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Admissions tests / ESAT / Physics / Thermal physics and matter

Demanding. 15 questions, 15 marks, about 26 minutes.

ESAT Physics: Thermal physics and matter, set 3

Conduction, convection and radiation, states of matter and the particle model, density, pressure, specific heat capacity and latent heat.

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  • Answer all questions. No calculator.
  • Each question has exactly one correct answer.
  1. 11 mark

    Rods P and Q are made of the same metal. Rod Q has three times the cross-sectional area of rod P, but only half of rod P's length. The temperature difference between the ends is the same for both rods. Compared with the rate of conduction along rod P, the rate of conduction along rod Q is:

    1. A 1.5 times as great
    2. B 3 times as great
    3. C 6 times as great
    4. D 2 times as great
  2. 21 mark

    Convection currents can transfer thermal energy through liquids and gases, but not through solids. Which statement best explains why convection cannot occur in a solid?

    1. A A solid's particles are held in fixed positions relative to their neighbours, so they cannot circulate to carry thermal energy as a convection current does; a heated solid instead transfers thermal energy by conduction, as vibrating particles pass energy to their neighbours.
    2. B Solids conduct thermal energy so efficiently that convection would make no additional difference to the rate of transfer.
    3. C A solid is always at a uniform temperature throughout, so there is no temperature difference within it to drive a convection current.
    4. D Convection requires the particles to be acted on by gravity, and gravity does not act on the particles of a solid.
  3. 31 mark

    A vacuum (Thermos) flask keeps a hot drink hot by reducing all three methods of thermal energy transfer. It has a vacuum gap between two glass walls, silvered (shiny) surfaces on the glass walls facing the vacuum, and a stopper made from an insulating plastic foam. Which correctly matches each feature to the transfer mechanism it mainly reduces?

    1. A Vacuum reduces conduction and convection, since there are no particles present to carry thermal energy across the gap; silvered walls reduce thermal radiation, since a shiny surface is a poor emitter and absorber of infrared radiation; the insulating stopper reduces conduction through the top of the flask.
    2. B Vacuum reduces thermal radiation, since there are no particles present to emit infrared radiation; silvered walls reduce convection, by reflecting any moving air back into the flask; the insulating stopper reduces conduction through the top.
    3. C Silvered walls reduce conduction, by reflecting thermal energy back into the flask; vacuum reduces thermal radiation, since radiation needs a medium to travel through; the insulating stopper reduces convection through the top.
    4. D Vacuum reduces conduction only, since convection needs a solid medium to occur in; silvered walls reduce convection, by preventing air currents forming near the glass; the insulating stopper reduces thermal radiation escaping through the top.
  4. 41 mark

    Object A has twice the surface area of object B, and both objects have identical, dark, matt surfaces. Object A is at a lower temperature than object B. Which statement is correct?

    1. A Object A definitely radiates thermal energy at a greater rate than object B, because a larger surface area always outweighs a smaller temperature.
    2. B Object A definitely radiates thermal energy at a lower rate than object B, because temperature has a far greater effect on the rate of radiation than surface area does.
    3. C It cannot be determined from this information alone which object radiates thermal energy at the greater rate, since both surface area and temperature affect the rate and they act in opposite directions here.
    4. D The two objects must radiate thermal energy at exactly the same rate, since the increase in area cancels out the decrease in temperature.
  5. 51 mark

    A 0.4 kg block of a certain metal cools from 45 degC to 20 degC, releasing 6000 J of thermal energy to its surroundings. What is the specific heat capacity of the metal?

    1. A 750 J/kg/degC
    2. B 600 J/kg/degC
    3. C 240 J/kg/degC
    4. D 15000 J/kg/degC
  6. 61 mark

    Two blocks, X and Y, are made of different materials and have equal mass. X has twice the specific heat capacity of Y. Both blocks are heated by identical heaters, supplying energy at the same constant rate, for the same length of time. Which statement correctly compares their temperature rises?

    1. A X's temperature rises by twice as much as Y's, since X has the larger specific heat capacity.
    2. B Both blocks' temperatures rise by the same amount, since they receive the same amount of thermal energy.
    3. C X's temperature rises by four times as much as Y's, since specific heat capacity affects temperature change according to a square law.
    4. D Y's temperature rises by twice as much as X's, since Y has the smaller specific heat capacity.
  7. 71 mark

    For most substances, the density of the solid phase is only slightly greater than the density of the liquid phase, but the density of the gas phase is very much lower than either. Which explanation, based on the particle model, best accounts for this pattern?

    1. A Gas particles move much faster than liquid or solid particles, and it is this greater speed, not particle spacing, that gives a gas its much lower density.
    2. B In the solid and liquid phases, particles are already close together, whereas in the gas phase particles are spaced far apart; this large increase in spacing on turning to gas produces the much lower density.
    3. C Liquid particles are spaced much further apart than solid particles, similar to the spacing in a gas, which is why liquids can flow and fill any shaped container.
    4. D Solid particles are heavier than liquid or gas particles of the same substance, which is why solids are the densest phase.
  8. 81 mark

    A fixed mass of gas at constant temperature occupies 600 cm^3 at a pressure of 200 kPa. It is compressed, at constant temperature, to a volume of 0.2 dm^3. What is the new pressure?

    1. A 66.7 kPa
    2. B 600000 kPa
    3. C 6000 kPa
    4. D 600 kPa
  9. 91 mark

    A fixed mass of gas is sealed inside a rigid-walled canister. The canister is heated, and at the same time a fault causes a dent to form that reduces the canister's internal volume. Which statement about the gas pressure is correct?

    1. A The pressure must increase, since both heating the gas and reducing its volume each act, independently, to increase its pressure.
    2. B The pressure must decrease, since a smaller volume means the gas particles have less far to travel between collisions, which reduces the force of each collision.
    3. C The pressure could increase, decrease, or stay the same, since heating tends to increase pressure while a smaller volume tends to decrease it, and these two effects generally cancel out.
    4. D The pressure will stay the same, since the mass of gas has not changed, and pressure depends only on the mass of gas present.
  10. 101 mark

    A 0.1 kg block of ice is at its melting point, 0 degC. It is heated so that it fully melts, and the resulting water is further heated up to 30 degC. Take the specific latent heat of fusion of ice as 300000 J/kg and the specific heat capacity of water as 4000 J/kg/degC. What is the total thermal energy needed for the whole process?

    1. A 30000 J
    2. B 12000 J
    3. C 42000 J
    4. D 312000 J
  11. 111 mark

    For a typical substance, the specific latent heat of vaporisation is very much greater than the specific latent heat of fusion. Which explanation best accounts for this?

    1. A Boiling always happens at a higher temperature than melting, and higher temperatures always require more energy to produce any change of state.
    2. B During melting, the particles are only partly freed from their fixed positions, so only some of the bonds between them need to be overcome; during vaporisation, the particles must be separated almost completely from one another, overcoming nearly all of the remaining forces between them, which needs much more energy.
    3. C Vaporisation involves a bigger increase in the substance's temperature than melting does, so it needs more energy to produce that bigger temperature change.
    4. D The particles themselves gain extra mass when a liquid turns into a gas, so more energy is needed to move this additional mass.
  12. 121 mark

    A sample of liquid has a mass of 0.048 kg and a volume of 40 cm^3. What is its density, in g/cm^3?

    1. A 1.2 g/cm^3
    2. B 0.0012 g/cm^3
    3. C 0.12 g/cm^3
    4. D 48 g/cm^3
  13. 131 mark

    A student finds the density of an irregularly shaped small stone. They measure its mass on a balance, then lower the stone on a thread into a measuring cylinder part-filled with water and record the rise in the water level as the stone's volume. Which of the following would make the student's calculated density come out too HIGH?

    1. A A thread tied around the stone is also submerged in the water, so the recorded volume rise includes the thread's volume as well as the stone's.
    2. B The student reads the final water level with a parallax error that makes them overestimate how much the level has risen.
    3. C The balance used to find the stone's mass has a zero error that makes it read a mass smaller than the stone's true mass.
    4. D The stone is not fully submerged when the water level is read, so part of it stays above the surface and does not displace any water.
  14. 141 mark

    A box exerts a force of 5000 N on the ground through its base, which measures 40 cm by 50 cm. What pressure, in Pa, does the box exert on the ground?

    1. A 2.5 Pa
    2. B 1000 Pa
    3. C 25000 Pa
    4. D 250 Pa
  15. 151 mark

    Point P is 2 m below the surface of a liquid of density 1200 kg/m^3. Point Q is 3 m below the surface of a different liquid, of density 800 kg/m^3. Ignoring atmospheric pressure, and taking the gravitational field strength g to be the same at both points, how do the hydrostatic pressures at P and Q compare?

    1. A The pressure at P is greater, since P's liquid has the greater density.
    2. B The pressure at P and the pressure at Q are equal.
    3. C The pressure at Q is greater, since Q is at the greater depth.
    4. D It cannot be compared without knowing the actual value of g.

Worked solutions

Every question below carries the reasoning, not just the answer. The official material for this test publishes a correct option letter and nothing else.

  1. Question 1Answer: C

    1. The rate at which a rod conducts thermal energy increases with a greater cross-sectional area and decreases with a greater length, for a fixed temperature difference between its ends, so the rate is proportional to area divided by length.
    2. Rod Q's cross-sectional area is three times rod P's, which on its own would triple the rate.
    3. Rod Q's length is half of rod P's, and halving the length on its own would double the rate.
    4. These two independent factors combine by multiplying: 3 x 2 = 6, so rod Q conducts six times as fast as rod P.
    5. Therefore the answer is C.
    • Why not A: This multiplies the area factor by the length factor instead of dividing by it, treating the rate as proportional to area x length rather than area / length, giving 3 x 0.5 = 1.5.
    • Why not B: This only accounts for the tripled cross-sectional area, which on its own would triple the rate, while ignoring that the halved length independently doubles the rate again.
    • Why not D: This only accounts for the halved length, which on its own would double the rate, while ignoring that the tripled cross-sectional area independently triples the rate again.

  2. Question 2Answer: A

    1. Convection is the transfer of thermal energy by the bulk movement of a fluid, in which particles that have been heated (and so become less dense) move from one place to another, carrying their extra energy with them.
    2. In a solid, particles are held in fixed positions relative to their neighbours by strong forces, so they can vibrate but cannot move from place to place to circulate as a fluid does.
    3. This is why a solid cannot support a convection current, and why thermal energy instead travels through a solid by conduction, as more energetic vibrating particles pass energy on to their neighbours.
    4. A solid conducting well, having a uniform temperature, or gravity not acting on it are all false claims and none of them is the real reason convection cannot occur in a solid.
    5. Therefore the answer is A.
    • Why not B: This wrongly implies convection is simply an inferior version of conduction that a good conductor makes redundant; the real reason a solid cannot convect is that its particles cannot move from place to place at all, regardless of how well it conducts.
    • Why not C: This wrongly claims a solid must be at a uniform temperature; a solid can easily have one end hotter than the other, exactly as in a conducting rod, so a temperature difference is not what is missing.
    • Why not D: This wrongly claims gravity does not act on solid particles; gravity acts on all matter regardless of state, so the absence of convection in a solid cannot be explained by gravity being switched off for it.

  3. Question 3Answer: A

    1. Conduction and convection both need particles to transfer thermal energy from one place to another, so removing the particles by creating a vacuum stops both of these mechanisms across the gap.
    2. Thermal radiation is infrared electromagnetic radiation, so unlike conduction and convection it can cross a vacuum; this is instead reduced by making the facing surfaces shiny, since a shiny surface is a poor absorber and emitter of infrared radiation.
    3. The stopper at the top is not a vacuum gap, so heat can still conduct through it; using an insulating material there reduces this remaining conduction path.
    4. Therefore the answer is A.
    • Why not B: This wrongly claims a vacuum blocks radiation; infrared radiation is an electromagnetic wave and crosses a vacuum readily, which is in fact why radiation is the one mechanism a vacuum alone cannot stop, and it wrongly assigns convection-blocking to the silvered walls instead of the vacuum.
    • Why not C: This wrongly claims silvered walls block conduction, and wrongly claims radiation needs a medium to travel through, when radiation is the one thermal transfer mechanism that can cross a vacuum, unlike conduction and convection.
    • Why not D: This wrongly claims convection needs a solid medium, when convection occurs in fluids such as air, not solids, and it swaps the roles of the silvered walls and the stopper.

  4. Question 4Answer: C

    1. Two things affect the rate of thermal radiation from a surface: the type and area of the surface, and its temperature, with a hotter object radiating much faster than a cooler one of the same surface and area.
    2. Object A has a larger surface area than object B, which on its own would tend to increase A's rate of emission.
    3. Object A is at a lower temperature than object B, which on its own would tend to decrease A's rate of emission relative to B, and temperature has a strong effect on this rate.
    4. Since these two effects act in opposite directions and no numerical values are given for either the areas or the temperatures, it is not possible to say which effect wins out.
    5. Therefore the answer is C.
    • Why not A: This wrongly assumes surface area always outweighs temperature; the rate of thermal radiation increases very strongly with temperature, so a lower temperature could easily outweigh a doubled area, and nothing here rules that out.
    • Why not B: This wrongly assumes temperature must always win out, denying that surface area could ever be the decisive factor when no actual values are given for either quantity.
    • Why not D: This wrongly assumes the two effects exactly cancel, but nothing in the question gives numerical values for the areas or the temperatures that would make such an exact cancellation happen.

  5. Question 5Answer: B

    1. Thermal energy transferred = mass x specific heat capacity x temperature change, whether the object is heating up or cooling down.
    2. The temperature change here is 45 - 20 = 25 degC, not the final temperature of 20 degC on its own.
    3. Rearranging for specific heat capacity gives specific heat capacity = thermal energy / (mass x temperature change).
    4. Substituting thermal energy = 6000 J, mass = 0.4 kg and temperature change = 25 degC gives 6000 / (0.4 x 25) = 6000 / 10 = 600 J/kg/degC.
    5. Therefore the answer is B.
    • Why not A: This uses the final temperature of 20 degC as if it were the temperature change, giving 6000 / (0.4 x 20) = 750, instead of using the actual temperature change of 45 - 20 = 25 degC.
    • Why not C: This leaves the mass out of the calculation, giving 6000 / 25 = 240, as if the mass were 1 kg rather than 0.4 kg.
    • Why not D: This leaves the temperature change out of the calculation, giving 6000 / 0.4 = 15000, as if the block's temperature had not changed at all.

  6. Question 6Answer: D

    1. Thermal energy transferred = mass x specific heat capacity x temperature change, so for a fixed mass and a fixed energy input, temperature change = thermal energy / (mass x specific heat capacity).
    2. Both blocks have equal mass and receive equal thermal energy, since they are heated by identical heaters for the same time, so their temperature changes are inversely proportional to their specific heat capacities.
    3. X has twice the specific heat capacity of Y, so for the same energy and mass, X's temperature change is half of what Y's is.
    4. Equivalently, Y's temperature rise is twice X's.
    5. Therefore the answer is D.
    • Why not A: This reverses the relationship: a larger specific heat capacity means a smaller temperature rise for the same energy and mass, so X should rise by less than Y, not more.
    • Why not B: This ignores specific heat capacity altogether; temperature change also depends on mass and specific heat capacity, not on the energy supplied alone, and the two blocks have different specific heat capacities.
    • Why not C: This invents a squared relationship; thermal energy = mass x specific heat capacity x temperature change makes temperature change inversely proportional to specific heat capacity itself, not to its square.

  7. Question 7Answer: B

    1. Density depends on how much mass is contained in a given volume, which for a fixed substance is set by how closely its particles are packed together.
    2. In solids and liquids, particles are close together, giving both phases similar densities, even though a liquid's arrangement is disordered compared with a solid's regular pattern.
    3. In the gas phase, particles are spread far apart with mostly empty space between them, so the same mass now occupies a much larger volume, giving a much lower density.
    4. Particle speed and particle mass do not change between phases of the same substance, so neither can explain the density pattern; only the large change in spacing between the liquid and gas phases can.
    5. Therefore the answer is B.
    • Why not A: This wrongly attributes the density difference to particle speed rather than particle spacing; density depends on how much mass is packed into a given volume, which is set by the spacing between particles, not by how fast they move.
    • Why not C: This wrongly claims liquid particle spacing is similar to a gas's; liquid particles remain close together, comparable to a solid's spacing, which is exactly why liquids and solids have similar densities while gases do not.
    • Why not D: This wrongly claims particles of the same substance change mass between phases; a substance's particles have the same mass whichever phase they are in, so this cannot explain the density differences between phases.

  8. Question 8Answer: D

    1. At constant temperature, a fixed mass of gas obeys pressure x volume = constant.
    2. Both volumes must be in the same units before using this rule; since 1 dm^3 = 1000 cm^3, the new volume of 0.2 dm^3 is 0.2 x 1000 = 200 cm^3.
    3. The constant is the initial pressure multiplied by the initial volume: 200 kPa x 600 cm^3 = 120000.
    4. The new pressure is this constant divided by the new volume: 120000 / 200 = 600 kPa.
    5. Therefore the answer is D.
    • Why not A: This treats pressure as directly proportional to volume instead of inversely proportional, calculating 200 x (200/600) = 66.7 rather than dividing the constant pressure-volume product by the new volume.
    • Why not B: This forgets to convert the new volume from dm^3 to cm^3 at all, treating 0.2 dm^3 as if it were 0.2 cm^3, giving 120000 / 0.2 = 600000.
    • Why not C: This misremembers the conversion factor as 1 dm^3 = 100 cm^3 instead of 1000 cm^3, turning 0.2 dm^3 into 20 cm^3 and giving 120000 / 20 = 6000.

  9. Question 9Answer: A

    1. For a fixed mass of gas, reducing its volume at a given temperature increases its pressure, and heating it at a given volume also increases its pressure, since faster-moving particles collide with the walls more often and with greater force.
    2. Here the gas is both heated and has its volume reduced, so both effects act in the same direction: both tend to increase the pressure.
    3. Since neither effect opposes the other, there is no cancellation to consider, and the pressure must increase overall.
    4. Therefore the answer is A.
    • Why not B: This gets the effect of a smaller volume backwards: a smaller volume actually increases the frequency of collisions with the walls, since particles have less far to travel between them, rather than reducing the force of each collision.
    • Why not C: This wrongly assumes the two effects oppose each other; reducing the volume of a fixed mass of gas increases its pressure, exactly as heating it does, so both effects act in the same direction here and there is nothing for them to cancel.
    • Why not D: This ignores volume and temperature entirely; pressure depends on volume and temperature as well as on the mass of gas present, not on mass alone.

  10. Question 10Answer: C

    1. Two separate stages need thermal energy here: melting the ice at constant temperature, and then heating the resulting water from 0 degC to 30 degC.
    2. Melting uses thermal energy = mass x specific latent heat of fusion = 0.1 x 300000 = 30000 J.
    3. Heating the water afterwards uses thermal energy = mass x specific heat capacity x temperature change = 0.1 x 4000 x 30 = 12000 J.
    4. The total energy needed is the sum of both stages: 30000 + 12000 = 42000 J.
    5. Therefore the answer is C.
    • Why not A: This calculates only the melting stage (0.1 x 300000 = 30000) and forgets to add the energy needed to then heat the melted water up to 30 degC.
    • Why not B: This calculates only the heating stage (0.1 x 4000 x 30 = 12000) and forgets to add the latent heat needed to melt the ice in the first place.
    • Why not D: This leaves the mass out of the melting-stage calculation, using 300000 as if it applied to 1 kg rather than 0.1 kg, then correctly adds the 12000 J heating stage: 300000 + 12000 = 312000.

  11. Question 11Answer: B

    1. Specific latent heat is the energy needed to change the state of a substance without changing its temperature, and it reflects how much bonding between particles must be overcome.
    2. Melting only needs to loosen particles from their fixed positions in a solid enough for them to move around each other as a liquid, so only some of the forces between them are overcome.
    3. Vaporisation needs to separate particles almost completely from one another, against nearly all of the remaining attractive forces, which takes much more energy for the same mass of substance.
    4. Since melting and vaporisation both happen at constant temperature, and particles do not change mass between phases, neither of those can explain the size difference.
    5. Therefore the answer is B.
    • Why not A: This wrongly claims that a higher temperature by itself demands more energy for a change of state; the energy needed for a change of state is set by the bonds being overcome, not by the temperature at which the change happens.
    • Why not C: This wrongly claims temperature changes during a change of state; temperature stays constant throughout both melting and boiling, so no temperature-change energy is involved in either latent heat at all.
    • Why not D: This wrongly claims particles gain mass on vaporising; a substance's particles keep the same mass whichever phase they are in, so this cannot explain the difference in latent heats.

  12. Question 12Answer: A

    1. Density is defined as density = mass / volume, and the units here (g/cm^3) require the mass in grams, not kilograms.
    2. Converting the mass: 0.048 kg x 1000 = 48 g.
    3. Substituting mass = 48 g and volume = 40 cm^3 gives density = 48 / 40.
    4. 48 / 40 = 1.2 g/cm^3.
    5. Therefore the answer is A.
    • Why not B: This forgets to convert the mass from kilograms to grams, dividing 0.048 by 40 directly to get 0.0012, instead of converting the mass to grams first.
    • Why not C: This misremembers the conversion factor between kg and g as 100 instead of 1000, turning 0.048 kg into 4.8 g and giving 4.8 / 40 = 0.12.
    • Why not D: This correctly converts the mass to 48 g but then forgets to divide by the volume at all, as if the volume were 1 cm^3 rather than 40 cm^3.

  13. Question 13Answer: D

    1. Density is calculated as mass divided by volume, so an error that makes the recorded volume smaller than the stone's true volume, or the recorded mass larger than its true mass, makes the calculated density come out too high.
    2. If the stone is not fully submerged, only the submerged part displaces water, so the recorded rise in water level understates the stone's true volume.
    3. Dividing the correctly measured mass by this understated volume gives a calculated density that is too high.
    4. A thread that also displaces water, a parallax error that overstates the volume rise, or a balance that under-reads the mass would each push the calculated density in the opposite direction, so none of those can be the cause of a result that is too high.
    5. Therefore the answer is D.
    • Why not A: A thread that also displaces water makes the recorded volume bigger than the stone's true volume, so dividing mass by this bigger volume gives a density that is too LOW, not too high.
    • Why not B: Overestimating how much the level has risen makes the recorded volume bigger than the stone's true volume, again giving a density that is too LOW, not too high.
    • Why not C: A mass reading that is too small makes the numerator in mass / volume too small, which makes the calculated density too LOW, not too high, and this is an error in the mass measurement rather than the volume measurement.

  14. Question 14Answer: C

    1. Pressure is defined as pressure = force / area, and giving the answer in pascals requires the area in square metres.
    2. Converting both side lengths to metres: 40 cm = 0.4 m and 50 cm = 0.5 m, so the base has area = 0.4 x 0.5 = 0.2 m^2.
    3. Substituting force = 5000 N and area = 0.2 m^2 gives pressure = 5000 / 0.2.
    4. 5000 / 0.2 = 25000 Pa.
    5. Therefore the answer is C.
    • Why not A: This uses the base's area in cm^2 (40 x 50 = 2000) directly in the formula without converting to square metres, giving 5000 / 2000 = 2.5 instead of converting the area first.
    • Why not B: This multiplies the force by the area (5000 x 0.2 = 1000) instead of dividing the force by the area, as the pressure formula requires.
    • Why not D: This converts only one of the two side lengths to metres, treating 40 cm as 0.4 m but leaving 50 cm as 50, giving an area of 0.4 x 50 = 20 instead of the correct 0.4 x 0.5 = 0.2 m^2.

  15. Question 15Answer: B

    1. Hydrostatic pressure is given by pressure = depth x density x g.
    2. For point P: depth x density = 2 x 1200 = 2400.
    3. For point Q: depth x density = 3 x 800 = 2400, the same value.
    4. Since g is the same for both points, and depth x density comes out equal for P and Q, the two hydrostatic pressures must be equal, even though neither the depth nor the density is the same at the two points.
    5. Therefore the answer is B.
    • Why not A: This compares density alone without also multiplying by depth; hydrostatic pressure depends on the product of depth and density together, not on density by itself.
    • Why not C: This compares depth alone without also multiplying by density; hydrostatic pressure depends on the product of depth and density together, not on depth by itself.
    • Why not D: This wrongly assumes the actual value of g is needed; since g is the same at both points, it multiplies both pressures equally and cancels out of any comparison between them, leaving only depth x density to compare.

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