SPH3U · Unit 3 test review

Energy and Society: Test Review

Everything for the Unit 3 test on one page: the key facts from all 5 lessons, the mistakes that cost the most marks, and a practice test that points you back to the lessons you need.

Key facts

Work, Power and Efficiency

$W = F d cos θ$ , measured in joules. Work is a scalar even though force and displacement are vectors.
A force perpendicular to the displacement does zero work — carrying a box across a level room is the standard case.
Negative work removes energy: friction, braking and lowering a load all do negative work.
$Σ W = W_{n e t} = W_{+} + W_{-}$ .
$P = \frac{W}{Δ t}$ , in watts, where $1 W = 1 J/s$ . Not on the formula sheet.
$efficiency = \frac{E _{u se f u l}}{E _{t o t a l}} \times 100% .$ Not on the formula sheet.
The 'lost' energy in an inefficient device is almost always thermal energy dispersed into the surroundings.

Kinetic Energy, Potential Energy and Conservation

$K E = \frac{1}{2} m v^{2}$ — doubling the speed quadruples the kinetic energy.
Kinetic energy is a scalar and is never negative, because the velocity is squared.
$PE = m g h$ , where $h$ is the vertical height above a reference level you choose and state.
Energy is never created or destroyed, only transformed or transferred.
Without friction, $K E_{i} + P E_{i} = K E_{f} + P E_{f}$ — mechanical energy is conserved.
With friction, the missing mechanical energy has become thermal energy: $K E_{i} + P E_{i} = K E_{f} + P E_{f} + E_{t h er ma l} .$
Energy methods ignore the path, which is what makes them work where kinematics cannot.

Thermal Energy, Heat Capacity and Phase Change

Temperature is average particle kinetic energy; thermal energy is the total; heat is thermal energy in transit.
Heat moves by conduction, convection and radiation — only radiation works through a vacuum.
$Q = m c Δ T$ for a temperature change, with $Δ T$ as final minus initial.
Water's specific heat is $4180\ \text{J/{(kg}\cdot^\circ\text{C)}}$ — unusually high, which is why it is a good coolant.
$Q_{re l e a se d} + Q_{ab sor b e d} = 0$ when two objects reach a common final temperature.
$Q = m L_{f}$ to melt or freeze, $Q = m L_{v}$ to boil or condense. Neither contains $Δ T$ .
For water, $L_{f} = 3.34 \times 1 0^{5} J/kg$ and $L_{v} = 2.26 \times 1 0^{6} J/kg$ .
During a phase change, temperature does not rise even though energy is being added.

Nuclear Energy, Half-Life and Energy Sources

Fission splits a heavy nucleus and drives every commercial reactor; fusion joins light nuclei and powers stars.
Ontario's CANDU reactors use heavy water, run on unenriched uranium, and can be refuelled while operating.
Half-life is the time for half the nuclei in a sample to decay. It is fixed for each isotope.
$A = A_{0} (\frac{1}{2})^{t / h}$ — use the same time unit for $t$ and $h$ .
Each half-life removes half of what remains: after three, one eighth is left, not zero.
Ontario's electricity is roughly 50–60% nuclear and about 25% hydroelectric, with coal phased out in 2014.
Wind and solar are intermittent, so a grid relying on them needs storage or dispatchable backup.

Thermal Energy in Buildings and the Environment

Air leakage is usually the single largest heat-loss path in an older house, ahead of walls, roof, windows and basement.
Insulation works by trapping still air in pockets small enough to stop convection currents forming.
R-value measures resistance to heat flow, so a larger value means slower loss, and the layers in an assembly add.
Heat escapes by the path of least resistance, so the weakest element sets the loss — upgrade that one first.
Double glazing blocks conduction with a low-conductivity gas, convection with a narrow gap, and radiation with a low-emissivity coating.
Thermal mass is a large $m c$ product, so $Q = m c Δ T$ gives a small $Δ T$ for a large $Q$ . It flattens temperature swings; it does not reduce the total heat flow.
A heat pump moves existing thermal energy rather than generating it, so its coefficient of performance — heat delivered over electricity used — is typically 2 to 4.
$1 kWh = 3.6 \times 1 0^{6} J$ , the unit electricity is billed in.

Where marks get lost

Forgetting $cos θ$ when the force is applied at an angle, which overstates the work every time. (Work, Power and Efficiency)
Leaving the calculator in radian mode, so $cos 3 0^{\circ}$ comes out as $0.154$ instead of $0.866$ . (Work, Power and Efficiency)
Claiming work is done while holding something still. No displacement means no work, however tiring it is. (Work, Power and Efficiency)
Treating work as a vector and giving it a direction. Work is a scalar; only its sign carries meaning. (Work, Power and Efficiency)
Dropping the minus sign on the work done by friction, which then appears to speed the object up. (Work, Power and Efficiency)
Confusing power with energy. A watt is a joule per second; a kilowatt-hour is an amount of energy, not a rate. (Work, Power and Efficiency)
Putting the wrong quantity on top in the efficiency formula. Useful output goes on top, always. (Work, Power and Efficiency)
Forgetting to square the velocity, or squaring after multiplying by the mass. Square $v$ first. (Kinetic Energy, Potential Energy and Conservation)
Thinking doubling the speed doubles the kinetic energy. It quadruples it. (Kinetic Energy, Potential Energy and Conservation)
Using the distance along a ramp as $h$ in $PE = m g h$ . Only the vertical rise counts. (Kinetic Energy, Potential Energy and Conservation)
Never stating the reference level for potential energy, so the numbers cannot be checked. (Kinetic Energy, Potential Energy and Conservation)
Applying $K E_{i} + P E_{i} = K E_{f} + P E_{f}$ where friction is significant. Add the thermal term. (Kinetic Energy, Potential Energy and Conservation)
Claiming energy is 'lost' in a way that breaks conservation. It becomes thermal energy — still there, just no longer useful. (Kinetic Energy, Potential Energy and Conservation)
Giving kinetic energy a direction or a negative value. It is a scalar and always positive. (Kinetic Energy, Potential Energy and Conservation)
Using $Δ T$ in $Q = m L$ . There is no temperature change during a phase change, which is the whole point. (Thermal Energy, Heat Capacity and Phase Change)
Treating a multi-stage problem as one calculation. Each warming stage and each phase change is separate. (Thermal Energy, Heat Capacity and Phase Change)
Using the specific heat of liquid water for ice or steam. All three values differ. (Thermal Energy, Heat Capacity and Phase Change)
Writing $Δ T$ as initial minus final, which flips every sign in a mixing problem. (Thermal Energy, Heat Capacity and Phase Change)
Confusing temperature with thermal energy — a spark is hotter than a bath but carries far less energy. (Thermal Energy, Heat Capacity and Phase Change)
Forgetting that mass must be in kilograms when $c$ is quoted per kilogram. (Thermal Energy, Heat Capacity and Phase Change)
Assuming heat always flows to the object with less thermal energy. It flows from higher temperature to lower, regardless of totals. (Thermal Energy, Heat Capacity and Phase Change)
Treating half-life as subtraction, so four half-lives means nothing remains. Each one halves what is left. (Nuclear Energy, Half-Life and Energy Sources)
Using different time units for $t$ and $h$ . Convert one so they match before dividing. (Nuclear Energy, Half-Life and Energy Sources)
Confusing fission with fusion. Fission splits heavy nuclei and is what reactors do; fusion joins light ones and is what stars do. (Nuclear Energy, Half-Life and Energy Sources)
Forgetting to divide by the half-life before applying the exponent. The exponent is $\frac{t}{h}$ , not $t$ . (Nuclear Energy, Half-Life and Energy Sources)
Calling every renewable source harmless. All of them have environmental costs; the comparison is between trade-offs. (Nuclear Energy, Half-Life and Energy Sources)
Ignoring intermittency when arguing for an all-wind-and-solar grid. Electricity has to be generated the instant it is used. (Nuclear Energy, Half-Life and Energy Sources)
Assuming a radioactive source becomes completely safe after one or two half-lives. (Nuclear Energy, Half-Life and Energy Sources)
Treating R-value as a measure of how much heat gets through. It measures resistance, so a higher R means less heat flow, not more. (Thermal Energy in Buildings and the Environment)
Insulating one element and expecting the whole house to improve in proportion. Heat leaves by the weakest path, so a leaky attic hatch undoes an excellent wall. (Thermal Energy in Buildings and the Environment)
Confusing thermal mass with insulation. A masonry wall stores a great deal of energy per degree but conducts readily — it flattens temperature swings rather than stopping heat flow. (Thermal Energy in Buildings and the Environment)
Saying a heat pump breaks conservation of energy because it is 'more than 100% efficient'. It moves existing thermal energy from outdoors to indoors; it does not create any. (Thermal Energy in Buildings and the Environment)
Using grams in $Q = m c Δ T$ when $c$ is quoted per kilogram — a factor of one thousand, which for a building is the difference between a kettle and a furnace. (Thermal Energy in Buildings and the Environment)

Practice test

25 questions from across the unit. Each one shows the lesson it comes from.

Work, Power and Efficiency
1
A force of $45 N$ pushes a box $12 m$ in the direction of the force. How much work is done, in joules?
J
Work, Power and Efficiency
2
A waiter carries a tray at constant height across a level room. How much work does he do on the tray?
Work, Power and Efficiency
3
Two students carry identical boxes up the same staircase. One takes 5 s, the other 10 s. Compare their work and their power.
Work, Power and Efficiency
4
Friction does $- 250 J$ of work on a sliding crate. What does the negative sign mean?
Work, Power and Efficiency
5
Order these devices from most efficient to least efficient.
1. 1Gas furnace (about 85%)
2. 2Incandescent bulb (about 5%)
3. 3Petrol car engine (about 25%)
4. 4Electric motor (about 90%)
Kinetic Energy, Potential Energy and Conservation
6
What is the kinetic energy, in joules, of a $4.0 kg$ object moving at $6.0 m/s$ ?
J
Kinetic Energy, Potential Energy and Conservation
7
How much gravitational potential energy, in joules, does a $3.0 kg$ book gain when lifted $1.5 m$ ?
J
Kinetic Energy, Potential Energy and Conservation
8
A pendulum gradually swings lower and eventually stops. Which statement is correct?
Kinetic Energy, Potential Energy and Conservation
9
State the law of conservation of energy in one sentence.
Kinetic Energy, Potential Energy and Conservation
10
A cart is released from rest at the top of a frictionless ramp. Order these moments by the cart's kinetic energy, largest first.
1. 1One quarter of the way up from the bottom
2. 2At the moment of release at the top
3. 3Halfway up the ramp
4. 4At the bottom of the ramp
Thermal Energy, Heat Capacity and Phase Change
11
How much heat, in joules, is needed to raise $0.50 kg$ of water by $30^{\circ} C$ ? Take $c = 4180\ \text{J/{(kg}\cdot^\circ\text{C)}}$ .
J
Thermal Energy, Heat Capacity and Phase Change
12
How much energy, in joules, is needed to melt $1.5 kg$ of ice at $0^{\circ} C$ ? Take $L_{f} = 3.34 \times 1 0^{5} J/kg$ .
J
Thermal Energy, Heat Capacity and Phase Change
13
A $2.0 kg$ aluminium block cools from $95^{\circ} C$ to $25^{\circ} C$ . How much energy does it release, in joules? Take $c = 900\ \text{J/{(kg}\cdot^\circ\text{C)}}$ .
J
Thermal Energy, Heat Capacity and Phase Change
14
How much energy, in joules, is needed to boil $0.25 kg$ of water already at $100^{\circ} C$ ? Take $L_{v} = 2.26 \times 1 0^{6} J/kg$ .
J
Thermal Energy, Heat Capacity and Phase Change
15
Order the stages of taking ice at $- 10^{\circ} C$ to steam at $110^{\circ} C$ .
1. 1Warm the steam from $100^{\circ} C$ to $110^{\circ} C$
2. 2Boil the water at $100^{\circ} C$
3. 3Warm the water from $0^{\circ} C$ to $100^{\circ} C$
4. 4Warm the ice from $- 10^{\circ} C$ to $0^{\circ} C$
5. 5Melt the ice at $0^{\circ} C$
Nuclear Energy, Half-Life and Energy Sources
16
A $64 g$ sample has a half-life of 3 days. How many grams remain after 12 days?
g
Nuclear Energy, Half-Life and Energy Sources
17
Which process powers the Sun?
Nuclear Energy, Half-Life and Energy Sources
18
What is the main engineering challenge of relying heavily on wind and solar generation?
Nuclear Energy, Half-Life and Energy Sources
19
In what year did Ontario close its last coal-fired electricity plant?
Nuclear Energy, Half-Life and Energy Sources
20
Order these isotopes from shortest half-life to longest.
1. 1Iodine-131 (8 days)
2. 2Plutonium-239 (24 100 years)
3. 3Cobalt-60 (5.27 years)
4. 4Technetium-99m (6 hours)
Thermal Energy in Buildings and the Environment
21
What does a higher R-value tell you about a building material?
Thermal Energy in Buildings and the Environment
22
Why is the gap in a double-glazed unit kept to roughly $12 mm$ rather than being made much wider?
Thermal Energy in Buildings and the Environment
23
Which heat-loss path is typically the largest in an older detached house?
Thermal Energy in Buildings and the Environment
24
An old brick school stays noticeably cool through a hot afternoon. What is the physics behind this?
Thermal Energy in Buildings and the Environment
25
Match each building feature to the mechanism it is designed to fight.
Weatherstripping around a door
Glass-fibre batt in a wall cavity
Low-emissivity coating on glass
Argon fill between two panes

Endless drill

Fresh numbers every time, for the calculation questions in this unit.

Endless drillnew numbers every time

Generating a problem…