Senior 3 practice book · Unit 4 of 10

Quantity of Heat and Heat Transfer

50 questions that complete the Senior 3 quiz for this unit: 20 core and 30 challenge. Easy and hard questions are mixed. Try each question, then tap “Show answer”.

Common misconceptions

Heat and temperature are the same thing.Temperature tells how hot something is (°C); heat is energy (J) that flows because of a temperature difference. A full bucket of warm water can hold more thermal energy than a cup of boiling water.
Cold flows into things, for example from ice into a drink.Only heat flows, always from the hotter body to the colder one. A drink cools because heat leaves it and goes into the ice.
A blanket or sweater gives out its own heat.Wool and blankets produce no heat. They trap air, a poor conductor, so they slow down the flow of heat, keeping warm things warm and cold things cold.
Water always boils at 100 °C.100 °C is the boiling point at standard sea-level pressure. Where the air pressure is lower, as in Kigali or Musanze, water boils at about 94–95 °C; in a pressure cooker it boils above 100 °C.
When water is cooled it always contracts.Water contracts as it cools down to 4 °C, but between 4 °C and 0 °C it expands, and it expands again on freezing. This is why ice floats and bottles of water burst in a freezer.

What this unit covers

Topics marked new are not tested much in the quiz, so this book gives them extra questions.

Heat and temperature; heat capacity and specific heat capacity (Q = mcΔθ)
Method of mixtures: heat lost = heat gained
Electrical method: measuring c and L with a heater (E = Pt = VIt), reducing heat losses
Latent heat of fusion and vaporisation; heating and cooling curves
Evaporation and boiling: cooling by evaporation, effect of pressure on boiling point
Conduction: good and poor conductors, factors affecting the rate of conduction
Convection currents in liquids and gases
Uses of convection: lake and land breezes, chimneys, ventilation
Radiation: good and poor emitters and absorbers
Reducing heat transfer: vacuum flask, insulation of houses and clothing
Linear expansion of solids and its effects (rails, bridges, bimetallic strip)
Expansion of liquids and gases; anomalous expansion of water; thermometers
Area and volume expansion (β ≈ 2α, γ ≈ 3α)

Go to the questions

Questions (1–50)

Easier and harder questions are mixed, just like in a real exam. The 30 harder ones are marked ★ Challenge.

1True or false
A matt black surface is both a good absorber and a good emitter of infrared radiation.
Show answer
Answer: True
Good absorbers are also good emitters; shiny surfaces are poor at both.
Common mistakeThinking black only absorbs and never emits misses that a black object also cools quickly by radiation.
2True or false · ★ Challenge
A vacuum flask can keep a cold drink cold for hours as well as keep hot tea hot.
Show answer
Answer: True
The flask reduces heat transfer in both directions, so heat from the room also enters only slowly.
Common mistakeThinking a flask only works for hot drinks forgets that it slows heat flow whichever way it goes.
3True or false · ★ Challenge
Convection cannot happen in a solid, because its particles cannot move from place to place.
Show answer
Answer: True
Convection needs the heated material itself to flow; in a solid the particles only vibrate about fixed positions.
Common mistakeThinking solids can have convection confuses vibrating particles (conduction) with flowing material (convection).
4True or false
For the same rise in temperature, gases expand much more than liquids, and liquids expand more than solids.
Show answer
Answer: True
Particles in a gas are far apart with weak forces, so a temperature rise increases the volume most.
Common mistakeThinking all materials expand equally ignores the different forces between their particles.
5True or false · ★ Challenge
When measuring specific heat capacity with an electric heater, a small amount of oil in the hole around the thermometer helps it read the block's temperature correctly.
Show answer
Answer: True
Oil fills the air gap, so heat is conducted well from the block to the thermometer bulb.
Common mistakeThinking the oil is there to heat the thermometer misses that air is a poor conductor that would slow the reading.
6True or false
Wet clothes on a line dry faster on a windy day, because the wind carries away the water vapour near the clothes.
Show answer
Answer: True
Moving air removes vapour from the surface, so more water molecules can escape and evaporation is faster.
Common mistakeThinking the wind dries clothes only by 'blowing water off' misses that it speeds up evaporation.
7Multiple choice · ★ Challenge
A steel plate has a circular hole in it. When the plate is heated, the hole:
1. ABecomes larger, as if it were made of steel
2. BBecomes smaller, as the steel expands into it
3. CStays the same, as there is no metal in it
4. DBecomes oval, as the steel stretches one way
Show answer
Answer: A. Becomes larger, as if it were made of steel
Every length in the plate grows by the same fraction, including the hole's diameter, so the hole gets bigger.
Common mistakeChoosing 'smaller' imagines the metal expanding inwards; the whole plate, hole included, scales up.
8Fill in the blank · ★ Challenge
If the linear expansivity of a solid is α, its area expansivity is about ______ and its volume expansivity is about 3α.
Show answer
Answer: 2α
An area has two lengths, each growing by a fraction αΔθ, so the area grows by about 2αΔθ.
Common mistakeAnswering α² multiplies the coefficients; the fractional increases add, giving 2α.
9True or false
When hot and cold water are mixed in an insulated flask, the fall in temperature of the hot water always equals the rise in temperature of the cold water.
Show answer
Answer: False
Heat lost equals heat gained, not temperature change; the temperature changes are equal only if the two masses are equal.
Common mistakeTreating temperature as the thing that is 'shared' forgets that the heat depends on mass as well as Δθ.
10Multiple choice · ★ Challenge
A builder wants heat from the hot sun to pass through a house wall as slowly as possible. Which change helps?
1. ABuilding the wall with a larger area
2. BBuilding the wall from steel sheets
3. CKeeping the outside of the wall hotter
4. DBuilding the same wall twice as thick
Show answer
Answer: D. Building the same wall twice as thick
The rate of conduction falls when the wall is thicker; it rises with larger area, a better conductor or a bigger temperature difference.
Common mistakeChoosing steel sheets forgets that metals are good conductors, which would let heat in faster.
11Multiple choice · ★ Challenge
Water in an open pot in Kigali boils a few degrees below the temperature at which it boils at the coast. What is the reason?
1. AKigali's tap water contains less salt than the sea
2. BAir pressure is lower at Kigali's altitude
3. CKigali is nearer the Sun, so less heat is needed
4. DKigali's air is warmer, so water needs less heat
Show answer
Answer: B. Air pressure is lower at Kigali's altitude
A liquid boils when its vapour pressure equals the air pressure; at about 1550 m the air pressure is lower, so this happens at a lower temperature.
Common mistakeChoosing 'warmer air' confuses the surroundings with the boiling point; the boiling point depends on pressure.
12Fill in the blank
Water has its greatest density, and so its smallest volume for a given mass, at ______ °C.
Show answer
Answer: 4
Above and below 4 °C the same mass of water occupies more volume.
Common mistakeAnswering 0 °C assumes water is densest when coldest; in fact ice and water near 0 °C are less dense than at 4 °C.
13Multiple choice · ★ Challenge
Some farmers keep milk cool in a clay pot standing in a bowl of water, with a wet cloth over it. How does this keep the milk cool?
1. AWater evaporating from outside takes latent heat from the pot
2. BThe wet cloth conducts cold into the milk from the outside air
3. CThe clay reflects sunlight away from the milk inside
4. DWater soaks into the milk and lowers its temperature
Show answer
Answer: A. Water evaporating from outside takes latent heat from the pot
Evaporation needs latent heat; the water takes it from the pot and the milk, so their temperature falls.
Common mistakeChoosing 'conducts cold' imagines cold flowing in; in fact heat flows out to evaporate the water.
14Fill in the blank
On a sunny afternoon the sand on the shore of Lake Kivu becomes much hotter than the lake water, because sand has a much lower ______.
Show answer
Answer: specific heat capacity
With a lower c, each kilogram of sand needs less energy for each degree of rise, so the same sunshine warms it more.
Common mistakeAnswering 'temperature' just repeats the observation; the reason is the lower specific heat capacity.
15Multiple choice · ★ Challenge
Water at 10 °C is slowly cooled to 0 °C (still liquid). How does its volume change?
1. AIt decreases steadily all the way to 0 °C
2. BIt increases steadily all the way to 0 °C
3. CIt stays constant until it freezes at 0 °C
4. DIt decreases down to 4 °C, then increases
Show answer
Answer: D. It decreases down to 4 °C, then increases
Water is densest at 4 °C; below 4 °C it expands again (anomalous expansion).
Common mistakeChoosing 'decreases steadily' applies the normal rule for liquids, which water does not obey between 4 °C and 0 °C.
16Multiple choice · ★ Challenge
On a sunny afternoon at Lake Kivu, which way does the breeze blow, and why?
1. AFrom land to lake: warm air spreads out over the water
2. BFrom lake to land: the cold water pushes the air along
3. CNo breeze: land and water warm up at the same rate
4. DFrom lake to land: air over the warm land rises
Show answer
Answer: D. From lake to land: air over the warm land rises
The land, with lower specific heat capacity, warms faster; air above it rises and cooler air from over the lake moves in (a lake breeze).
Common mistakeChoosing 'land to lake' forgets that it is the cooler, denser air that moves in to replace rising warm air.
17Fill in the blank
A tall chimney on a tea-factory boiler gives a strong draught because the hot gases inside are less ______ than the cold air outside, so they rise.
Show answer
Answer: dense
Hot gases expand, so their density falls and the denser cold air pushes them up the chimney.
Common mistakeAnswering 'heavy' is vague; it is the lower density that makes the hot gas rise.
18Multiple choice · ★ Challenge
Frost forms on the ground in high places like Nyungwe more often on clear nights than on cloudy nights. Why?
1. AOn clear nights the ground radiates heat into space
2. BOn cloudy nights clouds conduct heat down to the ground
3. COn clear nights cold air falls from space to the ground
4. DOn cloudy nights clouds warm the air by convection
Show answer
Answer: A. On clear nights the ground radiates heat into space
With no clouds, infrared radiation from the ground escapes to space; clouds absorb and send some back, keeping the ground warmer.
Common mistakeChoosing 'cold air falls from space' imagines cold coming in; the ground cools because it loses heat by radiation.
19Fill in the blank
While water boils at a constant temperature, the energy supplied separates the molecules completely; this energy is called the latent heat of ______.
Show answer
Answer: vaporisation
During boiling the energy goes into changing liquid to gas, not into raising the temperature.
Common mistakeAnswering 'fusion' mixes up the two changes: fusion is melting, vaporisation is liquid to gas.
20Multiple choice · ★ Challenge
Why does a hut with a thick grass-thatched roof stay cooler on a hot day than one with a thin iron-sheet roof?
1. AIron sheets reflect all the radiation back into the hut
2. BGrass gives out cold air that falls into the hut
3. CGrass traps air, a poor conductor, so less heat gets in
4. DIron is a poor conductor, so it keeps the heat in
Show answer
Answer: C. Grass traps air, a poor conductor, so less heat gets in
Thick thatch holds still air, which conducts heat badly; thin iron sheets are hot and conduct and radiate heat inside.
Common mistakeChoosing 'grass gives out cold' treats cold as a substance; the thatch only slows the flow of heat.
21Multiple choice · ★ Challenge
An iron cooking pot of mass 2.0 kg has a heat capacity of 900 J/°C. What is the specific heat capacity of iron?
1. A1800 J/(kg·°C)
2. B900 J/(kg·°C)
3. C4200 J/(kg·°C)
4. D450 J/(kg·°C)
Show answer
Answer: D. 450 J/(kg·°C)
c = C ÷ m = 900 ÷ 2.0 = 450 J/(kg·°C).
Common mistakeChoosing 1800 J/(kg·°C) multiplies by the mass; heat capacity C = mc, so c = C ÷ m.
22True or false
50 g of ice at 0 °C cools a drink more than 50 g of cold water at 0 °C.
Show answer
Answer: True
The ice first takes in latent heat to melt (334 J per gram) and then warms like the water, so it removes more heat from the drink.
Common mistakeThinking both cool equally because both are at 0 °C ignores the latent heat needed to melt the ice.
23Fill in the blank · ★ Challenge
During a race a runner loses 0.10 kg of sweat by evaporation. Taking the latent heat of vaporisation of sweat as 2.4 × 10⁶ J/kg, the heat removed from the body is ______ J.
Show answer
Answer: 2.4 × 10⁵ (240 000)
Q = mL = 0.10 × 2.4 × 10⁶ = 2.4 × 10⁵ J.
Common mistakeUsing Q = mcΔθ is wrong here: evaporation is a change of state, so Q = mL.
24Multiple choice
Where should an electric heater be placed to warm the whole of a room, and why?
1. ALow down, as the warm air rises and sets up convection
2. BHigh up, as heat moves downwards by convection
3. CHigh up, as the warm air sinks to fill the room
4. DAnywhere, as heat spreads out equally in all directions
Show answer
Answer: A. Low down, as the warm air rises and sets up convection
Air warmed by the heater expands, becomes less dense and rises; cooler air sinks to replace it, so a current carries heat around the room.
Common mistakeChoosing 'high up' forgets that warm air rises; a heater near the ceiling would leave the lower room cold.
25Multiple choice · ★ Challenge
Molten wax cools in a room. Its temperature every minute is: 80, 70, 62, 55, 55, 55, 55, 48, 42 °C. What is its freezing point, and what is happening while the temperature is constant?
1. A55 °C; the wax gives out latent heat as it solidifies
2. B55 °C; the wax stops losing heat to the air around it
3. C80 °C; the wax begins to freeze as soon as it cools
4. D42 °C; the wax has just finished becoming solid
Show answer
Answer: A. 55 °C; the wax gives out latent heat as it solidifies
The flat part at 55 °C is the freezing point; the wax still loses heat, but this is latent heat released as the liquid turns to solid.
Common mistakeChoosing 'stops losing heat' is wrong: the room is cooler, so heat still flows out; it comes from the change of state.
26Multiple choice
Which statement correctly describes a difference between evaporation and boiling?
1. ABoiling happens at any temperature, but from the surface only
2. BEvaporation needs a heater, but boiling happens on its own
3. CEvaporation happens at any temperature, from the surface only
4. DEvaporation warms the liquid, while boiling cools it down
Show answer
Answer: C. Evaporation happens at any temperature, from the surface only
Evaporation happens from the surface at all temperatures; boiling happens throughout the liquid at one temperature, the boiling point.
Common mistakeChoosing the first option swaps the two processes; boiling has a fixed temperature and bubbles form inside the liquid.
27Short answer · ★ Challenge
At night the breeze at Lake Kivu blows from the land towards the lake. Explain why.
Show answer
Model answer: Water has a high specific heat capacity, so at night it cools more slowly than the land and stays warmer. Air above the water is warmed, expands and rises; cooler, denser air from over the land flows out to replace it, giving a land breeze.
Common mistakeSaying the land is warmer at night reverses the facts: land loses heat faster because of its lower specific heat capacity.
28Short answer · ★ Challenge
Explain, in terms of particles and free electrons, why metals conduct heat much better than wood.
Show answer
Model answer: In all solids, hot particles vibrate more and pass energy to their neighbours, which is slow. Metals also have free electrons that move quickly through the metal and carry energy from the hot end to the cold end. Wood has no free electrons, so it conducts heat only slowly.
Common mistakeSaying 'metals are hard and wood is soft' gives no mechanism; the free electrons are the key difference.
29Multiple choice
Large fuel storage tanks at a petrol depot are usually painted white or silver. Why?
1. ATo make the tank walls better conductors of heat
2. BTo reflect sunlight, so that the fuel absorbs less heat
3. CTo make the tanks give out more heat by radiation at night
4. DTo stop convection currents forming in the fuel
Show answer
Answer: B. To reflect sunlight, so that the fuel absorbs less heat
Light, shiny surfaces are poor absorbers and good reflectors of radiation, so the fuel stays cooler and evaporates less.
Common mistakeChoosing 'better conductors' confuses paint colour with conduction; colour affects radiation.
30Short answer · ★ Challenge
Explain how a pressure cooker cooks beans faster than an open pot, and why it is especially useful in high places such as Musanze.
Show answer
Model answer: The sealed lid traps the steam, so the pressure inside rises above atmospheric pressure. Higher pressure raises the boiling point (to about 120 °C), and food in hotter water cooks faster. In high places the air pressure is low, so an open pot boils below 100 °C and food cooks slowly; the cooker overcomes this.
Common mistakeSaying the cooker 'adds more heat' misses the key idea: the higher pressure raises the boiling temperature.
31Short answer · ★ Challenge
In cold countries lakes freeze at the top in winter, but fish survive in the water below. Explain how the anomalous expansion of water makes this possible.
Show answer
Model answer: As the surface cools, water at 4 °C (the densest) sinks to the bottom. Water colder than 4 °C is less dense and stays at the top, where it freezes. Ice is less dense still, so it floats and acts as an insulating layer; the water below stays at about 4 °C.
Common mistakeSaying 'cold water sinks so the lake freezes from the bottom' applies the normal rule, which fails for water below 4 °C.
32Multiple choice
A bimetallic strip is made of brass, which expands more, and iron. What happens when it is heated?
1. AIt bends with the brass on the inside of the curve
2. BIt stays straight but becomes a little longer overall
3. CIt bends towards whichever side is hotter
4. DIt bends with the brass on the outside of the curve
Show answer
Answer: D. It bends with the brass on the outside of the curve
Brass becomes longer than the iron, so the longer metal must be on the outside of the curve.
Common mistakeChoosing 'brass on the inside' reverses the idea: the metal that expands more ends up on the longer, outer side.
33Multiple choice · ★ Challenge
A brass rod 2.0 m long expands by 1.9 mm when heated from 20 °C to 70 °C. What is the linear expansivity of brass?
1. A1.4 × 10⁻⁵ /°C
2. B1.9 × 10⁻⁵ /°C
3. C3.8 × 10⁻⁵ /°C
4. D1.9 × 10⁻² /°C
Show answer
Answer: B. 1.9 × 10⁻⁵ /°C
α = ΔL ÷ (L₀Δθ) = 0.0019 ÷ (2.0 × 50) = 1.9 × 10⁻⁵ /°C.
Common mistakeChoosing 1.9 × 10⁻² /°C leaves ΔL in mm; change 1.9 mm to 0.0019 m first.
34Multiple choice
In a method-of-mixtures experiment, why is the mixture stirred before the final temperature is read?
1. ASo that the stirrer adds heat to the mixture
2. BSo that all of it reaches one uniform temperature
3. CSo that the water evaporates and cools down faster
4. DSo that the mass of the mixture stays the same
Show answer
Answer: B. So that all of it reaches one uniform temperature
Without stirring, hot and cold layers remain and the thermometer reads the temperature of only one part.
Common mistakeChoosing 'the stirrer adds heat' treats stirring as a heat source; its purpose is mixing, not heating.
35Short answer · ★ Challenge
A metal lid is stuck tightly on a glass jar of honey. Explain why running hot water over the lid helps to open it, and explain why electricity cables are hung with some slack between poles.
Show answer
Model answer: The metal lid expands more than the glass for the same rise in temperature, so it becomes slightly looser. Cables contract on cold nights; if they were tight, the contraction could break them or pull the poles, so they are left with some slack.
Common mistakeSaying the hot water 'melts the honey' misses the main idea: different materials expand by different amounts.
36Multiple choice · ★ Challenge
A copper sheet of area 0.50 m² is heated through 100 °C. The linear expansivity of copper is 17 × 10⁻⁶ /°C. What is the increase in its area?
1. A8.5 × 10⁻⁴ m²
2. B1.7 × 10⁻³ m²
3. C2.6 × 10⁻³ m²
4. D3.4 × 10⁻³ m²
Show answer
Answer: B. 1.7 × 10⁻³ m²
β = 2α = 34 × 10⁻⁶ /°C; ΔA = βA₀Δθ = 34 × 10⁻⁶ × 0.50 × 100 = 1.7 × 10⁻³ m².
Common mistakeChoosing 8.5 × 10⁻⁴ m² uses α instead of 2α for an area.
37Multiple choice
Why are ventilation openings in a crowded classroom placed both near the floor and near the ceiling?
1. ACool air enters at the top and pushes warm air out below
2. BAir can only move when the openings are at one height
3. CWarm stale air leaves at the top; cool air enters below
4. DHigh openings let in sunlight that heats the room's air
Show answer
Answer: C. Warm stale air leaves at the top; cool air enters below
Warm air from people rises and escapes through high openings; fresh, cooler, denser air is drawn in low down, so a convection current flows.
Common mistakeChoosing 'cool air enters at the top' reverses convection: cool air is denser and moves to the bottom.
38Multiple choice · ★ Challenge
A joulemeter shows that 12 600 J of electrical energy was used to heat 0.30 kg of cooking oil from 20 °C to 41 °C. Ignoring heat losses, what is the specific heat capacity of the oil?
1. A600 J/(kg·°C)
2. B1020 J/(kg·°C)
3. C42 000 J/(kg·°C)
4. D2000 J/(kg·°C)
Show answer
Answer: D. 2000 J/(kg·°C)
Δθ = 41 − 20 = 21 °C; c = E ÷ (mΔθ) = 12 600 ÷ (0.30 × 21) = 2000 J/(kg·°C).
Common mistakeChoosing 1020 J/(kg·°C) uses the final temperature 41 °C instead of the rise of 21 °C.
39Multiple choice
A car's steel petrol tank is filled to the brim early on a cold morning. By midday some petrol has overflowed. Why?
1. AThe tank contracts in the heat and squeezes the petrol
2. BThe petrol evaporates and its vapour pushes it out
3. CThe petrol expands more than the steel tank as it warms
4. DThe mass of the petrol increases as its temperature rises
Show answer
Answer: C. The petrol expands more than the steel tank as it warms
Liquids expand much more than solids for the same temperature rise, so the petrol's volume grows more than the tank's.
Common mistakeChoosing 'mass grows' is wrong: heating changes the volume, never the mass.
40Multiple choice · ★ Challenge
To cool 0.30 kg of tea at 90 °C, a learner adds 0.10 kg of cold milk at 10 °C. Taking the specific heat capacity of both as 4200 J/(kg·°C) and ignoring heat losses, what is the final temperature?
1. A50 °C
2. B30 °C
3. C70 °C
4. D80 °C
Show answer
Answer: C. 70 °C
Heat lost = heat gained: 0.30 × (90 − θ) = 0.10 × (θ − 10), so 27 − 0.30θ = 0.10θ − 1 and θ = 28 ÷ 0.40 = 70 °C.
Common mistakeChoosing 50 °C takes the simple average of 90 and 10, which is only right for equal masses.
41Short answer
Explain why several thin layers of clothes keep you warmer on a cold morning in Musanze than one thin layer of the same material.
Show answer
Model answer: Air is trapped between the layers. Still air is a very poor conductor, and because it cannot move, convection is also reduced. So heat from the body escapes more slowly.
Common mistakeSaying the clothes 'make heat' is wrong; they only slow down the loss of the body's own heat.
42Multiple choice · ★ Challenge
Crushed ice at 0 °C is put in two funnels. Funnel A has a 50 W heater; funnel B has none. In 4.0 minutes, 46 g of water drips from A and 10 g from B. What is the specific latent heat of fusion of ice found from these results?
1. A2.6 × 10⁵ J/kg
2. B3.3 × 10⁵ J/kg
3. C5.6 × 10³ J/kg
4. D1.2 × 10⁶ J/kg
Show answer
Answer: B. 3.3 × 10⁵ J/kg
Ice melted by the heater = 46 − 10 = 36 g = 0.036 kg; E = Pt = 50 × 240 = 12 000 J; L = E ÷ m = 12 000 ÷ 0.036 ≈ 3.3 × 10⁵ J/kg.
Common mistakeChoosing 2.6 × 10⁵ J/kg uses all 46 g; funnel B shows that 10 g would have melted from the room's heat anyway.
43Short answer · ★ Challenge
Describe a fair experiment to compare how well a dull black surface and a shiny silver surface absorb radiation from a lamp.
Show answer
Model answer: Use two identical cans, one painted dull black and one shiny silver, each with the same mass of water at the same starting temperature. Place them the same distance from the same lamp and record the temperature of each every minute. The can whose temperature rises faster (the black one) is the better absorber.
Common mistakeUsing different amounts of water or different distances makes the test unfair, so the result cannot be trusted.
44Multiple choice
A small pot holds 0.5 kg of water and a large pot holds 3.0 kg of water. Both start at 20 °C on the same charcoal stove and are taken off at 60 °C. Which statement is correct?
1. ASame final temperature, but the large pot took six times the heat
2. BSame final temperature, so both pots took in exactly the same heat
3. CThe small pot took more heat, because it reached 60 °C first
4. DThe large pot is hotter, because it holds more heat energy
Show answer
Answer: A. Same final temperature, but the large pot took six times the heat
Q = mcΔθ: Δθ = 40 °C for both, but the mass is 6 times larger, so the large pot needed 6 times as much heat.
Common mistakeChoosing 'the same heat' confuses temperature (how hot) with heat (energy, which depends on the mass).
45Short answer · ★ Challenge
A dairy cooperative freezes 1.5 kg of water at 20 °C into ice at 0 °C. How much heat must the freezer remove? (c = 4200 J/(kg·°C), L of fusion = 334 000 J/kg)
Show answer
Model answer: Cooling the water to 0 °C: Q₁ = mcΔθ = 1.5 × 4200 × 20 = 126 000 J. Freezing it: Q₂ = mL = 1.5 × 334 000 = 501 000 J. Total = 627 000 J (627 kJ).
Common mistakeForgetting Q₂ (giving only 126 000 J) ignores that the water must lose latent heat to freeze, even with no temperature change.
46Multiple choice
Rods of copper, iron and glass of the same length and thickness each have a drawing pin fixed with wax at the far end. The near ends are heated equally. The pin on copper falls first, then iron; the glass pin stays. What does this show?
1. ACopper has the highest melting point of the three
2. BGlass conducts heat faster than iron does
3. CCopper is the best conductor of heat of the three
4. DAll three rods conduct heat at the same rate
Show answer
Answer: C. Copper is the best conductor of heat of the three
The wax melts first where heat arrives fastest, so copper conducts best and glass is a poor conductor.
Common mistakeChoosing 'highest melting point' looks at the wrong property; the test compares how fast heat travels along each rod.
47Short answer · ★ Challenge
To find the specific heat capacity of copper, a 0.20 kg copper block is heated in boiling water (100 °C) and quickly moved into 0.15 kg of water at 20 °C in a polystyrene cup. The final temperature is 29 °C. Calculate c for copper (c of water = 4200 J/(kg·°C)) and say whether heat losses make your value too high or too low.
Show answer
Model answer: Heat gained by water = 0.15 × 4200 × (29 − 20) = 5670 J. Heat lost by copper = 0.20 × c × (100 − 29) = 14.2c. So c = 5670 ÷ 14.2 ≈ 400 J/(kg·°C). Heat lost to the air (and cooling of the block on the way) means the water gains less, so the calculated value is too low.
Common mistakeUsing (100 − 20) for the copper forgets that the copper only cools down to the final temperature of 29 °C.
48Short answer · ★ Challenge
Three liquids P, Q and R, each of mass 0.50 kg, are each given 21 000 J of heat. Their temperature rises are P: 10 °C, Q: 20 °C, R: 14 °C. Calculate the specific heat capacity of each and say which is best for a hot-water bottle.
Show answer
Model answer: c = Q ÷ (mΔθ). P: 21 000 ÷ (0.50 × 10) = 4200 J/(kg·°C); Q: 21 000 ÷ (0.50 × 20) = 2100 J/(kg·°C); R: 21 000 ÷ (0.50 × 14) = 3000 J/(kg·°C). P is best: it stores the most heat per kilogram for each degree, so it gives out more heat as it cools.
Common mistakeChoosing Q because it 'heats up fastest' mixes up warming quickly with storing a lot of heat.
49Short answer
In the electrical method for finding the specific heat capacity of a metal block, why is the block wrapped in insulation (lagged), and how would heat losses affect the value found?
Show answer
Model answer: Lagging reduces the heat lost from the block to the surroundings. If heat is lost, the temperature rise is smaller than it should be, so c = Pt ÷ (mΔθ) comes out larger than the true value.
Common mistakeSaying heat losses make c smaller forgets that a smaller Δθ in the denominator makes the answer bigger.
50Short answer · ★ Challenge
The bulb of a mercury thermometer holds 0.20 cm³ of mercury, whose volume expansivity is 1.8 × 10⁻⁴ /°C. The capillary tube has a cross-sectional area of 1.0 × 10⁻⁴ cm². Ignoring the expansion of the glass, how far does the mercury thread move for each 1 °C rise? Suggest one way to make the thermometer more sensitive.
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Model answer: ΔV per °C = γV₀ = 1.8 × 10⁻⁴ × 0.20 = 3.6 × 10⁻⁵ cm³. Length = ΔV ÷ A = 3.6 × 10⁻⁵ ÷ 1.0 × 10⁻⁴ = 0.36 cm per °C. A narrower tube (or a larger bulb) makes the thread move further for each degree.
Common mistakeChoosing a wider tube to make it 'more sensitive' is wrong: the same extra volume then fills a shorter length.