a maximum.
State two reasons why future energy demands will be increasingly reliant on sources such as photovoltaic cells.
The radioactive nuclide beryllium-10 (Be-10) undergoes beta minus (β–) decay to form a stable boron (B) nuclide.
The initial number of nuclei in a pure sample of beryllium-10 is N0. The graph shows how the number of remaining beryllium nuclei in the sample varies with time.
An ice sample is moved to a laboratory for analysis. The temperature of the sample is –20 °C.
Identify the missing information for this decay.
On the graph, sketch how the number of boron nuclei in the sample varies with time.
After 4.3 × 106 years,
Show that the half-life of beryllium-10 is 1.4 × 106 years.
Beryllium-10 is used to investigate ice samples from Antarctica. A sample of ice initially contains 7.6 × 1011 atoms of beryllium-10. State the number of remaining beryllium-10 nuclei in the sample after 2.8 × 106 years.
State what is meant by thermal radiation.
Discuss how the frequency of the radiation emitted by a black body can be used to estimate the temperature of the body.
Calculate the peak wavelength in the intensity of the radiation emitted by the ice sample.
Derive the units of intensity in terms of fundamental SI units.
Titan is a moon of Saturn. The Titan-Sun distance is 9.3 times greater than the Earth-Sun distance.
Show that the intensity of the solar radiation at the location of Titan is 16 W m−2
Titan has an atmosphere of nitrogen. The albedo of the atmosphere is 0.22. The surface of Titan may be assumed to be a black body. Explain why the average intensity of solar radiation absorbed by the whole surface of Titan is 3.1 W m−2
Show that the equilibrium surface temperature of Titan is about 90 K.
The orbital radius of Titan around Saturn is and the period of revolution is .
Show that where is the mass of Saturn.
The orbital radius of Titan around Saturn is 1.2 × 109 m and the orbital period is 15.9 days. Estimate the mass of Saturn.
Cold milk enters a small sterilizing unit and flows over an electrical heating element.
The temperature of the milk is raised from 11 °C to 84 °C. A mass of 55 g of milk enters the sterilizing unit every second.
Specific heat capacity of milk = 3.9 kJ kg−1 K−1
The milk flows out through an insulated metal pipe. The pipe is at a temperature of 84 °C. A small section of the insulation has been removed from around the pipe.
Estimate the power input to the heating element. State an appropriate unit for your answer.
Outline whether your answer to (a) is likely to overestimate or underestimate the power input.
Discuss, with reference to the molecules in the liquid, the difference between milk at 11 °C and milk at 84 °C.
State how energy is transferred from the inside of the metal pipe to the outside of the metal pipe.
The missing section of insulation is 0.56 m long and the external radius of the pipe is 0.067 m. The emissivity of the pipe surface is 0.40. Determine the energy lost every second from the pipe surface. Ignore any absorption of radiation by the pipe surface.
Describe one other method by which significant amounts of energy can be transferred from the pipe to the surroundings.
The average temperature of ocean surface water is 289 K. Oceans behave as black bodies.
Show that the intensity radiated by the oceans is about 400 W m-2.
Explain why some of this radiation is returned to the oceans from the atmosphere.
The Moon has no atmosphere and orbits the Earth. The diagram shows the Moon with rays of light from the Sun that are incident at 90° to the axis of rotation of the Moon.
A black body is on the Moon’s surface at point A. Show that the maximum temperature that this body can reach is 400 K. Assume that the Earth and the Moon are the same distance from the Sun.
Another black body is on the Moon’s surface at point B.
Outline, without calculation, why the aximum temperature of the black body at point B is less than at point A.
The albedo of the Earth’s atmosphere is 0.28. Outline why the maximum temperature of a black body on the Earth when the Sun is overhead is less than that at point A on the Moon.
Outline why a force acts on the Moon.
Outline why this force does no work on the Moon.
Wind is incident on the blades of a wind turbine. The radius of the blades is 12 m. The following data are available for the air immediately before and after impact with the blades.
Determine the maximum power that can be extracted from the wind by this turbine.
Suggest why the answer in (a) is a maximum.
In a pumped storage hydroelectric system, water is stored in a dam of depth 34 m.
The water leaving the upper lake descends a vertical distance of 110 m and turns the turbine of a generator before exiting into the lower lake.
Water flows out of the upper lake at a rate of 1.2 × 105 m3 per minute. The density of water is 1.0 × 103 kg m–3.
Estimate the specific energy of water in this storage system, giving an appropriate unit for your answer.
Show that the average rate at which the gravitational potential energy of the water decreases is 2.5 GW.
The storage system produces 1.8 GW of electrical power. Determine the overall efficiency of the storage system.
After the upper lake is emptied it must be refilled with water from the lower lake and this requires energy. Suggest how the operators of this storage system can still make a profit.