Cambridge International AS And A Level Physics Coursebook 3rd Edition David Sang, Graham Jones, Gurinder Chadha, Richard Woodside - Solutions

In measurements of the specific heat capacity of a metal, energy losses to the surroundings are a source of error. Is this a systematic error or a random error? Justify your answer.
a. Define specific latent heat and explain the difference between latent heat of fusion and latent heat of vaporisation.b. An electric heater generating power of 120 W is immersed in a beaker of liquid that is placed on a balance. When the liquid begins to boil it is noticed that the mass of the
In an experiment to measure the specific heat capacity of water, a student uses an electrical heater to heat some water. His results are shown. Calculate a value for the heat capacity of water. Comment on any likely sources of error. mass of beaker = 150 g mass of beaker + water = 672 g current in
a. Explain why energy is needed for boiling even though the temperature of the liquid remains constant.This diagram shows an apparatus that can be used to measure the specific latent heat of vaporisation of nitrogen.b. Suggest why the nitrogen is contained in a vacuum flask.c. The change in mass of
A block of paraffin wax was heated gently, at a steady rate. Heating was continued after the wax had completely melted. The graph of Figure 19.16 shows how the material’s temperature varied during the experiment.a. For each section of the graph (AB, BC and CD), describe the state of the
a i. Explain what is meant by internal energy.ii. Explain what is meant by the absolute zero of temperature.b. An electric hot water heater has a power rating of 9.0 kW. The water is heated as it passes through the heater. Water flows through the heater at a speed of 1.2 m s−1 through pipes that
The specific latent heat of fusion of water is 330 kJ kg−1. Calculate the energy needed to change 2.0 g of ice into water at 0 °C. Suggest why the answer is much smaller than the amount of energy calculated in Worked example 3.
A sample of alcohol is heated with a 40 W heater until it boils. As it boils, the mass of the liquid decreases at a rate of 2.25 g per minute. Assuming that 80% of the energy supplied by the heater is transferred to the alcohol, estimate the specific latent heat of vaporisation of the alcohol. Give
‘It can be useful to recall that 1.0 kg of ordinary matter contains in the order of 1026 atoms.’ Making suitable estimates, test this statement.
A cylinder holds 140 m3 of nitrogen at room temperature and pressure. Moving slowly, so that there is no change in temperature, a piston is pushed to reduce the volume of the nitrogen to 42 m3.a. Calculate the pressure of the nitrogen after compression.b. Explain the effect on the temperature and
A balloon contains 0.04 m3 of air at a pressure of 120 kPa. Calculate the pressure required to reduce its volume to 0.025 m3 at constant temperature.
The atmospheric pressure is 100 kPa, equivalent to the pressure exerted by a column of water 10 m high. A bubble of oxygen of volume 0.42 cm3 is released by a water plant at a depth of 25 m. Calculate the volume of the bubble when it reaches the surface. State any assumptions you make.
State and explain, in terms of the kinetic model (the movement of molecules), what happens to the pressure inside a tyre when more molecules at the same temperature are pumped into the tyre.
A gas is enclosed inside a cylinder that is fitted with a freely moving piston.The gas is initially in equilibrium with a volume V1 and a pressure p. The gas is then cooled slowly. The piston moves into the cylinder until the volume of the gas is reduced to V2 and the pressure remains at p.What is
Explain, using the kinetic model, why a can containing air may explode if the temperature rises.
An ideal gas is made to expand slowly at a constant temperature.Which statement is correct?A. The heat energy transferred to the gas is zero.B. The internal energy of the gas increases.C. The work done by the gas is equal to the heat energy added to it.D. The work done by the gas is zero.
The mass of one atom of carbon-12 is 12 u. Determine:a. The mass of one atom of carbon-12 in kg, given that 1 u = 1.66 × 10−27 kgb. The number of atoms and the number of moles in 54 g of carbonc. The number of atoms in 1.0 kg of carbon.
a. State how many atoms there are in:i. A mole of helium gas (a molecule of helium has one atom)ii. A mole of chlorine gas (a molecule of chlorine has two atoms)iii. A kilomole of neon gas (a molecule of neon has one atom).b. A container holds four moles of carbon dioxide of molecular formula
A bar of gold-197 has a mass of 1.0 kg. Calculate:a. The mass of one gold atom in kg.b. The number of gold atoms in the barc. The number of moles of gold in the bar.(An atom of gold contains 197 nucleons and has a mass of 197 u.)
For the questions that follow, you will need the following value:R = 8.31 J mol−1 K−1At what temperature (in K) will 1.0 mol of a gas occupy 1.0 m3 at a pressure of 1.0 × 104 Pa?
A cylinder contains 4.0 × 10−2 m3 of carbon dioxide at a pressure of 4.8 × 105 Pa at room temperature.Calculate:a. The number of moles of carbon dioxideb. The mass of carbon dioxide.(Molar mass of carbon dioxide = 44 g or one molecule of carbon dioxide has mass 44 u.)
Calculate the volume of 1 mole of ideal gas at a pressure of 1.01 × 105 Pa and at a temperature of 0 °C.
A vessel of volume 0.20 m3 contains 3.0 × 1026 molecules of gas at a temperature of 127 °C. Calculate the pressure exerted by the gas on the vessel walls.
For the questions that follow, you will need the following value:R = 8.31 J mol−1 K−1Calculate the volume of 5.0 mol of an ideal gas at a pressure of 1.0 × 105 Pa and a temperature of 200 °C.
a. Calculate the root-mean-square speed of helium molecules at room temperature and pressure. (Density of helium at room temperature and pressure = 0.179 kg m−3.)b. Compare this speed with the average speed of air molecules at the same temperature and pressure.
For the questions that follow, you will need the following value:R = 8.31 J mol−1 K−1At what temperature would 1.0 kg of oxygen occupy 1.0 m3 at a pressure of 1.0 × 105 Pa? (Molar mass of O2 = 32 g mol−1.)
A sample of neon is contained in a cylinder at 27 °C. Its temperature is raised to 243 °C.a. Calculate the kinetic energy of the neon atoms at:i. 27 °Cii. 243 °C.b. Calculate the ratio of the speeds of the molecules at the two temperatures.
For the questions that follow, you will need the following value:R = 8.31 J mol−1 K−1A cylinder of hydrogen has a volume of 0.100 m3. Its pressure is found to be 20 atmospheres at 20 °C.a. Calculate the mass of hydrogen in the cylinder.b. If it were instead filled with oxygen to the same
A truck is to cross the Sahara desert. The journey begins just before dawn when the temperature is 3 °C. The volume of air held in each tyre is 1.50 m3 and the pressure in the tyres is 3.42 × 105 Pa.a. Explain how the air molecules in the tyre exert a pressure on the tyre walls.b. Calculate
Check that the SI base units on the left-hand side of the equation:p = 1/3 (Nm/V) < c2 > are the same as those on the right-hand side.
The ideal gas equation is pV = 1/3 Nm < c2 >.a. State the meaning of the symbols N, m and < c2 >.b. A cylinder of helium-4 contains gas with volume 4.1 × 104 cm3 at a pressure of 6.0 × 105 Pa and a temperature of 22 °C. You may assume helium acts as an ideal gas and that a
The quantity Nm is the total mass of the molecules of the gas, i.e. the mass of the gas. At room temperature, the density of air is about 1.29 kg m−3 at a pressure of 105 pa.a. Use these figures to deduce the value of 2> for air molecules at room temperature.b. Find a typical
Calculate the mean translational k.e. of atoms in an ideal gas at 27 °C.
The atoms in a gas have a mean translational k.e. equal to 5.0 × 10−21 J. Calculate the temperature of the gas in K and in °C.
Four molecules have speeds 200, 400, 600 and 800 m s−1. Calculate:a. Their mean speed < c >b. The square of their mean speed < c >2c. Their mean-square speed < c2 >d. Their root-mean-square speed cr.m.s..
Calculate the root-mean square speed of the molecules of hydrogen at 20 °C given that each molecule of hydrogen has mass 3.35 × 10−27 kg.
Show that, if the mean speed of the molecules in an ideal gas is doubled, the thermodynamic temperature of the gas increases by a factor of four.
A fixed mass of gas expands to twice its original volume at a constant temperature. How do the following change?a. The pressure of the gasb. The mean translational kinetic energy of its molecules.
Air consists of molecules of oxygen (molar mass = 32 g mol−1) and nitrogen (molar mass = 28 g mol−1). Calculate the mean translational k.e. of these molecules in air at 20 °C. Use your answer to calculate the root-mean-square speed of each type of molecule.
Show that the change in the internal energy of one mole of an ideal gas per unit change in temperature is always a constant. What is this constant?
Which of the three field diagrams in Figure 21.7 represents:a. Two positive charges repelling each other?b. Two negative charges?c. Two opposite charges? i ii iii
A pair of charged parallel plates are arranged horizontally in a vacuum. The upper plate carries a negative charge and the lower plate is earthed. An electron enters the space between the plates at right angles to the electric field.In which direction is the electric field between the plates and in
Many molecules are described as polar; that is, they have regions that are positively or negatively charged, though they are neutral overall. Draw a diagram to show how sausage-shaped polar molecules like those shown in Figure 21.8 might realign themselves in a solid. +. +,
A pair of charged parallel plates are 2.0 cm apart and there is a potential difference of 5.0 kV across the plates.A charged ion between the plates experiences a force of 1.2 × 10−13 N due to the field.What is the charge on the ion?A. 1.6 × 10−19 CB. 4.8 × 10−19 CC. 2.5 × 10−15 CD. 4.0
Figure 21.9 shows the electric field pattern between a thundercloud and a building. State and explain where the electric field strength is greatest.
Figure 21.4 shows apparatus used to investigate the field between a pair of charged, parallel plates.a. Explain why the piece of gold foil deflects in the manner shown.b. State and explain what would be observed if the gold foil momentarily touched the negatively charged plate. charged gold foil
Figure 21.12 shows an arrangement of parallel plates, each at a different voltage. The electric field lines are shown in the space between the first pair. Copy and complete the diagram to show the electric field lines in the other two spaces. OV +2.0 kv +6.0 kV OV earth
A charged dust particle in an electric field experiences a force of 4.4 × 10−13 N. The charge on the particle is 8.8 × 10−17 C. Calculate the electric field strength.
Calculate the electric field strength at a point where a charge of 20 mC experiences a force vertically downwards of 150 N.
Calculate the potential difference that must be applied across a pair of parallel plates, placed 4 cm apart, to produce an electric field of 4000 V m−1.
Calculate the electric field strength between two parallel charged plates, separated by 40 cm and with a potential difference between them of 1000 V.
A potential difference of 2.4 kV is applied across a pair of parallel plates. The electric field strength between the plates is 3.0 × 104 V m−1.a. Calculate the separation of the plates.b. The plates are now moved so that they are 2.0 cm apart. Calculate the electric field strength produced in
An electron is situated in a uniform electric field. The electric force that acts on it is 8 × 10−16 N. What is the strength of the electric field? (Electron charge e = 1.6 × 10−19 C.)
A variable power supply is connected across a pair of parallel plates. The potential difference across the plates is doubled and the distance between the plates is decreased to one-third of the original. State by what factor the electric field changes. Explain your reasoning.
Air is usually a good insulator. However, a spark can jump through dry air when the electric field strength is greater than about 40,000 V cm−1. This is called electrical breakdown. The spark shows that electrical charge is passing through the air–there is a current. (Do not confuse this with a
In Figure 21.16, two parallel plates are shown, separated by 25 cm.a. Copy the diagram and draw field lines to represent the field between the plates.b. What is the potential difference between points A and B?c. What is the electric field strength at C, and at D?d. Calculate the electric force on a
A particle of charge +2 μC is placed between two parallel plates, 10 cm apart and with a potential difference of 5 kV between them. Calculate the field strength between the plates, and the force exerted on the charge.
a. Define what is meant by the electric field strength at a point.In a particle accelerator, a proton, initially at rest, is accelerated between two metal plates, as shown.b. Calculate the force on the proton due to the electric field.c. Calculate the work done on the proton by the electric field
We are used to experiencing accelerations that are usually less than 10 m s−2. For example, when we fall, our acceleration is about 9.81 m s−2. When a car turns a corner sharply at speed, its acceleration is unlikely to be more than 5 m s−2. However, if you were an electron, you would be used
This diagram shows the structure of a spark plug in an internal combustion engine. The magnified section shows the end of the spark plug, with some of the lines of force representing the electric field.i. Copy the field lines from the diagram. On your copy, draw arrows on the lines of force to show
a. Use a diagram to explain how the electric force on a charged particle could be used to separate a beam of electrons (e−) and positrons (e+) into two separate beams. (A positron is a positively charged particle that has the same mass as an electron but opposite charge. Positron–electron pairs
You will need the following data to answer the following questions. (You may take the charge of each sphere to be situated at its centre.)ε0 = 8.85 × 10−12 F m−1A metal sphere of radius 20 cm carries a positive charge of +2.0 μC.a. What is the electric field strength at a distance of 25 cm
How does the potential V change with the distance r from a point charge?A. V ∝ rB. V ∝ r2C. V ∝ r−1D. V ∝ r−2
The electric field strength 20 cm from an isolated point charge is 1.9 × 104 N C−1.What is the electric field strength 30 cm from the charge?A. 8.4 × 103 N C−1B. 1.3 × 104 N C−1C. 2.9 × 104 N C−1D. 4.3 × 104 N C−1
a. What is the electrical potential energy of a charge of + 1 C placed at each of the points A, B, C, D between the charged, parallel plates shown in Figure 22.15?b. What would be the potential energy of a + 2 C charge at each of these points? (C is halfway between A and B, D is halfway between C
On a copy of this diagram, draw the electric fields between the charged objects. a b +2 kV Figure 22.17
A Van de Graaff generator has a spherical dome of radius 10 cm. It is charged up to a potential of 100,000 V (100 kV). How much charge is stored on the dome? What is the potential at a distance of 10 cm from the dome?
Two parallel plates are 4 cm apart and have a potential difference of 2.5 kV between them.a. Calculate the electric field strength between the plates.b. A small piece of dust carrying a charge of + 2.4 nC moves into the space between the plates.i. Calculate the force on the dust particle.ii. The
a. How much work is done in moving a + 1 C charge along the following paths shown in Figure 22.16: from E to H; from E to F; from F to G; from H to E?b. How do your answers differ for a:i. −1 C charge?ii. +2 C charge? H +5 kV F G E OV earth
A small sphere carries a charge of 2.4 × 10−9 C. Calculate the electric field strength at a distance of:a. 2 cm from the centre of the sphereb. 4 cm from the centre of the sphere.
A conducting sphere of diameter 6.0 cm is mounted on an insulating base. The sphere is connected to a power supply that has an output voltage of 20 kV.a. Calculate the charge on the sphere.b. Calculate the electric field strength at the surface of the sphere.
The nucleus of a hydrogen atom carries a charge of + 1.60 × 10−19 C. Its electron is at a distance of 1.05 × 10−10 m from the nucleus. Calculate the ionisation potential of hydrogen.
a. Define electric field strength.b. Two charged conducting spheres, each of radius 1.0 cm, are placed with their centres 10 cm apart, as shown.Sphere A carries a charge of +2.0 × 10−9 C.The graph shows how the electric field strength between the two spheres varies with distance x.i. Determine
Astrologers believe that the planets exert an influence on us, particularly at the moment of birth.a. Calculate the gravitational force on a 4.0 kg baby caused by Mars when the planet is at its closest to the Earth at a distance of 100,000,000 km. Mars has a mass 6.4 × 1023 kg.b. Calculate the
Ganymede is the largest of Jupiter’s moons, with a mass of 1.48 × 1023 kg. It orbits Jupiter with an orbital radius of 1.07 × 106 km and it rotates on its own axis with a period of 7.15 days. It has been suggested that to monitor an unmanned landing craft on the surface of Ganymede a
You will need the data for the mass and radius of the Earth and the Moon from Table 17.1 to answer this question.Gravitational constant G = 6.67 × 10−11 N m2 kg−2.a. Determine the gravitational potential at the surface of the Earth.b. Determine the gravitational potential at the surface of the
The Earth orbits the Sun with a period of 1 year at an orbital radius of 1.50 × 1011 m. Calculate:a. The orbital speed of the Earthb. The centripetal acceleration of the Earthc. The Sun’s gravitational field strength at the Earth.
During the manned Moon landings in the 1960s, the command module orbited the Moon in an elliptic orbit with a maximum height of 310 km above the surface of the Moon, whilst the lunar module descended and landed on the Moon’s surface.a. Explain why the potential energy of the command module varied
The planet Mars has a mass of 6.4 × 1023 kg and a diameter of 6790 km.a i. Calculate the acceleration due to gravity at the planet’s surface.ii. Calculate the gravitational potential at the surface of the planet.b. A rocket is to return some samples of Martian material to Earth. Write down how
Calculate the orbital speed of an artificial satellite travelling 200 km above the Earth’s surface. (The radius of Earth is 6.4 × 106 m and its mass is 6.0 × 1024 kg.)
a. Explain what is meant by the gravitational potential at a point.b. This diagram shows the gravitational potential near a planet of mass M and radius R.On a copy of the diagram, draw similar curves:i. For a planet of the same radius but of mass 2M–label this i.ii. For a planet of the same mass
A satellite orbiting a few hundred kilometres above the Earth’s surface will experience a slight frictional drag from the Earth’s (very thin) atmosphere. Draw a diagram to show how you would expect the satellite’s orbit to change as a result. How can this problem be overcome if it is desired
a. Explain what is meant by the gravitational field strength at a point.This diagram shows the dwarf planet, Pluto, and its moon, Charon. These can be considered to be a double planetary system orbiting each other about their joint centre of mass.b. Calculate the gravitational pull on Charon due to
For any future mission to Mars, it would be desirable to set up a system of three or four geostationary (or ‘martostationary’) satellites around Mars to allow communication between the planet and Earth.Calculate the radius of a suitable orbit around Mars.Mars has mass 6.4 × 1023 kg and a
This diagram shows the variation of the Earth’s gravitational field strength with distance from its centre.a. Determine the gravitational field strength at a height equal to 2R above the Earth’s surface, where R is the radius of the Earth.b. A satellite is put into an orbit at this height.
Although some international telephone signals are sent via satellites in geostationary orbits, most are sent along cables on the Earth’s surface. This reduces the time delay between sending and receiving the signal. Estimate this time delay for communication via a satellite, and explain why it is
Calculate the potential energy of a spacecraft of mass 250 kg when it is 20,000 km from the planet Mars. (Mass of Mars = 6.4 × 1023 kg, radius of Mars = 3.4 × 106 m.)
The Moon and the Sun both contribute to the tides on the Earth’s oceans. Which has a bigger pull on each kilogram of seawater, the Sun or the Moon?
Mercury, the smallest of the eight recognised planets, has a diameter of 4.88 × 106 m and a mean density of 5.4 × 103 kg m−3.a. Calculate the gravitational field at its surface.b. A man has a weight of 900 N on the Earth’s surface. What would his weight be on the surface of Mercury?
Jupiter’s mass is 320 times that of the Earth and its radius is 11.2 times the Earth’s. The Earth’s surface gravitational field strength is 9.81 N kg−1. Calculate the gravitational field strength close to the surface of Jupiter.
This diagram shows the Earth’s gravitational field.a. Copy the diagram and add arrows to show the direction of the field.b. Explain why the formula for potential energy gained (mgΔh) can be used to find the increase in potential energy when an aircraft climbs to a height of 10,000 m, but cannot
a. Calculate the Earth’s gravitational field strength at the position of the Moon.b. Calculate the force the Earth exerts on the Moon. Hence, determine the Moon’s acceleration towards the Earth.
It is suggested that the mass of a mountain could be measured by the deflection from the vertical of a suspended mass. This diagram shows the principle.a. Copy the diagram and draw arrows to represent the forces acting on the mass. Label the arrows.b. The whole mass of the mountain, 3.8 × 1012 kg,
a. Calculate the gravitational field strength:i. Close to the surface of the Moonii. Close to the surface of the Sun.b. Suggest how your answers help to explain why the Moon has only a thin atmosphere, while the Sun has a dense atmosphere.
Two small spheres each of mass 20 g hang side by side with their centres 5.00 mm apart. Calculate the gravitational attraction between the two spheres.
Mount Everest is approximately 9.0 km high. Estimate how much less a mountaineer of mass 100 kg (including backpack) would weigh at its summit, compared to her weight at sea level. Would this difference be measurable with bathroom scales?
Consider the dwarf planet Pluto to be an isolated sphere of radius 1.2 × 106 m and mass of 1.27 × 1022 kg.What is the gravitational potential at the surface of Pluto?A. −0.59 J kg−1B. −7.1 × 105 J kg−1C. 0.59 J kg-1D. 7.1 × 105 J kg−1
Estimate the gravitational force of attraction between two people sitting side by side on a park bench. How does this force compare with the gravitational force exerted on each of them by the Earth (in other words, their weight)?
An astronaut is on a planet of mass 0.50ME and radius 0.75rE, where ME is the mass of the Earth and rE is the radius of the Earth. What is the gravitational field strength at the surface of the planet?A. 6.5 N kg−1B. 8.7 N kg−1C. 11 N kg−1D. 12 N kg−1
Calculate the gravitational force of attraction between:a. Two objects separated by a distance of 1.0 cm and each having a mass of 100 g.b. Two asteroids separated by a distance of 4.0 109 m and each having a mass of 5.0 × 1010 kg.c. A satellite of mass 1.4 × 104 kg orbiting the Earth at a

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Cambridge International AS And A Level Physics Coursebook 3rd Edition David Sang, Graham Jones, Gurinder Chadha, Richard Woodside - Solutions

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