ESAT Physics: Thermal physics and matter, set 2

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

1. 11 mark

   A metal spoon and a wooden spoon have both been resting on a kitchen worktop in a room at 18 degC for several hours, so both spoons are genuinely at the same temperature. When touched, the metal spoon feels distinctly colder than the wooden spoon. Which statement correctly explains this?

   1. A The metal spoon must actually be at a lower temperature than the wooden spoon, because it feels colder to touch.
   2. B Metal conducts thermal energy away from the hand much faster than wood does, so more energy leaves the hand per second even though both spoons are at the same temperature.
   3. C Metal has a lower specific heat capacity than wood, so it releases stored heat into the hand more quickly, producing a cooling sensation.
   4. D The wooden spoon absorbs infrared radiation from the hand, while the metal spoon reflects it, so only the wooden spoon warms up.
2. 21 mark

   A metal rod conducts thermal energy at a steady rate between its hot and cold ends. It is replaced by a second rod of the same material, with the same temperature difference between its ends, but with half the length and half the cross-sectional area of the original. Compared with the original rate of conduction, what is the new rate of conduction along the rod?

   1. A Half the original rate
   2. B Double the original rate
   3. C A quarter of the original rate
   4. D The same as the original rate
3. 31 mark

   On a sunny day near the coast, the land heats up faster than the sea. This produces a sea breeze, a wind that blows from the sea towards the land. Which statement correctly explains why this convection-driven wind blows in that direction?

   1. A Air above the warmer land expands and becomes less dense, so it rises; cooler, denser air from over the sea moves in near the ground to replace it, producing a breeze blowing from sea to land.
   2. B Air above the warmer land contracts and becomes denser, so it sinks towards the ground and pushes outwards towards the sea, creating a breeze that blows from land to sea.
   3. C The sea absorbs thermal energy faster than the land, so warm air rises from above the sea and cooler air flows in from the land to replace it.
   4. D Air pressure over the land and the sea stays equal throughout the day, and the breeze is caused entirely by the rotation of the Earth rather than by any difference in air density.
4. 41 mark

   The cooling element of a refrigerator is placed near the top of the inside compartment, rather than near the bottom. Which statement best explains why this position allows the whole fridge to cool effectively by convection?

   1. A Air cooled by the element becomes less dense, so it sinks to the bottom of the fridge, pushing warmer air upward past the element to be cooled in turn.
   2. B The position of the cooling element makes no real difference; cooled air would circulate around the fridge just as well whether the element were at the top or the bottom.
   3. C Air cooled by the element becomes denser and sinks towards the bottom; warmer, less dense air then rises past the element to be cooled in turn, setting up a current that cools the whole fridge.
   4. D The element cools the fridge mainly by emitting thermal radiation downward onto the food and shelves below, rather than by convection.
5. 51 mark

   A hot metal sphere cools by emitting thermal radiation into a cooler room. Which single change, made on its own, would increase the rate at which the sphere loses energy by radiation?

   1. A Painting the sphere's surface with a light, shiny coating
   2. B Moving the sphere to a room at a higher temperature, reducing the difference in temperature between the sphere and its surroundings
   3. C Wrapping the sphere in a reflective foil layer
   4. D Increasing the surface area of the sphere exposed to the room, while keeping its temperature the same
6. 61 mark

   Coastal towns tend to have a smaller difference between their average summer and winter temperatures than inland towns at a similar latitude. This is partly because water, which dominates the coastal climate, has a much higher specific heat capacity than rock and soil. Which statement best explains this in terms of specific heat capacity?

   1. A Water reflects more sunlight than rock or soil, so less thermal energy reaches the sea in summer, keeping coastal temperatures lower overall.
   2. B For the same mass and the same energy transferred, water's temperature changes far less than rock or soil's, because water has a higher specific heat capacity; this makes the sea heat up and cool down more slowly, moderating nearby air temperatures.
   3. C Water conducts thermal energy away from the coast much faster than rock or soil does, keeping coastal regions at a steadier temperature.
   4. D Because water has a higher specific heat capacity, it needs less thermal energy than rock or soil to produce the same temperature change, so the sea reaches a stable temperature almost immediately.
7. 71 mark

   A 2 kg block of iron (specific heat capacity 450 J/kg/degC) cools from 100 degC to 20 degC, releasing all of its thermal energy to melt ice at 0 degC (specific latent heat of fusion of ice = 360000 J/kg). Assuming no energy is lost elsewhere, what mass of ice is melted?

   1. A 0.2 kg
   2. B 0.05 kg
   3. C 0.25 kg
   4. D 5 kg
8. 81 mark

   Gases can be compressed (squeezed into a smaller volume) far more easily than liquids or solids can. Which statement correctly explains this in terms of the particle model?

   1. A Gas particles are lighter than liquid or solid particles, so less force is needed to push them into a smaller space.
   2. B Gas particles move much faster than liquid or solid particles, and this greater speed is what allows them to be squeezed into a smaller volume.
   3. C Gas particles are spread far apart with large gaps between them, so squeezing them closer together removes mostly empty space; liquid and solid particles are already close together, leaving very little space left to remove.
   4. D Gases have weaker forces between their particles than liquids or solids, and it is this weaker attraction, rather than the spacing between particles, that allows gases to be compressed.
9. 91 mark

   Two identical rigid, sealed containers, P and Q, hold equal amounts of the same gas. Container P is kept at 400 K and container Q is kept at 300 K. Which statement correctly compares the pressure of the gas in each container, and explains why?

   1. A Container Q has the higher pressure, because cooling the gas strengthens the attractive forces between its particles, pulling them together and raising the pressure.
   2. B The two containers have the same pressure, because they hold equal amounts of the same gas and pressure depends only on the amount of gas present, not on its temperature.
   3. C Container Q has the higher pressure, because its slower-moving particles spend more time in contact with the walls during each collision, transferring more force overall.
   4. D Container P has the higher pressure, because its gas particles have more kinetic energy at the higher temperature, so they move faster on average and collide with the walls more often and with greater force.
10. 101 mark

    A fixed mass of gas at constant temperature has its volume halved three times in succession, so its final volume is one eighth of the original volume. By what factor has its pressure changed, compared with the original?

    1. A It has increased eightfold.
    2. B It has increased sixfold.
    3. C It has decreased to one eighth of its original value.
    4. D It has doubled.
11. 111 mark

    Steam at 100 degC striking bare skin typically causes a more severe burn than the same mass of boiling water at 100 degC. Which statement correctly explains this in terms of latent heat?

    1. A Steam is actually hotter than 100 degC, since it has absorbed extra latent heat while changing from water into steam, and this higher temperature is what causes the worse burn.
    2. B As the steam condenses on the skin, it releases its latent heat of vaporisation in addition to cooling down from 100 degC, delivering more total energy to the skin than the same mass of water at 100 degC alone.
    3. C Steam particles move faster than liquid water particles at the same temperature, and this greater speed transfers more thermal energy on contact with the skin.
    4. D Steam is denser than liquid water, so a given volume of steam delivers a greater mass, and therefore more thermal energy, to the skin than the same volume of water.
12. 121 mark

    The specific latent heat of vaporisation of water is 2000000 J/kg (2 x 10^6 J/kg). How much thermal energy is needed to boil away 0.05 kg of water at 100 degC, with no change in temperature?

    1. A 2000000 J
    2. B 50000 J
    3. C 100000 J
    4. D 1000000 J
13. 131 mark

    A student measures the mass of an irregularly shaped stone as 45 g. They lower it into a measuring cylinder containing 60 cm^3 of water, and the water level rises to 75 cm^3. What is the density of the stone?

    1. A 3 g/cm^3
    2. B 0.6 g/cm^3
    3. C 0.75 g/cm^3
    4. D 0.33 g/cm^3
14. 141 mark

    A woman's weight stays the same, but she changes from wearing flat shoes with a total sole contact area of 400 cm^2 to stiletto heels with a total contact area of 4 cm^2. By what factor does the pressure she exerts on the ground change?

    1. A It decreases to one hundredth of its original value.
    2. B It increases 396-fold.
    3. C It increases 4-fold.
    4. D It increases 100-fold.
15. 151 mark

    A tank contains a liquid of density 1200 kg/m^3. At a certain depth, the hydrostatic pressure is 24000 Pa. Take g = 10 N/kg and ignore atmospheric pressure. What is the depth?

    1. A 20 m
    2. B 2 m
    3. C 2400 m
    4. D 0.5 m

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: B

   1. Both spoons are genuinely at the same temperature, 18 degC, as stated, so the different sensation is not caused by a real temperature difference between them.
   2. What the hand senses is the rate at which thermal energy leaves it, not the object's temperature directly.
   3. Metal is a much better thermal conductor than wood, because of its free, delocalised electrons, so it conducts thermal energy away from the warmer hand far more quickly than wood does.
   4. This faster rate of energy loss from the hand is what produces the sensation of the metal spoon feeling colder.
   5. Therefore the answer is B.
   • Why not A: This confuses the sensation of temperature with actual temperature; both spoons genuinely are at 18 degC, as the question states. The feeling of cold comes from how fast heat leaves the hand, not from a real temperature difference between the spoons.
   • Why not C: This muddles specific heat capacity, which is about how much energy is needed to change temperature, with thermal conductivity, which is about how fast energy is transferred. It is metal's high thermal conductivity, not its specific heat capacity, that explains the effect.
   • Why not D: This wrongly invokes radiation and reflection as the mechanism. The hand and spoon are in direct contact, so the dominant transfer here is conduction, not radiation; there is no basis for one spoon reflecting energy away and the other absorbing it.

2. Question 2Answer: D

   1. The rate of conduction along a rod depends directly on its cross-sectional area and inversely on its length, for a fixed material and temperature difference.
   2. Halving the cross-sectional area, on its own, would halve the rate of conduction.
   3. Halving the length, on its own, would double the rate of conduction, since a shorter path lets energy cross more quickly.
   4. Applying both changes together multiplies these two effects: halving the rate, then doubling it, leaves the rate unchanged.
   5. Therefore the answer is D.
   • Why not A: This applies the effect of halving the cross-sectional area, which does halve the rate on its own, but ignores that the rod's length has also been halved, which independently doubles the rate; the two effects must be combined, not just the first one applied.
   • Why not B: This applies the effect of halving the length, which does double the rate on its own since rate of conduction is inversely proportional to length, but ignores that the cross-sectional area has also been halved, which independently halves the rate.
   • Why not C: This treats both a smaller area and a smaller length as each independently slowing conduction down, but a smaller length actually speeds conduction up, since rate is inversely proportional to length; the two changes act in opposite directions, not the same one.

3. Question 3Answer: A

   1. On a sunny day, land heats up faster than the sea because land has a much lower specific heat capacity than water.
   2. The air directly above the land is warmed and expands, becoming less dense than the air above the sea.
   3. This warmer, less dense air rises, and cooler, denser air from over the sea flows in near ground level to take its place, which is felt as a breeze blowing from sea to land.
   4. This continual replacement is a convection current set up by the density difference between the air over the land and the air over the sea.
   5. Therefore the answer is A.
   • Why not B: This reverses the density change caused by heating: warmed air expands and becomes less dense, so it rises, rather than contracting and sinking as this option claims; it also gets the resulting wind direction backwards.
   • Why not C: This reverses which surface heats up faster. The question states that land heats up faster than sea on a sunny day, so it is the air above the land, not the sea, that warms, expands and rises first.
   • Why not D: This denies that any density difference exists and invents an unrelated cause; a sea breeze is a local convection current driven directly by the land heating faster than the sea, not by the Earth's rotation, which only matters on a much larger scale.

4. Question 4Answer: C

   1. Cooling a gas removes thermal energy from its particles, so on average they slow down and move closer together, making the cooled air denser.
   2. Denser air sinks, so air cooled at the top of the fridge sinks towards the bottom.
   3. As it sinks, warmer, less dense air is displaced upward past the cooling element, where it too is cooled and then sinks in turn.
   4. This continual cycle is a convection current that circulates cooled air throughout the whole compartment, which would not happen if the coldest air were produced at the bottom with nowhere to sink to.
   5. Therefore the answer is C.
   • Why not A: This reverses the density change: cooling air makes it contract and become denser, not less dense, which is why it sinks; claiming it becomes less dense gives the wrong reason for the correct direction of movement.
   • Why not B: This is not true: if the element were near the bottom, the coldest, densest air produced there would simply stay at the bottom rather than circulating, since it has nowhere denser below it to sink past; placing the element near the top lets the whole compartment's air pass it and be cooled in turn.
   • Why not D: This names thermal radiation, but the element's job here is convection: it cools the air in direct contact with it, and it is the resulting density-driven air movement, not radiation reaching the food, that cools the whole fridge.

5. Question 5Answer: D

   1. The rate at which an object loses energy by thermal radiation depends on its surface colour and texture, its surface area, and the temperature difference between it and its surroundings.
   2. A light, shiny surface, or a reflective foil layer, both reduce the rate of emission, since dark, matt surfaces are the good emitters.
   3. Reducing the temperature difference between the sphere and the room reduces, rather than increases, the rate of radiation.
   4. Increasing the exposed surface area, with everything else unchanged, gives more surface from which energy can be radiated each second, increasing the rate of energy loss.
   5. Therefore the answer is D.
   • Why not A: This is the wrong direction: light, shiny surfaces are poor emitters of thermal radiation, so painting the sphere this way would decrease, not increase, its rate of energy loss.
   • Why not B: This is the wrong direction: reducing the temperature difference between the sphere and its surroundings reduces the rate at which it radiates net energy away, rather than increasing it.
   • Why not C: This is the wrong direction: a reflective foil surface is a poor emitter of thermal radiation, so wrapping the sphere in it would reduce, not increase, the rate of energy loss by radiation.

6. Question 6Answer: B

   1. Specific heat capacity c is defined by thermal energy = mass x c x temperature change, so temperature change = thermal energy / (mass x c).
   2. For the same mass and the same energy transferred to or from it, a higher specific heat capacity gives a smaller temperature change.
   3. Water has a much higher specific heat capacity than rock or soil, so for a similar amount of energy gained in summer or lost in winter, the sea's temperature changes far less than the land's would.
   4. This slower, smaller temperature change in the sea moderates the temperature of the air above and near it, giving coastal areas a smaller seasonal range than inland areas.
   5. Therefore the answer is B.
   • Why not A: This invokes reflection of sunlight, not specific heat capacity, as the mechanism; the question is specifically about the effect of a high specific heat capacity, which concerns how much temperature change a given energy transfer produces, not how much energy is absorbed in the first place.
   • Why not C: This describes thermal conductivity, a different property from specific heat capacity; conduction is about how quickly energy is transferred within or between materials, not about how much a material's temperature changes for a given energy input.
   • Why not D: This reverses what a higher specific heat capacity means: a higher value means MORE energy, not less, is needed to produce the same temperature change in the same mass, so the sea's temperature changes more slowly, not almost immediately.

7. Question 7Answer: A

   1. The energy released as the iron cools is thermal energy = mass x specific heat capacity x temperature change = 2 x 450 x (100 - 20).
   2. 100 - 20 = 80, so the energy released = 2 x 450 x 80 = 72000 J.
   3. This energy melts ice according to thermal energy = mass of ice x specific latent heat of fusion, so mass of ice melted = energy released / specific latent heat = 72000 / 360000.
   4. 72000 / 360000 = 0.2 kg.
   5. Therefore the answer is A.
   • Why not B: This uses the final temperature of 20 degC as if it were the temperature change, instead of the actual fall of 100 - 20 = 80 degC, giving 2 x 450 x 20 = 18000 J released and then 18000 / 360000 = 0.05 kg melted.
   • Why not C: This uses the initial temperature of 100 degC as if it were the temperature change, instead of the actual fall of 100 - 20 = 80 degC, giving 2 x 450 x 100 = 90000 J released and then 90000 / 360000 = 0.25 kg melted.
   • Why not D: This divides the specific latent heat by the energy released, the wrong way round: mass melted = energy released / specific latent heat, not specific latent heat / energy released, which gives an answer far larger than the mass of iron itself.

8. Question 8Answer: C

   1. In a gas, particles are spread far apart, with large gaps of empty space between them, because the forces between them are too weak to hold them close together.
   2. Squeezing a gas into a smaller volume mostly removes this empty space between particles, which is possible because there is so much of it.
   3. In a liquid or a solid, particles are already close together, touching or nearly touching their neighbours, so there is very little empty space left to remove.
   4. This is why gases can be compressed far more easily than liquids or solids, which strongly resist further compression.
   5. Therefore the answer is C.
   • Why not A: This attributes compressibility to the mass of individual particles, but particle mass does not change when a substance is compressed; it is the large amount of empty space between gas particles, not their mass, that allows a gas to be squeezed into a smaller volume.
   • Why not B: This confuses particle speed with particle spacing; gas particles do move faster than those in a liquid or solid, but this is not what makes a gas easy to compress. It is the large gaps between the widely spaced particles that can be squeezed out.
   • Why not D: The weaker forces between gas particles explain why a gas has no fixed shape or volume, but they are not directly what makes a gas compressible; it is the large empty spaces between gas particles, present because those forces are weak enough to let particles spread out, that leave room for compression.

9. Question 9Answer: D

   1. Gas pressure is caused by particles colliding with the walls of their container.
   2. A higher temperature gives gas particles more kinetic energy, so they move faster on average.
   3. Faster-moving particles collide with the container walls more frequently and with greater force per collision.
   4. Container P is at the higher temperature (400 K, compared with Q's 300 K), so its particles move faster on average, giving P the higher pressure.
   5. Therefore the answer is D.
   • Why not A: The kinetic theory used here treats the forces between gas particles as negligible; it is the particles' speed and how often and how hard they strike the walls that determines pressure, not an increase in attractive forces on cooling, which this model does not include.
   • Why not B: This ignores the effect of temperature on particle speed entirely. Equal amounts of the same gas can still exert different pressures if they are at different temperatures, because temperature affects how fast the particles move and therefore how often and how hard they strike the walls.
   • Why not C: This is not how gas particle collisions work: slower particles do not spend meaningfully longer in contact with a wall in a way that increases the force transferred; on the contrary, faster particles transfer more force per collision and collide more often, which is why the hotter gas has the higher pressure.

10. Question 10Answer: A

    1. At constant temperature, pressure and volume of a fixed mass of gas are inversely proportional: pressure x volume = constant.
    2. Halving the volume once, on its own, doubles the pressure, since the same constant product must be maintained.
    3. Volume is halved three times in succession, so the final volume is (1/2) x (1/2) x (1/2) = 1/8 of the original volume.
    4. Since pressure is inversely proportional to volume, the pressure increases by the reciprocal factor: 2 x 2 x 2 = 8 times the original pressure.
    5. Therefore the answer is A.
    • Why not B: This adds the doubling effect of each halving (2 + 2 + 2 = 6) instead of multiplying them together; each successive halving of volume doubles the pressure again, so the three effects compound by multiplication, not addition: 2 x 2 x 2 = 8.
    • Why not C: This treats pressure as directly proportional to volume, so that pressure falls in the same ratio as volume; pressure and volume of a fixed mass of gas at constant temperature are inversely proportional, so a smaller volume gives a LARGER pressure, not a smaller one.
    • Why not D: This only accounts for the effect of one halving of the volume, giving a single doubling of pressure, rather than compounding the effect of all three successive halvings.

11. Question 11Answer: B

    1. Changing from a gas back to a liquid (condensing) releases the latent heat of vaporisation that was absorbed during boiling; temperature alone does not capture this stored energy.
    2. When steam at 100 degC touches the skin, it condenses into liquid water at 100 degC, releasing its latent heat of vaporisation into the skin.
    3. Only after condensing does this water then cool further, releasing additional energy just as boiling water at 100 degC would.
    4. So steam delivers its ordinary cooling energy plus the extra latent heat released on condensation, which boiling water alone cannot release, making the burn worse.
    5. Therefore the answer is B.
    • Why not A: The question states the steam and the water are both at 100 degC; steam's latent heat was absorbed earlier, during boiling, and does not raise its temperature above 100 degC. The extra energy delivered to the skin comes from the latent heat released on condensation, not from the steam being hotter.
    • Why not C: Temperature is a measure of average particle kinetic energy, so particles of steam and liquid water at the same temperature of 100 degC have the same average kinetic energy; the extra energy steam delivers comes from the change of state it undergoes on the skin, not from faster-moving particles.
    • Why not D: This is factually backwards: steam is far less dense than liquid water, since its particles are spread much further apart, so a given volume of steam contains a smaller mass of water, not a greater one, than the same volume of liquid water.

12. Question 12Answer: C

    1. Boiling away water at constant temperature needs thermal energy = mass x specific latent heat of vaporisation.
    2. Substituting mass = 0.05 kg and specific latent heat of vaporisation = 2000000 J/kg gives thermal energy = 0.05 x 2000000.
    3. 0.05 x 2000000 = 100000 J.
    4. Therefore the answer is C.
    • Why not A: This leaves the mass out of the calculation altogether, giving the specific latent heat value itself as the answer, as if the mass being vaporised were 1 kg rather than the 0.05 kg actually stated.
    • Why not B: This applies an extra, unwarranted halving to the correctly calculated energy (2000000 x 0.05 = 100000), as if the formula required a further division by 2 with no physical basis for doing so.
    • Why not D: This misplaces the decimal point in the mass, using 0.5 kg instead of the 0.05 kg actually stated, giving ten times the correct energy.

13. Question 13Answer: A

    1. The volume of the irregularly shaped stone equals the increase in the water level it causes when lowered in: 75 - 60 = 15 cm^3.
    2. Density is defined as density = mass / volume.
    3. Substituting mass = 45 g and volume = 15 cm^3 gives density = 45 / 15.
    4. 45 / 15 = 3 g/cm^3.
    5. Therefore the answer is A.
    • Why not B: This uses the final water level, 75 cm^3, as if it were the stone's volume on its own, rather than finding how much the level rose because of the stone: 45 / 75 = 0.6.
    • Why not C: This uses the initial water level, 60 cm^3, as if it were the stone's volume, rather than the increase caused by lowering the stone in: 45 / 60 = 0.75.
    • Why not D: This adds the initial and final readings together (60 + 75 = 135) instead of subtracting them to find the volume the stone displaced, giving 45 / 135 = 0.33.

14. Question 14Answer: D

    1. Pressure is defined as pressure = force / area, so for the same force, pressure is inversely proportional to the contact area.
    2. Going from flat shoes (400 cm^2) to heels (4 cm^2) reduces the contact area by a factor of 400 / 4 = 100.
    3. Since her weight (force) has not changed, the pressure she exerts increases by the same factor that the area decreased by.
    4. So the pressure exerted by the heels is 100 times the pressure exerted by the flat shoes.
    5. Therefore the answer is D.
    • Why not A: This treats pressure as directly proportional to contact area, so a smaller area gives a smaller pressure; pressure and area are inversely proportional for a fixed force, so a much smaller contact area gives a much LARGER pressure, not a smaller one.
    • Why not B: This subtracts the two areas (400 - 4 = 396) instead of dividing them; comparing pressures at a fixed force means comparing the ratio of the areas, not their difference.
    • Why not C: This uses the heel's contact area, 4 cm^2, directly as the multiplying factor, rather than the ratio between the two areas (400 / 4 = 100), which is what actually determines how many times greater the pressure becomes.

15. Question 15Answer: B

    1. Hydrostatic pressure is given by pressure = h x rho x g, where h is the depth, rho is the liquid's density, and g is the gravitational field strength.
    2. Rearranging for depth gives h = pressure / (rho x g).
    3. Substituting pressure = 24000 Pa, rho = 1200 kg/m^3 and g = 10 N/kg gives h = 24000 / (1200 x 10) = 24000 / 12000.
    4. 24000 / 12000 = 2 m.
    5. Therefore the answer is B.
    • Why not A: This leaves the gravitational field strength g out of the calculation, computing only pressure / density (24000 / 1200 = 20) rather than pressure / (density x g).
    • Why not C: This leaves the density out of the calculation, computing only pressure / g (24000 / 10 = 2400) rather than including the density as well.
    • Why not D: This inverts the calculation, computing (density x g) / pressure = 12000 / 24000 = 0.5, instead of pressure / (density x g) as the rearranged formula requires.