Energy: conservation, transformation, flow

Evidence: The graph shows all three cups starting at 80 °C. After 20 minutes the foam cup is at 63 °C, the ceramic mug at 49 °C and the steel mug at 38 °C.

Step by step:

1. Find the temperature drop for each cup over the same 20 minutes: foam 80 - 63 = 17 °C, ceramic 80 - 49 = 31 °C, steel 80 - 38 = 42 °C.
2. All cups held the same 200 g of water, so the biggest temperature drop means the most thermal energy lost in the same time.
3. The steel line is also the steepest on the graph from the very first reading (66 °C at 4 minutes).

The water in the steel mug lost thermal energy the fastest. Steel is a metal, a good conductor, so heat passed through its walls quickly.

Tip: On a temperature–time graph, a steeper line means a faster change. Compare lines over the same time interval.

Evidence: The stem says the flashlight "runs on batteries" and the bulb "shines and becomes warm." Those are the starting and ending forms of energy.

Step by step:

1. A battery stores chemical energy in the substances inside it.
2. When the switch closes, a chemical reaction pushes charges through the wire: chemical energy becomes electrical energy.
3. In the bulb, electrical energy becomes light (radiant) energy. The bulb also gets warm, so some becomes thermal energy.
4. Check with conservation: chemical in = light + heat out. No energy is created or destroyed.

The correct chain is chemical → electrical → light and thermal.

Tip: For any device, ask "What goes in?" and "What comes out?" Then fill in the middle step. Heat almost always appears as an extra output.

Evidence: The stem says the warm air "expands and rises" and cooler air "flows toward the shore to take its place." Thermal energy is being carried from place to place by a fluid (air) that is moving.

Step by step:

1. Conduction is transfer by direct contact, particle to particle, such as a hot pan handle warming your hand. The breeze is not about two objects touching.
2. Convection is transfer by the movement of a fluid (a liquid or a gas). Warm fluid is less dense and rises; cooler, denser fluid sinks or flows in to replace it. That is exactly the circulation described.
3. Radiation is transfer by electromagnetic waves, like sunlight crossing space. The Sun heats the sand by radiation, but the moving air itself is convection.

The answer is convection.

Check: A convection current always has a loop: warm fluid rises, cool fluid moves in. The sea breeze has both parts.

Tip: Link each method to a key word: contact = conduction, moving fluid = convection, waves / no matter needed = radiation.

Evidence: The graph shows the sand at 20 °C at 0 min and 55 °C at 10 min, rising by 7 °C between each pair of points 2 minutes apart (20, 27, 34, 41, 48, 55).

Step by step:

1. Find the change in temperature, not the final temperature: \Delta T = 55 - 20 = 35\text{ °C}.
2. Find the time: 10 - 0 = 10 minutes.
3. Divide: \text{rate} = \frac{35\text{ °C}}{10\text{ min}} = 3.5\text{ °C per minute}
4. The points are 2 minutes apart, so each step of 7 °C covers 2 minutes, not 1 minute.

The sand warmed by about 3.5 °C each minute.

Check: 3.5 \times 2 = 7 °C per 2-minute step, which matches the spacing of the points on the graph.

Tip: Always check the scale of the time axis. A rate is a change divided by the time it took, so subtract the starting value first.

Evidence: The passage says "All EM waves travel through empty space at the same speed" and "speed equals frequency times wavelength: v = f\lambda." The table lists the AM radio's frequency as 1.0 \times 10^{6} Hz, the smallest in the table.

Step by step:

1. Since v is the same for every EM wave, \lambda = \dfrac{v}{f}. A smaller frequency gives a longer wavelength.
2. Compare the powers of ten: 10^{6} (AM radio) < 10^{9} (Wi-Fi) < 10^{14} (remote, tanning lamp) < 10^{18} (X-ray).
3. The AM radio has the lowest frequency, so its waves have the longest wavelength. In fact, \lambda = \dfrac{3.0 \times 10^8}{1.0 \times 10^6} = 300 m.

The answer is the AM radio.

Check: The X-ray machine has the largest frequency, so it has the shortest wavelength, the opposite end of the list.

Tip: For EM waves, frequency and wavelength move in opposite directions. Big frequency number means short wavelength and high energy.

Evidence: The passage says "energy moved from the hot water, through the cup walls, into the cooler room air" and that "materials that slow it down are called insulators." The graph shows the foam cup cooled the least: from 80 °C to 63 °C in 20 minutes.

Step by step:

1. Heat flows from hot (water) to cold (room air), passing through the cup wall by conduction.
2. All cups had the same water, starting temperature, shape and room, so the cup material is the variable that changed.
3. Foam cooled the slowest, so foam must slow heat flow the most. That makes foam an insulator.
4. Choices about "cold" moving or foam adding heat break basic rules of heat transfer.

The answer is Foam is an insulator, so it slowed the flow of thermal energy from the water to the cooler air.

Tip: Heat always flows from hot to cold. "Cold" never flows. If a choice says cold moved, cross it out.

Evidence: The passage states that EM waves "do not need a medium (matter) to travel through, so they can cross the vacuum of space. That is how energy from the Sun reaches Earth."

Step by step:

1. Conduction needs particles touching each other; a vacuum has almost no particles.
2. Convection needs a moving liquid or gas; there is none to carry heat across space.
3. Radiation is energy carried by electromagnetic waves, which need no matter.
4. So sunlight and infrared reach Earth by radiation, exactly as the passage says.

The answer is "They do not need a medium (matter) to travel through, so they can cross the vacuum of space."

Tip: When a question asks you to "explain" with the passage, find the sentence that gives a cause, not one that is merely true. All EM waves having the same speed is true, but it does not explain how they cross a vacuum.

Evidence: In the diagram, gamma rays are at the right end and radio waves at the left end. The arrow pointing right is labeled "Increasing frequency and energy," and the arrow pointing left is labeled "Increasing wavelength." The passage adds: "a wave with a higher frequency must have a shorter wavelength."

Step by step:

1. Gamma is to the right of radio, so gamma has the higher frequency and more energy.
2. Wavelength increases to the left, toward radio, so gamma has the shorter wavelength.
3. This fits the rule speed = frequency × wavelength: with the same speed, a higher frequency must pair with a shorter wavelength.

Gamma rays have a shorter wavelength and a higher frequency than radio waves.

Tip: For EM waves, frequency and wavelength always move in opposite directions. Any choice that makes both bigger (or both smaller) is wrong.

Evidence: The table lists Wind 120 GWh, Hydroelectric 70 GWh and Solar 60 GWh, and a total of 1,000 GWh. The passage defines renewable sources as those "replaced naturally in a human lifetime, such as sunlight, wind and flowing water."

Step by step:

1. Pick out the renewable rows: wind, hydroelectric (flowing water) and solar.
2. Add them: 120 + 70 + 60 = 250 GWh.
3. Divide by the total and change to a percent: \frac{250}{1{,}000} \times 100\% = 25\%
4. Context check: the council wants at least 40%, so Millbrook is still 15 percentage points short of its goal.

The answer is 25%.

Tip: In table questions, decide which rows count before you add. Most wrong answers come from including or leaving out one row.

Evidence: The stem says sunlight "charges the battery" in the day and "the battery powers a small bulb" at night. Energy must be stored in between.

Step by step:

1. Daytime: the panel absorbs light (radiant) energy and turns it into electrical energy.
2. Storage: charging the battery drives chemical reactions inside it, so the energy is stored as chemical energy.
3. Night: the battery's chemical energy is turned back into electrical energy in the circuit.
4. Output: the bulb turns electrical energy into light energy (plus a little thermal energy).

The answer is light → electrical → chemical → electrical → light.

Check: Every step has a cause in the story: panel, charging, battery, bulb. No step is skipped, and the chain begins and ends with light.

Tip: When a device stores energy for later (batteries, food, fuel), look for chemical energy in the middle of the chain.

Evidence: The passage says "Rain and melting snow in the mountains refill the lake every year." It also says the water "flows out into the river below the dam."

Step by step:

1. A renewable source is replaced naturally within a human lifetime. A nonrenewable source, like coal, takes millions of years to form and is used up.
2. The water is not destroyed; it flows on down the river. The lake is refilled each year by rain and snow, so the source is replaced naturally and quickly.
3. Efficiency (90%) tells how well the dam converts energy, not whether the source is replaced. The fact that some energy becomes thermal energy and sound does not decide the classification either; every energy conversion wastes some energy.

The answer is Renewable, because rain and melting snow refill the lake every year.

Check: Ask: Will it run out if we keep using it for 50 years? The lake keeps being refilled, so no.

Tip: Do not confuse renewable with efficient or clean. Classify by the replacement rate of the source.

Evidence: The passage defines specific heat as "The thermal energy needed to raise the temperature of 1 g of a substance by 1 °C" and gives water 4.18\ \text{J/(g}\cdot\text{°C)} and sand about 0.84\ \text{J/(g}\cdot\text{°C)}. Both samples were 200 g under the same model of lamp.

Step by step:

1. The setup was controlled: same mass (200 g), same starting temperature (20 °C), same lamp, same distance. So the difference must come from the materials.
2. Water's specific heat is about 5 times sand's (4.18 \div 0.84 \approx 5). Each gram of water needs about 5 times as much energy to warm by 1 °C.
3. With similar energy arriving, the water's temperature climbs more slowly (1 °C per minute versus 3.5 °C per minute for sand).

The answer is Water has a higher specific heat, so each gram needs more energy to warm by 1 °C.

Check: This matches real life: the ocean stays cooler than the beach in the afternoon and warmer at night.

Tip: High specific heat = slow to heat up and slow to cool down. Low specific heat = quick temperature change.

Evidence: The formula KE = \frac{1}{2}mv^2 shows that kinetic energy depends on the square of the speed. The speed goes from 12 m/s to 24 m/s, so it doubles.

Step by step:

1. Write the ratio, letting m and \frac{1}{2} cancel: \frac{KE_{24}}{KE_{12}} = \frac{\frac{1}{2}m(24)^2}{\frac{1}{2}m(12)^2} = \frac{576}{144} = 4
2. Another way: doubling v makes v^2 become 2^2 = 4 times larger.
3. Mass is unchanged, so only the speed term matters.

The kinetic energy becomes 4 times as large.

Check: Try any mass, say 1,000 kg: \frac{1}{2}(1000)(12^2) = 72{,}000 J and \frac{1}{2}(1000)(24^2) = 288{,}000 J; 288{,}000 \div 72{,}000 = 4.

Tip: Because speed is squared, doubling speed quadruples kinetic energy and tripling speed makes it 9 times larger. This is why braking distance grows so fast with speed.

Evidence: The diagram labels B at 0.05 m and D at 0.10 m above the lowest point. The passage explains that as the bob drops, "gravitational potential energy changes into kinetic energy"; the bob also starts with a fixed amount of energy at A.

Step by step:

1. Potential energy depends on height (PE = mgh). B (0.05 m) is lower than D (0.10 m), so the bob has less potential energy at B.
2. The bob's total energy cannot increase after it is released, and air resistance only removes a little. The energy "missing" from potential energy at B is kinetic energy.
3. So the bob has more kinetic energy (it moves faster) at B than at D.
4. Direction of travel does not matter: B is on the way down and D is on the way up, but only the height decides the split.

The answer is The bob has more kinetic energy at B than at D, because B is lower.

Check: At the very top of each side (A and E) the bob is momentarily still. D is close to E, so it should be fairly slow.

Tip: In a swinging or rolling system, compare heights: lower point = less potential energy = more kinetic energy.

Evidence: The passage gives the car's mass ("500 kg"), says it starts "at rest at point A," and explains that "friction with the track and air resistance turn a small part of it into thermal energy and sound along the way." The diagram shows A at 40 m and B at 0 m.

Step by step:

1. Total energy at A (all potential, since the car is at rest): PE = 500 \times 9.8 \times 40 = 196{,}000 J.
2. At B the height is 0 m, so potential energy is 0. If no energy were transformed by friction, kinetic energy would be 196,000 J.
3. Measured kinetic energy is 180,000 J. Difference: 196{,}000 - 180{,}000 = 16{,}000 J.
4. Energy cannot be destroyed, so the missing 16,000 J became thermal energy and sound, exactly as the passage describes.

The answer is About 16,000 J was changed into thermal energy and sound by friction and air resistance.

Tip: If energy seems to be "missing," it was transformed, usually into heat. Any choice saying energy was destroyed or created breaks the law of conservation of energy.

Evidence: The table shows the incandescent bulb takes in 60 J each second and gives out 3 J of light each second. The passage states: "All of the energy that does not come out as light becomes thermal energy."

Step by step:

1. By the law of conservation of energy, energy in = energy out (all forms together).
2. Energy out = light + thermal energy, so 60 = 3 + \text{thermal}.
3. Solve: \text{thermal} = 60 - 3 = 57\text{ J each second}

The bulb changes 57 J into thermal energy each second.

Check: 57 + 3 = 60 J, so every joule that went in is accounted for. That is why an incandescent bulb gets too hot to touch.

Tip: In conservation-of-energy questions, the "missing" energy is never gone. It usually turns into thermal energy (and sometimes sound), and you find it by subtraction.

Evidence: The graph shows the sand rising 7 °C every 2 minutes (20, 27, 34, 41, 48, 55 °C) and the water rising 2 °C every 2 minutes (20, 22, 24, 26, 28, 30 °C). Both patterns are straight lines.

Step by step:

1. Sand at 10 min: 55 °C. One more 2-minute step adds 7 °C: 55 + 7 = 62 °C.
2. Water at 10 min: 30 °C. One more 2-minute step adds 2 °C: 30 + 2 = 32 °C.
3. Check the pairing: the sand must stay the hotter of the two, because it warms faster.

The best prediction is sand about 62 °C, water about 32 °C.

Check: Using per-minute rates gives the same result: sand 3.5 \times 12 = 42 °C above 20 °C, so 62 °C; water 1 \times 12 = 12 °C above 20 °C, so 32 °C.

Tip: To extend a straight-line trend, find the steady change per step and add one more step. Keep each series separate so you do not swap them.

Evidence: The stem gives PE = 88{,}200\text{ J}, m = 60\text{ kg} and g = 9.8\ \text{m/s}^2. The unknown is h.

Step by step:

1. Start with PE = mgh and divide both sides by mg: h = \frac{PE}{mg}
2. Compute the denominator: mg = 60 \times 9.8 = 588 (this is the hiker's weight in newtons).
3. Divide: h = \frac{88{,}200}{588} = 150\text{ m}

The hilltop is 150 m higher than the start.

Check: Put it back in: 60 \times 9.8 \times 150 = 88{,}200 J. It matches.

Tip: To work backwards in a formula with three multiplied letters, divide the known result by the product of the two letters you know.

Evidence: The passage says the bob has a mass of "2.0 kg" and is released "from rest" at A, which the diagram puts at 0.20 m. C is the lowest point (0 m).

Step by step:

1. Energy at A (all potential): PE = mgh = 2.0 \times 9.8 \times 0.20 = 3.92 J.
2. With no air resistance, all of it becomes kinetic energy at C: KE = 3.92 J.
3. Solve KE = \frac{1}{2}mv^2 for v: v^2 = \frac{2 \times KE}{m} = \frac{2 \times 3.92}{2.0} = 3.92 \qquad v = \sqrt{3.92} \approx 1.98\text{ m/s}

The bob moves at about 2.0 m/s at C.

Check: \frac{1}{2}(2.0)(1.98)^2 \approx 3.92 J, matching the starting energy.

Tip: Released from rest at height h means you can set mgh = \frac{1}{2}mv^2 at the bottom. Remember the last step: take the square root to get v.

Evidence: The diagram shows A at 0.20 m and E at 0.18 m. The passage says that "air resistance changes a small amount of the bob's energy into thermal energy." At both A and E the bob is momentarily at rest, so all of its mechanical energy is potential energy.

Step by step:

1. PE_A = 2.0 \times 9.8 \times 0.20 = 3.92 J.
2. PE_E = 2.0 \times 9.8 \times 0.18 = 3.528 J.
3. Difference: 3.92 - 3.528 = 0.392 \approx 0.39 J.
4. Energy cannot be destroyed, so this 0.39 J was not lost from the universe. Air resistance changed it into thermal energy (the air and bob warmed very slightly).

The answer is About 0.39 J of the bob's energy was changed into thermal energy by air resistance.

Check: 0.39 J is about 10% of 3.92 J, a "small amount," just as the passage says.

Tip: When a ball or pendulum does not return to its starting height, the energy did not disappear. Calculate the difference in PE and call it thermal energy (and sound).

Evidence: The passage defines efficiency as useful energy out divided by total energy in, times 100%. The new bulb's useful output is 3 J each second and its efficiency is 40%.

Step by step:

1. Write the efficiency as a decimal: 40\% = 0.40.
2. Set up the formula: 0.40 = \dfrac{3\text{ J}}{\text{energy in}}.
3. Solve for the energy in by dividing: \text{energy in} = \frac{3}{0.40} = 7.5\text{ J each second}

The new bulb needs 7.5 J each second.

Check: 3 \div 7.5 = 0.40 = 40\%. The answer also fits the trend in the table: the more efficient the bulb, the less energy goes in (60 J, 15 J, 10 J, and now 7.5 J).

Tip: When you know the efficiency and the useful output, divide to find the input. The input must always be larger than the output.

Evidence: The table shows incandescent 60 J in, CFL 15 J in, LED 10 J in, and each gives "3" J of light out per second. The passage says the bulbs give off "the same amount of light."

Step by step:

1. Efficiencies: incandescent 3 \div 60 = 5\%; CFL 3 \div 15 = 20\%; LED 3 \div 10 = 30\%.
2. Claim about saving energy: switching from incandescent to LED saves 60 - 10 = 50 J each second for the same light. Supported.
3. Claim that the LED is 6 times as efficient as the CFL: the LED uses 10 J and the incandescent 60 J, so it is the incandescent that uses 6 times as much. The LED is 30\% \div 20\% = 1.5 times as efficient as the CFL. Not supported.
4. Claim that the LED gives more light: all bulbs give 3 J of light. Not supported.
5. Claim about the CFL wasting the most: the CFL wastes 15 - 3 = 12 J, but the incandescent wastes 57 J. Not supported.

The supported claim is Replacing an incandescent bulb with an LED bulb saves 50 J of electrical energy each second without reducing the light.

Check: 60 - 10 = 50, and the light stays at 3 J for both.

Tip: On which claim is supported items, do the quick math for each choice. Watch for claims that mix up which item is compared with which.

Evidence: The passage gives the speed of EM waves as "about 3.0 \times 10^8 m/s" and the wave equation v = f\lambda. The stem gives \lambda = 0.10 m.

Step by step:

1. Rearrange for frequency: f = \dfrac{v}{\lambda}.
2. Substitute: f = \frac{3.0 \times 10^8\text{ m/s}}{0.10\text{ m}}
3. Dividing by 0.10 is the same as multiplying by 10, which raises the exponent by one: f = 3.0 \times 10^9\text{ Hz}

The frequency is 3.0 \times 10^{9} Hz (3 GHz).

Check: This is close to the Wi-Fi router's 5.0 \times 10^9 Hz in the table, and both are microwaves, so the size makes sense. Also 3.0 \times 10^9 \times 0.10 = 3.0 \times 10^8. ✓

Tip: Units guide the setup: (m/s) ÷ m = 1/s = Hz. If your units do not come out as hertz, you have set up the division the wrong way.