Unit 12 — End of Topic Tests (reviewer copy: all keys and model answers visible)

[
 {
  "value": 340,
  "misconception": "you gave the total converted energy instead of the thermal share — subtract the light and sound from the 340 J",
  "feedback": "This answer is wrong — 340 J is everything the television converted. The thermal share is what remains after light and sound: 340 − 48 − 10 = 282 J."
 },
 {
  "value": 58,
  "misconception": "you gave the light plus sound instead of what remains — 48 + 10 = 58 J is the part already accounted for",
  "feedback": "This answer is wrong — 58 J is the light and sound together. The thermal share is the remainder: 340 − 58 = 282 J."
 },
 {
  "value": 398,
  "misconception": "you added everything together — energy in must equal energy out, so the thermal share is 340 minus the 58 J of light and sound",
  "feedback": "This answer is wrong — adding makes more energy leave than entered. Conservation demands 340 in = 340 out, so thermal = 340 − 48 − 10 = 282 J."
 },
 {
  "value": 292,
  "misconception": "you subtracted only the light — the 10 J of sound must be accounted for too",
  "feedback": "This answer is wrong — 340 − 48 leaves the sound unaccounted. Subtract both named outputs: 340 − 48 − 10 = 282 J."
 }
]

{
 "keyExplanation": "Energy cannot be created or destroyed, so all 340 J must leave in some form. Light and sound account for 48 J + 10 J = 58 J. The rest becomes thermal energy: 340 J − 58 J = 282 J.",
 "anticipatedWrong": [
  {
   "value": 340,
   "misconception": "you gave the total converted energy instead of the thermal share — subtract the light and sound from the 340 J",
   "feedback": "This answer is wrong — 340 J is everything the television converted. The thermal share is what remains after light and sound: 340 − 48 − 10 = 282 J."
  },
  {
   "value": 58,
   "misconception": "you gave the light plus sound instead of what remains — 48 + 10 = 58 J is the part already accounted for",
   "feedback": "This answer is wrong — 58 J is the light and sound together. The thermal share is the remainder: 340 − 58 = 282 J."
  },
  {
   "value": 398,
   "misconception": "you added everything together — energy in must equal energy out, so the thermal share is 340 minus the 58 J of light and sound",
   "feedback": "This answer is wrong — adding makes more energy leave than entered. Conservation demands 340 in = 340 out, so thermal = 340 − 48 − 10 = 282 J."
  },
  {
   "value": 292,
   "misconception": "you subtracted only the light — the 10 J of sound must be accounted for too",
   "feedback": "This answer is wrong — 340 − 48 leaves the sound unaccounted. Subtract both named outputs: 340 − 48 − 10 = 282 J."
  }
 ]
}

[
 {
  "value": 320,
  "misconception": "you gave the total converted energy instead of the thermal share — subtract the light and sound from the 320 J",
  "feedback": "This answer is wrong — 320 J is everything the projector converted. Thermal = 320 − 36 − 23 = 261 J."
 },
 {
  "value": 59,
  "misconception": "you gave the light plus sound instead of what remains — 36 + 23 = 59 J is the part already accounted for",
  "feedback": "This answer is wrong — 59 J is the light and sound together. Thermal is the remainder: 320 − 59 = 261 J."
 },
 {
  "value": 379,
  "misconception": "you added everything together — energy in must equal energy out, so the thermal share is 320 minus the 59 J of light and sound",
  "feedback": "This answer is wrong — adding makes more leave than entered. 320 in = 320 out, so thermal = 261 J."
 },
 {
  "value": 284,
  "misconception": "you subtracted only the light — the 23 J of sound must be accounted for too",
  "feedback": "This answer is wrong — 320 − 36 leaves the sound unaccounted. Subtract both: 320 − 36 − 23 = 261 J."
 }
]

{
 "keyExplanation": "Energy cannot be created or destroyed, so all 320 J must leave in some form. Light and sound account for 36 J + 23 J = 59 J. The rest becomes thermal energy: 320 J − 59 J = 261 J.",
 "anticipatedWrong": [
  {
   "value": 320,
   "misconception": "you gave the total converted energy instead of the thermal share — subtract the light and sound from the 320 J",
   "feedback": "This answer is wrong — 320 J is everything the projector converted. Thermal = 320 − 36 − 23 = 261 J."
  },
  {
   "value": 59,
   "misconception": "you gave the light plus sound instead of what remains — 36 + 23 = 59 J is the part already accounted for",
   "feedback": "This answer is wrong — 59 J is the light and sound together. Thermal is the remainder: 320 − 59 = 261 J."
  },
  {
   "value": 379,
   "misconception": "you added everything together — energy in must equal energy out, so the thermal share is 320 minus the 59 J of light and sound",
   "feedback": "This answer is wrong — adding makes more leave than entered. 320 in = 320 out, so thermal = 261 J."
  },
  {
   "value": 284,
   "misconception": "you subtracted only the light — the 23 J of sound must be accounted for too",
   "feedback": "This answer is wrong — 320 − 36 leaves the sound unaccounted. Subtract both: 320 − 36 − 23 = 261 J."
  }
 ]
}

[
 {
  "value": 450,
  "misconception": "you gave the total converted energy instead of the thermal share — subtract the motion and sound from the 450 J",
  "feedback": "This answer is wrong — 450 J is everything the blender converted. Thermal = 450 − 92 − 17 = 341 J."
 },
 {
  "value": 109,
  "misconception": "you gave the motion plus sound instead of what remains — 92 + 17 = 109 J is the part already accounted for",
  "feedback": "This answer is wrong — 109 J is the motion and sound together. Thermal is the remainder: 450 − 109 = 341 J."
 },
 {
  "value": 559,
  "misconception": "you added everything together — energy in must equal energy out, so the thermal share is 450 minus the 109 J of motion and sound",
  "feedback": "This answer is wrong — adding makes more leave than entered. 450 in = 450 out, so thermal = 341 J."
 },
 {
  "value": 358,
  "misconception": "you subtracted only the motion — the 17 J of sound must be accounted for too",
  "feedback": "This answer is wrong — 450 − 92 leaves the sound unaccounted. Subtract both: 450 − 92 − 17 = 341 J."
 }
]

{
 "keyExplanation": "Energy cannot be created or destroyed, so all 450 J must leave in some form. Motion and sound account for 92 J + 17 J = 109 J. The rest becomes thermal energy: 450 J − 109 J = 341 J.",
 "anticipatedWrong": [
  {
   "value": 450,
   "misconception": "you gave the total converted energy instead of the thermal share — subtract the motion and sound from the 450 J",
   "feedback": "This answer is wrong — 450 J is everything the blender converted. Thermal = 450 − 92 − 17 = 341 J."
  },
  {
   "value": 109,
   "misconception": "you gave the motion plus sound instead of what remains — 92 + 17 = 109 J is the part already accounted for",
   "feedback": "This answer is wrong — 109 J is the motion and sound together. Thermal is the remainder: 450 − 109 = 341 J."
  },
  {
   "value": 559,
   "misconception": "you added everything together — energy in must equal energy out, so the thermal share is 450 minus the 109 J of motion and sound",
   "feedback": "This answer is wrong — adding makes more leave than entered. 450 in = 450 out, so thermal = 341 J."
  },
  {
   "value": 358,
   "misconception": "you subtracted only the motion — the 17 J of sound must be accounted for too",
   "feedback": "This answer is wrong — 450 − 92 leaves the sound unaccounted. Subtract both: 450 − 92 − 17 = 341 J."
  }
 ]
}

[
 {
  "value": 280,
  "misconception": "you gave the total converted energy instead of the thermal share — subtract the motion and sound from the 280 J",
  "feedback": "This answer is wrong — 280 J is everything the machine converted. Thermal = 280 − 63 − 9 = 208 J."
 },
 {
  "value": 72,
  "misconception": "you gave the motion plus sound instead of what remains — 63 + 9 = 72 J is the part already accounted for",
  "feedback": "This answer is wrong — 72 J is the motion and sound together. Thermal is the remainder: 280 − 72 = 208 J."
 },
 {
  "value": 352,
  "misconception": "you added everything together — energy in must equal energy out, so the thermal share is 280 minus the 72 J of motion and sound",
  "feedback": "This answer is wrong — adding makes more leave than entered. 280 in = 280 out, so thermal = 208 J."
 },
 {
  "value": 217,
  "misconception": "you subtracted only the motion — the 9 J of sound must be accounted for too",
  "feedback": "This answer is wrong — 280 − 63 leaves the sound unaccounted. Subtract both: 280 − 63 − 9 = 208 J."
 }
]

{
 "keyExplanation": "Energy cannot be created or destroyed, so all 280 J must leave in some form. Motion and sound account for 63 J + 9 J = 72 J. The rest becomes thermal energy: 280 J − 72 J = 208 J.",
 "anticipatedWrong": [
  {
   "value": 280,
   "misconception": "you gave the total converted energy instead of the thermal share — subtract the motion and sound from the 280 J",
   "feedback": "This answer is wrong — 280 J is everything the machine converted. Thermal = 280 − 63 − 9 = 208 J."
  },
  {
   "value": 72,
   "misconception": "you gave the motion plus sound instead of what remains — 63 + 9 = 72 J is the part already accounted for",
   "feedback": "This answer is wrong — 72 J is the motion and sound together. Thermal is the remainder: 280 − 72 = 208 J."
  },
  {
   "value": 352,
   "misconception": "you added everything together — energy in must equal energy out, so the thermal share is 280 minus the 72 J of motion and sound",
   "feedback": "This answer is wrong — adding makes more leave than entered. 280 in = 280 out, so thermal = 208 J."
  },
  {
   "value": 217,
   "misconception": "you subtracted only the motion — the 9 J of sound must be accounted for too",
   "feedback": "This answer is wrong — 280 − 63 leaves the sound unaccounted. Subtract both: 280 − 63 − 9 = 208 J."
  }
 ]
}

[
 {
  "value": 540,
  "misconception": "you gave the total converted energy instead of the thermal share — subtract the motion and light from the 540 J",
  "feedback": "This answer is wrong — 540 J is everything the scooter converted. Thermal = 540 − 210 − 26 = 304 J."
 },
 {
  "value": 236,
  "misconception": "you gave the motion plus light instead of what remains — 210 + 26 = 236 J is the part already accounted for",
  "feedback": "This answer is wrong — 236 J is the motion and light together. Thermal is the remainder: 540 − 236 = 304 J."
 },
 {
  "value": 776,
  "misconception": "you added everything together — energy in must equal energy out, so the thermal share is 540 minus the 236 J of motion and light",
  "feedback": "This answer is wrong — adding makes more leave than entered. 540 in = 540 out, so thermal = 304 J."
 },
 {
  "value": 330,
  "misconception": "you subtracted only the motion — the 26 J of light must be accounted for too",
  "feedback": "This answer is wrong — 540 − 210 leaves the light unaccounted. Subtract both: 540 − 210 − 26 = 304 J."
 }
]

{
 "keyExplanation": "Energy cannot be created or destroyed, so all 540 J must leave in some form. Motion and light account for 210 J + 26 J = 236 J. The rest becomes thermal energy: 540 J − 236 J = 304 J.",
 "anticipatedWrong": [
  {
   "value": 540,
   "misconception": "you gave the total converted energy instead of the thermal share — subtract the motion and light from the 540 J",
   "feedback": "This answer is wrong — 540 J is everything the scooter converted. Thermal = 540 − 210 − 26 = 304 J."
  },
  {
   "value": 236,
   "misconception": "you gave the motion plus light instead of what remains — 210 + 26 = 236 J is the part already accounted for",
   "feedback": "This answer is wrong — 236 J is the motion and light together. Thermal is the remainder: 540 − 236 = 304 J."
  },
  {
   "value": 776,
   "misconception": "you added everything together — energy in must equal energy out, so the thermal share is 540 minus the 236 J of motion and light",
   "feedback": "This answer is wrong — adding makes more leave than entered. 540 in = 540 out, so thermal = 304 J."
  },
  {
   "value": 330,
   "misconception": "you subtracted only the motion — the 26 J of light must be accounted for too",
   "feedback": "This answer is wrong — 540 − 210 leaves the light unaccounted. Subtract both: 540 − 210 − 26 = 304 J."
  }
 ]
}

[
 {
  "value": 25916,
  "misconception": "you kept the energy the same because the temperature change is the same — three times the mass needs three times the energy",
  "feedback": "This answer is wrong — 25916 J warms only the 310 g. Three times the grams need three times the shares: 3 × 25916 J = 77748 J."
 },
 {
  "value": 8638.67,
  "misconception": "you divided by three instead of multiplying — more mass needs more energy",
  "feedback": "This answer is wrong — dividing gives less energy for more water. Three times the mass needs three times the energy: 77748 J."
 }
]

{
 "keyExplanation": "Same material, same temperature change — only the mass differs. 930 g is three times 310 g. Three times the mass needs three times the energy: 3 × 25916 J = 77748 J.",
 "anticipatedWrong": [
  {
   "value": 25916,
   "misconception": "you kept the energy the same because the temperature change is the same — three times the mass needs three times the energy",
   "feedback": "This answer is wrong — 25916 J warms only the 310 g. Three times the grams need three times the shares: 3 × 25916 J = 77748 J."
  },
  {
   "value": 8638.67,
   "misconception": "you divided by three instead of multiplying — more mass needs more energy",
   "feedback": "This answer is wrong — dividing gives less energy for more water. Three times the mass needs three times the energy: 77748 J."
  }
 ]
}

[
 {
  "value": 14965.33,
  "misconception": "you scaled by the ratio of the final readings (64/24) — the energy follows the ratio of the CHANGES, not the finals",
  "feedback": "This answer is wrong — 64 and 24 are readings, not changes. The changes are 10 °C and 50 °C: five times the change, so 5 × 5612 J = 28060 J."
 },
 {
  "value": 5612,
  "misconception": "you kept the energy the same because the sample is the same — a bigger temperature change needs proportionally more energy",
  "feedback": "This answer is wrong — 5612 J pays for only a 10 °C change. A 50 °C change costs five shares: 28060 J."
 }
]

{
 "keyExplanation": "Same sample, so the mass and material are fixed — only the temperature CHANGE matters. The first change is 24 − 14 = 10 °C; the second is 64 − 14 = 50 °C — five times the change. Five times the change needs five times the energy: 5 × 5612 J = 28060 J.",
 "anticipatedWrong": [
  {
   "value": 14965.33,
   "misconception": "you scaled by the ratio of the final readings (64/24) — the energy follows the ratio of the CHANGES, not the finals",
   "feedback": "This answer is wrong — 64 and 24 are readings, not changes. The changes are 10 °C and 50 °C: five times the change, so 5 × 5612 J = 28060 J."
  },
  {
   "value": 5612,
   "misconception": "you kept the energy the same because the sample is the same — a bigger temperature change needs proportionally more energy",
   "feedback": "This answer is wrong — 5612 J pays for only a 10 °C change. A 50 °C change costs five shares: 28060 J."
  }
 ]
}

[
 {
  "value": 188936.0,
  "misconception": "you used the final temperature instead of the temperature change — ΔT = 56.5 − 44.0 = 12.5 °C",
  "feedback": "This answer is wrong — 56.5 is a reading, not a change. ΔT = 12.5 °C, so q = 800.0 × 4.18 × 12.5 = 41,800 J."
 },
 {
  "value": 52.25,
  "misconception": "you left out the mass — all three quantities on the right multiply",
  "feedback": "This answer is wrong — 4.18 × 12.5 covers only one gram. Multiply by the 800.0 g as well: q = 41,800 J."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 800.0 g\nc = 4.18 J/(g·°C)\nΔT = 56.5 − 44.0 = 12.5 °C\nWrite down the equation:\nq = mcΔT\nSubstitute in the values, and calculate:\nq = 800.0 × 4.18 × 12.5\nq = 41,800 J\nWater's high specific heat capacity makes tens of thousands of joules a sensible size for warming a big kettle's worth of water through 12.5 °C.",
 "anticipatedWrong": [
  {
   "value": 188936.0,
   "misconception": "you used the final temperature instead of the temperature change — ΔT = 56.5 − 44.0 = 12.5 °C",
   "feedback": "This answer is wrong — 56.5 is a reading, not a change. ΔT = 12.5 °C, so q = 800.0 × 4.18 × 12.5 = 41,800 J."
  },
  {
   "value": 52.25,
   "misconception": "you left out the mass — all three quantities on the right multiply",
   "feedback": "This answer is wrong — 4.18 × 12.5 covers only one gram. Multiply by the 800.0 g as well: q = 41,800 J."
  }
 ]
}

[
 {
  "value": 1.28,
  "misconception": "you divided by the mass only — divide by both the mass and the temperature change",
  "feedback": "This answer is wrong — divide by m AND ΔT together: c = 640 ÷ (500.0 × 10.0) = 0.128 J/(g·°C)."
 },
 {
  "value": 64.0,
  "misconception": "you divided by the temperature change only — divide by both the mass and the temperature change",
  "feedback": "This answer is wrong — divide by m AND ΔT together: c = 640 ÷ (500.0 × 10.0) = 0.128 J/(g·°C)."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nq = 640 J\nm = 500.0 g\nΔT = 10.0 °C\nWrite down the equation:\nq = mcΔT\nMake c the subject:\nc = q ÷ (m × ΔT)\nSubstitute in the values, and calculate:\nc = 640 ÷ (500.0 × 10.0)\nc = 0.128 J/(g·°C)\nThat is the table value for lead — a very low specific heat capacity, which is why a small energy input warms the sinker so easily.",
 "anticipatedWrong": [
  {
   "value": 1.28,
   "misconception": "you divided by the mass only — divide by both the mass and the temperature change",
   "feedback": "This answer is wrong — divide by m AND ΔT together: c = 640 ÷ (500.0 × 10.0) = 0.128 J/(g·°C)."
  },
  {
   "value": 64.0,
   "misconception": "you divided by the temperature change only — divide by both the mass and the temperature change",
   "feedback": "This answer is wrong — divide by m AND ΔT together: c = 640 ÷ (500.0 × 10.0) = 0.128 J/(g·°C)."
  }
 ]
}

[
 {
  "value": -4600,
  "misconception": "you reported a negative value — heat lost and heat gained are magnitudes here, and 'lost' already carries the direction",
  "feedback": "This answer is wrong in form — give the size of the transfer: the steel block lost 4600 J."
 },
 {
  "value": 9200,
  "misconception": "you doubled the energy, counting it once leaving the block and once entering the water — it is the same 4600 J, transferred once",
  "feedback": "This answer is wrong — one transfer, counted from either end: the block lost exactly the 4600 J the water gained."
 }
]

{
 "keyExplanation": "The chest is insulated, so no energy escapes to anything else, and the heat lost by the hotter object equals the heat gained by the colder object. The water gained 4600 J, so the steel block lost exactly 4600 J — one transfer, counted from either end.",
 "anticipatedWrong": [
  {
   "value": -4600,
   "misconception": "you reported a negative value — heat lost and heat gained are magnitudes here, and 'lost' already carries the direction",
   "feedback": "This answer is wrong in form — give the size of the transfer: the steel block lost 4600 J."
  },
  {
   "value": 9200,
   "misconception": "you doubled the energy, counting it once leaving the block and once entering the water — it is the same 4600 J, transferred once",
   "feedback": "This answer is wrong — one transfer, counted from either end: the block lost exactly the 4600 J the water gained."
  }
 ]
}

[
 {
  "value": 209,
  "misconception": "you used the solid's 10.0 g as m — the calorimeter reads the WATER, so the water's mass goes into q = mcΔT",
  "feedback": "This answer is wrong — the 10.0 g is the dissolving solid, not the absorber. Use the water's 260.0 g: q = 260.0 × 4.18 × 5.0 = 5,434 J."
 },
 {
  "value": 28474.16,
  "misconception": "you used the final temperature instead of the temperature change — ΔT = 26.2 − 21.2 = 5.0 °C",
  "feedback": "This answer is wrong — 26.2 is a reading, not a change. ΔT = 5.0 °C, so q = 5,434 J."
 },
 {
  "value": 1300,
  "misconception": "you left out c — every gram of water charges 4.18 J per degree",
  "feedback": "This answer is wrong — 260.0 × 5.0 skips the price per gram per degree. Multiply by 4.18: q = 5,434 J."
 }
]

{
 "keyExplanation": "The calorimeter measures the process through the WATER. For the water:\nm = 260.0 g (the water, not the 10.0 g solid)\nc = 4.18 J/(g·°C)\nΔT = 26.2 − 21.2 = 5.0 °C\nWrite down the equation:\nq = mcΔT\nSubstitute in the values, and calculate:\nq = 260.0 × 4.18 × 5.0\nq = 5,434 J\nThe water warmed, so the dissolving RELEASED 5,434 J into it.",
 "anticipatedWrong": [
  {
   "value": 209,
   "misconception": "you used the solid's 10.0 g as m — the calorimeter reads the WATER, so the water's mass goes into q = mcΔT",
   "feedback": "This answer is wrong — the 10.0 g is the dissolving solid, not the absorber. Use the water's 260.0 g: q = 260.0 × 4.18 × 5.0 = 5,434 J."
  },
  {
   "value": 28474.16,
   "misconception": "you used the final temperature instead of the temperature change — ΔT = 26.2 − 21.2 = 5.0 °C",
   "feedback": "This answer is wrong — 26.2 is a reading, not a change. ΔT = 5.0 °C, so q = 5,434 J."
  },
  {
   "value": 1300,
   "misconception": "you left out c — every gram of water charges 4.18 J per degree",
   "feedback": "This answer is wrong — 260.0 × 5.0 skips the price per gram per degree. Multiply by 4.18: q = 5,434 J."
  }
 ]
}

[
 {
  "value": 2364,
  "misconception": "you kept the energy the same because the temperature change is the same — three times the mass needs three times the energy",
  "feedback": "This answer is wrong — 2364 J warms only the 120 g. Three times the grams need three times the shares: 3 × 2364 J = 7092 J."
 },
 {
  "value": 788,
  "misconception": "you divided by three instead of multiplying — more mass needs more energy",
  "feedback": "This answer is wrong — dividing gives less energy for more oil. Three times the mass needs three times the energy: 7092 J."
 }
]

{
 "keyExplanation": "Same material, same temperature change — only the mass differs. 360 g is three times 120 g. Three times the mass needs three times the energy: 3 × 2364 J = 7092 J.",
 "anticipatedWrong": [
  {
   "value": 2364,
   "misconception": "you kept the energy the same because the temperature change is the same — three times the mass needs three times the energy",
   "feedback": "This answer is wrong — 2364 J warms only the 120 g. Three times the grams need three times the shares: 3 × 2364 J = 7092 J."
  },
  {
   "value": 788,
   "misconception": "you divided by three instead of multiplying — more mass needs more energy",
   "feedback": "This answer is wrong — dividing gives less energy for more oil. Three times the mass needs three times the energy: 7092 J."
  }
 ]
}

[
 {
  "value": 11913,
  "misconception": "you scaled by the ratio of the final temperatures, 57 ÷ 27, instead of the ratio of the changes — the changes are 40 °C and 10 °C",
  "feedback": "This answer is wrong — 57 ÷ 27 compares readings, not changes. The changes are 10 °C and 40 °C, so the energy is 4 × 5643 J = 22572 J."
 },
 {
  "value": 5643,
  "misconception": "you kept the energy the same because it is the same sample — the temperature change quadrupled, so the energy quadruples",
  "feedback": "This answer is wrong — 5643 J covers only a 10 °C change. A 40 °C change on the same sample needs four times as much: 22572 J."
 }
]

{
 "keyExplanation": "Work with the CHANGES, not the final temperatures. First change: 27 − 17 = 10 °C. Second change: 57 − 17 = 40 °C — four times as large. Four times the change needs four times the energy: 4 × 5643 J = 22572 J.",
 "anticipatedWrong": [
  {
   "value": 11913,
   "misconception": "you scaled by the ratio of the final temperatures, 57 ÷ 27, instead of the ratio of the changes — the changes are 40 °C and 10 °C",
   "feedback": "This answer is wrong — 57 ÷ 27 compares readings, not changes. The changes are 10 °C and 40 °C, so the energy is 4 × 5643 J = 22572 J."
  },
  {
   "value": 5643,
   "misconception": "you kept the energy the same because it is the same sample — the temperature change quadrupled, so the energy quadruples",
   "feedback": "This answer is wrong — 5643 J covers only a 10 °C change. A 40 °C change on the same sample needs four times as much: 22572 J."
  }
 ]
}

[
 {
  "value": 7.9,
  "misconception": "you substituted the mass in kilograms — m must be in grams, and 2.00 kg = 2000 g",
  "feedback": "This answer is wrong — one thousand times too small. Convert first: 2.00 kg = 2000 g, so q = 2000 × 0.790 × 5.0 = 7900 J."
 },
 {
  "value": 790.0,
  "misconception": "you converted 2.00 kg to 200 g — kilo- means one thousand, so 2.00 kg = 2000 g",
  "feedback": "This answer is wrong — ten times too small. 2.00 kg = 2000 g, so q = 2000 × 0.790 × 5.0 = 7900 J."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 2.00 kg = 2000 g\nc = 0.790 J/(g·°C)\nΔT = 5.0 °C\nWrite down the equation:\nq = mcΔT\nSubstitute in the values, and calculate:\nq = 2000 × 0.790 × 5.0\nq = 7900 J\nThe mass must go in as grams because c is joules per GRAM per degree — kilo- means one thousand, so 2.00 kg is 2000 g.",
 "anticipatedWrong": [
  {
   "value": 7.9,
   "misconception": "you substituted the mass in kilograms — m must be in grams, and 2.00 kg = 2000 g",
   "feedback": "This answer is wrong — one thousand times too small. Convert first: 2.00 kg = 2000 g, so q = 2000 × 0.790 × 5.0 = 7900 J."
  },
  {
   "value": 790.0,
   "misconception": "you converted 2.00 kg to 200 g — kilo- means one thousand, so 2.00 kg = 2000 g",
   "feedback": "This answer is wrong — ten times too small. 2.00 kg = 2000 g, so q = 2000 × 0.790 × 5.0 = 7900 J."
  }
 ]
}

[
 {
  "value": 5.0,
  "misconception": "you stopped at the temperature change — 5.0 °C is ΔT; add it to the initial temperature to get the final temperature",
  "feedback": "This answer is wrong — 5.0 °C is the CHANGE. Final temperature = 13.5 + 5.0 = 18.5 °C."
 },
 {
  "value": 34.4,
  "misconception": "you divided by the mass only, skipping the specific heat capacity, before adding to the initial temperature",
  "feedback": "This answer is wrong — divide by both m and c: ΔT = 5016 ÷ (240.0 × 4.18) = 5.0 °C, so the final temperature is 18.5 °C."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nq = 5016 J\nm = 240.0 g\nc = 4.18 J/(g·°C)\ninitial temperature = 13.5 °C\nWrite down the equation:\nq = mcΔT\nMake ΔT the subject:\nΔT = q ÷ (m × c)\nSubstitute in the values, and calculate:\nΔT = 5016 ÷ (240.0 × 4.18)\nΔT = 5.0 °C\nThe water warms by 5.0 °C, so its final temperature is 13.5 + 5.0 = 18.5 °C.",
 "anticipatedWrong": [
  {
   "value": 5.0,
   "misconception": "you stopped at the temperature change — 5.0 °C is ΔT; add it to the initial temperature to get the final temperature",
   "feedback": "This answer is wrong — 5.0 °C is the CHANGE. Final temperature = 13.5 + 5.0 = 18.5 °C."
  },
  {
   "value": 34.4,
   "misconception": "you divided by the mass only, skipping the specific heat capacity, before adding to the initial temperature",
   "feedback": "This answer is wrong — divide by both m and c: ΔT = 5016 ÷ (240.0 × 4.18) = 5.0 °C, so the final temperature is 18.5 °C."
  }
 ]
}

[
 {
  "value": -1730,
  "misconception": "you reported a negative value — heat lost and heat gained are magnitudes here, and 'gain' already carries the direction",
  "feedback": "This answer is wrong in form — give the size of the transfer: the water gained 1730 J."
 },
 {
  "value": 3460,
  "misconception": "you doubled the energy, counting it once leaving the bolt and once entering the water — it is the same 1730 J, transferred once",
  "feedback": "This answer is wrong — one transfer, counted from either end: the water gained exactly the 1730 J the bolt lost."
 }
]

{
 "keyExplanation": "The canister is sealed and insulated, so no energy escapes to anything else. The heat lost by the hotter object equals the heat gained by the colder object: the bolt lost 1730 J, so the water gained 1730 J.",
 "anticipatedWrong": [
  {
   "value": -1730,
   "misconception": "you reported a negative value — heat lost and heat gained are magnitudes here, and 'gain' already carries the direction",
   "feedback": "This answer is wrong in form — give the size of the transfer: the water gained 1730 J."
  },
  {
   "value": 3460,
   "misconception": "you doubled the energy, counting it once leaving the bolt and once entering the water — it is the same 1730 J, transferred once",
   "feedback": "This answer is wrong — one transfer, counted from either end: the water gained exactly the 1730 J the bolt lost."
  }
 ]
}

[
 {
  "value": 39877.2,
  "misconception": "you used the final temperature instead of the temperature change — ΔT = 26.5 − 24.0 = 2.5 °C",
  "feedback": "This answer is wrong — 26.5 is a reading, not a change. ΔT = 2.5 °C, so q = 360.0 × 4.18 × 2.5 = 3,762 J."
 },
 {
  "value": 900,
  "misconception": "you left out c — every gram of water charges 4.18 J per degree",
  "feedback": "This answer is wrong — 360.0 × 2.5 skips the price per gram per degree. Multiply by 4.18: q = 3,762 J."
 }
]

{
 "keyExplanation": "The calorimeter measures the reaction through the WATER. For the water:\nm = 360.0 g\nc = 4.18 J/(g·°C)\nΔT = 26.5 − 24.0 = 2.5 °C\nWrite down the equation:\nq = mcΔT\nSubstitute in the values, and calculate:\nq = 360.0 × 4.18 × 2.5\nq = 3,762 J\nThe water warmed, so the reaction RELEASED 3,762 J into it.",
 "anticipatedWrong": [
  {
   "value": 39877.2,
   "misconception": "you used the final temperature instead of the temperature change — ΔT = 26.5 − 24.0 = 2.5 °C",
   "feedback": "This answer is wrong — 26.5 is a reading, not a change. ΔT = 2.5 °C, so q = 360.0 × 4.18 × 2.5 = 3,762 J."
  },
  {
   "value": 900,
   "misconception": "you left out c — every gram of water charges 4.18 J per degree",
   "feedback": "This answer is wrong — 360.0 × 2.5 skips the price per gram per degree. Multiply by 4.18: q = 3,762 J."
  }
 ]
}

[
 {
  "value": 12122,
  "misconception": "you kept the energy the same because the temperature change is the same — twice the mass needs twice the energy",
  "feedback": "This answer is wrong — 12122 J warms only the 580 g. Twice the grams need twice the shares: 2 × 12122 J = 24244 J."
 },
 {
  "value": 6061,
  "misconception": "you divided by two instead of multiplying — more mass needs more energy",
  "feedback": "This answer is wrong — dividing gives less energy for more water. Twice the mass needs twice the energy: 24244 J."
 }
]

{
 "keyExplanation": "Same material, same temperature change — only the mass differs. 1160 g is twice 580 g. Twice the mass needs twice the energy: 2 × 12122 J = 24244 J.",
 "anticipatedWrong": [
  {
   "value": 12122,
   "misconception": "you kept the energy the same because the temperature change is the same — twice the mass needs twice the energy",
   "feedback": "This answer is wrong — 12122 J warms only the 580 g. Twice the grams need twice the shares: 2 × 12122 J = 24244 J."
  },
  {
   "value": 6061,
   "misconception": "you divided by two instead of multiplying — more mass needs more energy",
   "feedback": "This answer is wrong — dividing gives less energy for more water. Twice the mass needs twice the energy: 24244 J."
  }
 ]
}

[
 {
  "value": 1708,
  "misconception": "you kept the energy the same because it is the same sample — three times the change needs three times the energy",
  "feedback": "This answer is wrong — 1708 J covers only a 4 °C change. A 12 °C change on the same sample needs 3 × 1708 J = 5124 J."
 },
 {
  "value": 569,
  "misconception": "you divided by three instead of multiplying — a bigger change needs more energy",
  "feedback": "This answer is wrong — dividing gives less energy for a bigger change. Three times the change needs three times the energy: 5124 J."
 }
]

{
 "keyExplanation": "Same material, same mass — only the temperature change differs. 12 °C is three times 4 °C, and three times the change needs three times the energy: 3 × 1708 J = 5124 J.",
 "anticipatedWrong": [
  {
   "value": 1708,
   "misconception": "you kept the energy the same because it is the same sample — three times the change needs three times the energy",
   "feedback": "This answer is wrong — 1708 J covers only a 4 °C change. A 12 °C change on the same sample needs 3 × 1708 J = 5124 J."
  },
  {
   "value": 569,
   "misconception": "you divided by three instead of multiplying — a bigger change needs more energy",
   "feedback": "This answer is wrong — dividing gives less energy for a bigger change. Three times the change needs three times the energy: 5124 J."
  }
 ]
}

[
 {
  "value": 29134.6,
  "misconception": "you used the final temperature instead of the temperature change — ΔT = 41.0 − 31.0 = 10.0 °C",
  "feedback": "This answer is wrong — 41.0 is a reading, not a change. ΔT = 41.0 − 31.0 = 10.0 °C, giving q = 7106 J."
 },
 {
  "value": 41.8,
  "misconception": "you left out the mass — all three quantities on the right multiply",
  "feedback": "This answer is wrong — 4.18 × 10.0 covers only one gram. Multiply by the 170.0 g as well: q = 7106 J."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 170.0 g\nc = 4.18 J/(g·°C)\nΔT = 41.0 − 31.0 = 10.0 °C\nWrite down the equation:\nq = mcΔT\nSubstitute in the values, and calculate:\nq = 170.0 × 4.18 × 10.0\nq = 7106 J",
 "anticipatedWrong": [
  {
   "value": 29134.6,
   "misconception": "you used the final temperature instead of the temperature change — ΔT = 41.0 − 31.0 = 10.0 °C",
   "feedback": "This answer is wrong — 41.0 is a reading, not a change. ΔT = 41.0 − 31.0 = 10.0 °C, giving q = 7106 J."
  },
  {
   "value": 41.8,
   "misconception": "you left out the mass — all three quantities on the right multiply",
   "feedback": "This answer is wrong — 4.18 × 10.0 covers only one gram. Multiply by the 170.0 g as well: q = 7106 J."
  }
 ]
}

[
 {
  "value": 794.2,
  "misconception": "you left out c and divided the energy by the temperature change alone — every gram of water charges 4.18 J per degree",
  "feedback": "This answer is wrong — 3971 ÷ 5.0 skips the price per gram per degree. Divide by c × ΔT: m = 3971 ÷ (4.18 × 5.0) = 190 g."
 },
 {
  "value": 950.0,
  "misconception": "you left out the temperature change and divided the energy by c alone — the 5.0 °C change multiplies c in the divisor",
  "feedback": "This answer is wrong — 3971 ÷ 4.18 covers only one degree of warming. Divide by c × ΔT: m = 3971 ÷ (4.18 × 5.0) = 190 g."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nq = 3971 J\nc = 4.18 J/(g·°C)\nΔT = 5.0 °C\nWrite down the equation:\nq = mcΔT\nMake m the subject:\nm = q ÷ (c × ΔT)\nSubstitute in the values, and calculate:\nm = 3971 ÷ (4.18 × 5.0)\nm = 190 g",
 "anticipatedWrong": [
  {
   "value": 794.2,
   "misconception": "you left out c and divided the energy by the temperature change alone — every gram of water charges 4.18 J per degree",
   "feedback": "This answer is wrong — 3971 ÷ 5.0 skips the price per gram per degree. Divide by c × ΔT: m = 3971 ÷ (4.18 × 5.0) = 190 g."
  },
  {
   "value": 950.0,
   "misconception": "you left out the temperature change and divided the energy by c alone — the 5.0 °C change multiplies c in the divisor",
   "feedback": "This answer is wrong — 3971 ÷ 4.18 covers only one degree of warming. Divide by c × ΔT: m = 3971 ÷ (4.18 × 5.0) = 190 g."
  }
 ]
}

[
 {
  "value": -2840,
  "misconception": "you reported a negative value — heat lost and heat gained are magnitudes here, and the words carry the direction",
  "feedback": "This answer is wrong in form — give the size of the transfer: the water gained 2840 J."
 },
 {
  "value": 1420,
  "misconception": "you split the transfer in half between the brick and the water — the whole 2840 J moves into the water",
  "feedback": "This answer is wrong — nothing is split. Inside the insulated box the water gains everything the brick loses: 2840 J."
 }
]

{
 "keyExplanation": "The storage box is sealed and insulated, so the transferred energy has nowhere else to go. Heat lost equals heat gained: the brick lost 2840 J, so the water gained exactly 2840 J.",
 "anticipatedWrong": [
  {
   "value": -2840,
   "misconception": "you reported a negative value — heat lost and heat gained are magnitudes here, and the words carry the direction",
   "feedback": "This answer is wrong in form — give the size of the transfer: the water gained 2840 J."
  },
  {
   "value": 1420,
   "misconception": "you split the transfer in half between the brick and the water — the whole 2840 J moves into the water",
   "feedback": "This answer is wrong — nothing is split. Inside the insulated box the water gains everything the brick loses: 2840 J."
  }
 ]
}

[
 {
  "value": 62.7,
  "misconception": "you used the solid's mass instead of the water's — the equation is run on the WATER, the substance whose temperature was measured",
  "feedback": "This answer is wrong — the 6.0 g of solid is the trap. Use the water's 180.0 g: q = 180.0 × 4.18 × 2.5 = 1881 J absorbed."
 },
 {
  "value": 9028.8,
  "misconception": "you used a single reading instead of the temperature change — ΔT is the size of the drop, 14.5 − 12.0 = 2.5 °C",
  "feedback": "This answer is wrong — 12.0 is a reading, not a change. The drop is 2.5 °C, so q = 1881 J absorbed."
 }
]

{
 "keyExplanation": "Write down the values in the question — for the water:\nm = 180.0 g\nc = 4.18 J/(g·°C)\nΔT = 14.5 − 12.0 = 2.5 °C (a drop of 2.5 °C)\nWrite down the equation:\nq = mcΔT\nSubstitute in the values, and calculate:\nq = 180.0 × 4.18 × 2.5\nq = 1881 J — absorbed, because the water cooled. The solid's 6.0 g never enters the calculation — the water is the substance measured.",
 "anticipatedWrong": [
  {
   "value": 62.7,
   "misconception": "you used the solid's mass instead of the water's — the equation is run on the WATER, the substance whose temperature was measured",
   "feedback": "This answer is wrong — the 6.0 g of solid is the trap. Use the water's 180.0 g: q = 180.0 × 4.18 × 2.5 = 1881 J absorbed."
  },
  {
   "value": 9028.8,
   "misconception": "you used a single reading instead of the temperature change — ΔT is the size of the drop, 14.5 − 12.0 = 2.5 °C",
   "feedback": "This answer is wrong — 12.0 is a reading, not a change. The drop is 2.5 °C, so q = 1881 J absorbed."
  }
 ]
}

[
 {
  "value": 517,
  "misconception": "you kept the energy the same because the temperature change is the same — three times the mass needs three times the energy",
  "feedback": "This answer is wrong — 517 J warms only the 220 g. Three times the grams need three times the shares: 3 × 517 J = 1551 J."
 },
 {
  "value": 172,
  "misconception": "you divided by three instead of multiplying — more mass needs more energy",
  "feedback": "This answer is wrong — dividing gives less energy for more beads. Three times the mass needs three times the energy: 1551 J."
 }
]

{
 "keyExplanation": "Same material, same temperature change — only the mass differs. 660 g is three times 220 g. Three times the mass needs three times the energy: 3 × 517 J = 1551 J.",
 "anticipatedWrong": [
  {
   "value": 517,
   "misconception": "you kept the energy the same because the temperature change is the same — three times the mass needs three times the energy",
   "feedback": "This answer is wrong — 517 J warms only the 220 g. Three times the grams need three times the shares: 3 × 517 J = 1551 J."
  },
  {
   "value": 172,
   "misconception": "you divided by three instead of multiplying — more mass needs more energy",
   "feedback": "This answer is wrong — dividing gives less energy for more beads. Three times the mass needs three times the energy: 1551 J."
  }
 ]
}

[
 {
  "value": 9737,
  "misconception": "you scaled by the ratio of the final temperatures, 79 ÷ 39, instead of the ratio of the changes — the changes are 50 °C and 10 °C",
  "feedback": "This answer is wrong — 79 ÷ 39 compares readings, not changes. The changes are 10 °C and 50 °C, so the energy is 5 × 4807 J = 24035 J."
 },
 {
  "value": 4807,
  "misconception": "you kept the energy the same because it is the same sample — the change is five times larger, so the energy is too",
  "feedback": "This answer is wrong — 4807 J covers only a 10 °C change. A 50 °C change on the same sample needs 5 × 4807 J = 24035 J."
 }
]

{
 "keyExplanation": "Work with the CHANGES, not the final temperatures. First change: 39 − 29 = 10 °C. Second change: 79 − 29 = 50 °C — five times as large. Five times the change needs five times the energy: 5 × 4807 J = 24035 J.",
 "anticipatedWrong": [
  {
   "value": 9737,
   "misconception": "you scaled by the ratio of the final temperatures, 79 ÷ 39, instead of the ratio of the changes — the changes are 50 °C and 10 °C",
   "feedback": "This answer is wrong — 79 ÷ 39 compares readings, not changes. The changes are 10 °C and 50 °C, so the energy is 5 × 4807 J = 24035 J."
  },
  {
   "value": 4807,
   "misconception": "you kept the energy the same because it is the same sample — the change is five times larger, so the energy is too",
   "feedback": "This answer is wrong — 4807 J covers only a 10 °C change. A 50 °C change on the same sample needs 5 × 4807 J = 24035 J."
  }
 ]
}

[
 {
  "value": 2880,
  "misconception": "you slipped the decimal in c — metal's value is 0.128 J/(g·°C), not 1.28",
  "feedback": "This answer is wrong — ten times too large. With c = 0.128, q = 225.0 × 0.128 × 10.0 = 288 J."
 },
 {
  "value": 1.28,
  "misconception": "you left out the mass — all three quantities on the right multiply",
  "feedback": "This answer is wrong — 0.128 × 10.0 covers only one gram. Multiply by the 225.0 g as well: q = 288 J."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 225.0 g\nc = 0.128 J/(g·°C)\nΔT = 10.0 °C\nWrite down the equation:\nq = mcΔT\nSubstitute in the values, and calculate:\nq = 225.0 × 0.128 × 10.0\nq = 288 J\nLead's very low specific heat capacity is why so little energy warms the whole counterweight.",
 "anticipatedWrong": [
  {
   "value": 2880,
   "misconception": "you slipped the decimal in c — metal's value is 0.128 J/(g·°C), not 1.28",
   "feedback": "This answer is wrong — ten times too large. With c = 0.128, q = 225.0 × 0.128 × 10.0 = 288 J."
  },
  {
   "value": 1.28,
   "misconception": "you left out the mass — all three quantities on the right multiply",
   "feedback": "This answer is wrong — 0.128 × 10.0 covers only one gram. Multiply by the 225.0 g as well: q = 288 J."
  }
 ]
}

[
 {
  "value": 2.35,
  "misconception": "you divided by the mass only — divide by both the mass and the temperature change",
  "feedback": "This answer is wrong — divide by m AND ΔT together: c = 376 ÷ (160.0 × 10.0) = 0.235 J/(g·°C)."
 },
 {
  "value": 37.6,
  "misconception": "you divided by the temperature change only — divide by both the mass and the temperature change",
  "feedback": "This answer is wrong — divide by m AND ΔT together: c = 376 ÷ (160.0 × 10.0) = 0.235 J/(g·°C)."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nq = 376 J\nm = 160.0 g\nΔT = 10.0 °C\nWrite down the equation:\nq = mcΔT\nMake c the subject:\nc = q ÷ (m × ΔT)\nSubstitute in the values, and calculate:\nc = 376 ÷ (160.0 × 10.0)\nc = 0.235 J/(g·°C)\nThat is the table value for silver — the calculation just identified a real metal's specific heat capacity.",
 "anticipatedWrong": [
  {
   "value": 2.35,
   "misconception": "you divided by the mass only — divide by both the mass and the temperature change",
   "feedback": "This answer is wrong — divide by m AND ΔT together: c = 376 ÷ (160.0 × 10.0) = 0.235 J/(g·°C)."
  },
  {
   "value": 37.6,
   "misconception": "you divided by the temperature change only — divide by both the mass and the temperature change",
   "feedback": "This answer is wrong — divide by m AND ΔT together: c = 376 ÷ (160.0 × 10.0) = 0.235 J/(g·°C)."
  }
 ]
}

[
 {
  "value": -3190,
  "misconception": "you reported a negative value — heat lost and heat gained are magnitudes here, and 'lost' already carries the direction",
  "feedback": "This answer is wrong in form — give the size of the transfer: the weight lost 3190 J."
 },
 {
  "value": 6380,
  "misconception": "you doubled the energy, counting it once leaving the weight and once entering the water — it is the same 3190 J, transferred once",
  "feedback": "This answer is wrong — one transfer, counted from either end: the weight lost exactly the 3190 J the water gained."
 }
]

{
 "keyExplanation": "The carrier is sealed and insulated, so no energy escapes and none appears from anywhere else. Heat lost equals heat gained, so the weight lost exactly what the water gained: 3190 J.",
 "anticipatedWrong": [
  {
   "value": -3190,
   "misconception": "you reported a negative value — heat lost and heat gained are magnitudes here, and 'lost' already carries the direction",
   "feedback": "This answer is wrong in form — give the size of the transfer: the weight lost 3190 J."
  },
  {
   "value": 6380,
   "misconception": "you doubled the energy, counting it once leaving the weight and once entering the water — it is the same 3190 J, transferred once",
   "feedback": "This answer is wrong — one transfer, counted from either end: the weight lost exactly the 3190 J the water gained."
  }
 ]
}

[
 {
  "value": 355.3,
  "misconception": "you used the capsule's mass instead of the water's — the equation is run on the WATER, the substance whose temperature was measured",
  "feedback": "This answer is wrong — the 8.5 g capsule is the trap. Use the water's 85.0 g: q = 85.0 × 4.18 × 10.0 = 3553 J released."
 },
 {
  "value": 15455.6,
  "misconception": "you used the final temperature instead of the temperature change — ΔT = 43.5 − 33.5 = 10.0 °C",
  "feedback": "This answer is wrong — 43.5 is a reading, not a change. ΔT = 10.0 °C, so q = 3553 J released."
 }
]

{
 "keyExplanation": "Write down the values in the question — for the water:\nm = 85.0 g\nc = 4.18 J/(g·°C)\nΔT = 43.5 − 33.5 = 10.0 °C\nWrite down the equation:\nq = mcΔT\nSubstitute in the values, and calculate:\nq = 85.0 × 4.18 × 10.0\nq = 3553 J — released, because the water warmed. The capsule's 8.5 g never enters the calculation.",
 "anticipatedWrong": [
  {
   "value": 355.3,
   "misconception": "you used the capsule's mass instead of the water's — the equation is run on the WATER, the substance whose temperature was measured",
   "feedback": "This answer is wrong — the 8.5 g capsule is the trap. Use the water's 85.0 g: q = 85.0 × 4.18 × 10.0 = 3553 J released."
  },
  {
   "value": 15455.6,
   "misconception": "you used the final temperature instead of the temperature change — ΔT = 43.5 − 33.5 = 10.0 °C",
   "feedback": "This answer is wrong — 43.5 is a reading, not a change. ΔT = 10.0 °C, so q = 3553 J released."
  }
 ]
}

[
 {
  "value": 2758,
  "misconception": "you kept the energy the same because the temperature change is the same — twice the mass needs twice the energy",
  "feedback": "This answer is wrong — 2758 J warms only the 280 g. Twice the grams need twice the shares: 2 × 2758 J = 5516 J."
 },
 {
  "value": 11032,
  "misconception": "you multiplied by four instead of two — doubling the mass doubles the energy, nothing more",
  "feedback": "This answer is wrong — 11032 J is a quadrupling. Twice the mass needs exactly twice the energy: 5516 J."
 }
]

{
 "keyExplanation": "Same material, same temperature change — only the mass differs. 560 g is twice 280 g. Twice the mass needs twice the energy: 2 × 2758 J = 5516 J.",
 "anticipatedWrong": [
  {
   "value": 2758,
   "misconception": "you kept the energy the same because the temperature change is the same — twice the mass needs twice the energy",
   "feedback": "This answer is wrong — 2758 J warms only the 280 g. Twice the grams need twice the shares: 2 × 2758 J = 5516 J."
  },
  {
   "value": 11032,
   "misconception": "you multiplied by four instead of two — doubling the mass doubles the energy, nothing more",
   "feedback": "This answer is wrong — 11032 J is a quadrupling. Twice the mass needs exactly twice the energy: 5516 J."
  }
 ]
}

[
 {
  "value": 14578,
  "misconception": "you scaled by the ratio of the final temperatures, 36 ÷ 16, instead of the ratio of the changes — the changes are 30 °C and 10 °C",
  "feedback": "This answer is wrong — 36 ÷ 16 compares readings, not changes. The changes are 10 °C and 30 °C, so the energy is 3 × 6479 J = 19437 J."
 },
 {
  "value": 6479,
  "misconception": "you kept the energy the same because it is the same sample — three times the change needs three times the energy",
  "feedback": "This answer is wrong — 6479 J covers only a 10 °C change. A 30 °C change on the same sample needs 3 × 6479 J = 19437 J."
 }
]

{
 "keyExplanation": "Work with the CHANGES, not the final temperatures. First change: 16 − 6 = 10 °C. Second change: 36 − 6 = 30 °C — three times as large. Three times the change needs three times the energy: 3 × 6479 J = 19437 J.",
 "anticipatedWrong": [
  {
   "value": 14578,
   "misconception": "you scaled by the ratio of the final temperatures, 36 ÷ 16, instead of the ratio of the changes — the changes are 30 °C and 10 °C",
   "feedback": "This answer is wrong — 36 ÷ 16 compares readings, not changes. The changes are 10 °C and 30 °C, so the energy is 3 × 6479 J = 19437 J."
  },
  {
   "value": 6479,
   "misconception": "you kept the energy the same because it is the same sample — three times the change needs three times the energy",
   "feedback": "This answer is wrong — 6479 J covers only a 10 °C change. A 30 °C change on the same sample needs 3 × 6479 J = 19437 J."
  }
 ]
}

[
 {
  "value": -7315,
  "misconception": "you reported a negative value — q is a magnitude here, and the word 'released' carries the direction",
  "feedback": "This answer is wrong in form — give the size of the transfer, 7315 J, with the direction carried by 'released'."
 },
 {
  "value": 99484,
  "misconception": "you used a single reading instead of the temperature change — ΔT is the size of the drop, 68.0 − 63.0 = 5.0 °C",
  "feedback": "This answer is wrong — 68.0 is a reading, not a change. The drop is 5.0 °C, so q = 350.0 × 4.18 × 5.0 = 7315 J released."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 350.0 g\nc = 4.18 J/(g·°C)\nΔT = 68.0 − 63.0 = 5.0 °C (a drop of 5.0 °C)\nWrite down the equation:\nq = mcΔT\nSubstitute in the values, and calculate:\nq = 350.0 × 4.18 × 5.0\nq = 7315 J — released, because the water cooled",
 "anticipatedWrong": [
  {
   "value": -7315,
   "misconception": "you reported a negative value — q is a magnitude here, and the word 'released' carries the direction",
   "feedback": "This answer is wrong in form — give the size of the transfer, 7315 J, with the direction carried by 'released'."
  },
  {
   "value": 99484,
   "misconception": "you used a single reading instead of the temperature change — ΔT is the size of the drop, 68.0 − 63.0 = 5.0 °C",
   "feedback": "This answer is wrong — 68.0 is a reading, not a change. The drop is 5.0 °C, so q = 350.0 × 4.18 × 5.0 = 7315 J released."
  }
 ]
}

[
 {
  "value": 20.9,
  "misconception": "you divided by the mass only and dropped the specific heat capacity — divide by both",
  "feedback": "This answer is wrong — divide by m AND c together: ΔT = 7942 ÷ (380.0 × 4.18) = 5.0 °C."
 },
 {
  "value": 1900.0,
  "misconception": "you divided by the specific heat capacity only and dropped the mass — divide by both",
  "feedback": "This answer is wrong — divide by m AND c together: ΔT = 7942 ÷ (380.0 × 4.18) = 5.0 °C."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nq = 7942 J\nm = 380.0 g\nc = 4.18 J/(g·°C)\nWrite down the equation:\nq = mcΔT\nMake ΔT the subject:\nΔT = q ÷ (m × c)\nSubstitute in the values, and calculate:\nΔT = 7942 ÷ (380.0 × 4.18)\nΔT = 5.0 °C",
 "anticipatedWrong": [
  {
   "value": 20.9,
   "misconception": "you divided by the mass only and dropped the specific heat capacity — divide by both",
   "feedback": "This answer is wrong — divide by m AND c together: ΔT = 7942 ÷ (380.0 × 4.18) = 5.0 °C."
  },
  {
   "value": 1900.0,
   "misconception": "you divided by the specific heat capacity only and dropped the mass — divide by both",
   "feedback": "This answer is wrong — divide by m AND c together: ΔT = 7942 ÷ (380.0 × 4.18) = 5.0 °C."
  }
 ]
}

[
 {
  "value": -2465,
  "misconception": "you reported a negative value — heat lost and heat gained are magnitudes here, and 'gain' already carries the direction",
  "feedback": "This answer is wrong in form — give the size of the transfer: the water gained 2465 J."
 },
 {
  "value": 4930,
  "misconception": "you doubled the energy, counting it once leaving the clamp and once entering the water — it is the same 2465 J, transferred once",
  "feedback": "This answer is wrong — one transfer, counted from either end: the water gained exactly the 2465 J the clamp lost."
 }
]

{
 "keyExplanation": "The crate is sealed and insulated, so the transferred energy has nowhere else to go. The heat lost by the hotter object equals the heat gained by the colder object: 2465 J out of the clamp means 2465 J into the water.",
 "anticipatedWrong": [
  {
   "value": -2465,
   "misconception": "you reported a negative value — heat lost and heat gained are magnitudes here, and 'gain' already carries the direction",
   "feedback": "This answer is wrong in form — give the size of the transfer: the water gained 2465 J."
  },
  {
   "value": 4930,
   "misconception": "you doubled the energy, counting it once leaving the clamp and once entering the water — it is the same 2465 J, transferred once",
   "feedback": "This answer is wrong — one transfer, counted from either end: the water gained exactly the 2465 J the clamp lost."
  }
 ]
}

[
 {
  "value": 188.1,
  "misconception": "you used the solid's mass instead of the water's — the equation is run on the WATER, the substance whose temperature was measured",
  "feedback": "This answer is wrong — the 9.0 g of solid is the trap. Use the water's 210.0 g: q = 210.0 × 4.18 × 5.0 = 4389 J released."
 },
 {
  "value": 14483.7,
  "misconception": "you used the final temperature instead of the temperature change — ΔT = 16.5 − 11.5 = 5.0 °C",
  "feedback": "This answer is wrong — 16.5 is a reading, not a change. ΔT = 5.0 °C, so q = 4389 J released."
 }
]

{
 "keyExplanation": "Write down the values in the question — for the water:\nm = 210.0 g\nc = 4.18 J/(g·°C)\nΔT = 16.5 − 11.5 = 5.0 °C\nWrite down the equation:\nq = mcΔT\nSubstitute in the values, and calculate:\nq = 210.0 × 4.18 × 5.0\nq = 4389 J — released, because the water warmed. The solid's 9.0 g never enters the calculation.",
 "anticipatedWrong": [
  {
   "value": 188.1,
   "misconception": "you used the solid's mass instead of the water's — the equation is run on the WATER, the substance whose temperature was measured",
   "feedback": "This answer is wrong — the 9.0 g of solid is the trap. Use the water's 210.0 g: q = 210.0 × 4.18 × 5.0 = 4389 J released."
  },
  {
   "value": 14483.7,
   "misconception": "you used the final temperature instead of the temperature change — ΔT = 16.5 − 11.5 = 5.0 °C",
   "feedback": "This answer is wrong — 16.5 is a reading, not a change. ΔT = 5.0 °C, so q = 4389 J released."
  }
 ]
}

[
 {
  "value": -39.0,
  "misconception": "you read the first plateau — that is the melting temperature; boiling is the SECOND plateau, the higher one",
  "feedback": "This answer is wrong — you read the first plateau — that is the melting temperature; boiling is the SECOND plateau, the higher one."
 },
 {
  "value": 390.0,
  "misconception": "you read the top of the curve instead of a plateau — the boiling temperature is the height where the curve flattens the second time",
  "feedback": "This answer is wrong — you read the top of the curve instead of a plateau — the boiling temperature is the height where the curve flattens the second time."
 }
]

{
 "keyExplanation": "Find the second flat plateau — its height is the boiling temperature. The plateau sits at 357 °C, so mercury boils at 357 °C. The other plateau is the melting temperature."
}

[
 {
  "value": 351.0,
  "misconception": "you read the second plateau — that is the boiling temperature; melting is the FIRST plateau, the lower one",
  "feedback": "This answer is wrong — you read the second plateau — that is the boiling temperature; melting is the FIRST plateau, the lower one."
 },
 {
  "value": 25.0,
  "misconception": "you read the start of the curve instead of a plateau — the melting temperature is the height where the curve first flattens",
  "feedback": "This answer is wrong — you read the start of the curve instead of a plateau — the melting temperature is the height where the curve first flattens."
 }
]

{
 "keyExplanation": "Find the first flat plateau — its height is the melting temperature. The plateau sits at 63 °C, so palmitic acid melts at 63 °C. The other plateau is the boiling temperature."
}

[
 {
  "value": 340.0,
  "misconception": "you read the second plateau — that is the boiling temperature; melting is the FIRST plateau, the lower one",
  "feedback": "This answer is wrong — you read the second plateau — that is the boiling temperature; melting is the FIRST plateau, the lower one."
 },
 {
  "value": 150.0,
  "misconception": "you read the start of the curve instead of a plateau — the melting temperature is the height where the curve first flattens",
  "feedback": "This answer is wrong — you read the start of the curve instead of a plateau — the melting temperature is the height where the curve first flattens."
 }
]

{
 "keyExplanation": "Find the first flat plateau — its height is the melting temperature. The plateau sits at 216 °C, so anthracene melts at 216 °C. The other plateau is the boiling temperature."
}

[
 {
  "value": 299.0,
  "misconception": "you read the second plateau — that is the boiling temperature; melting is the FIRST plateau, the lower one",
  "feedback": "This answer is wrong — you read the second plateau — that is the boiling temperature; melting is the FIRST plateau, the lower one."
 },
 {
  "value": 15.0,
  "misconception": "you read the start of the curve instead of a plateau — the melting temperature is the height where the curve first flattens",
  "feedback": "This answer is wrong — you read the start of the curve instead of a plateau — the melting temperature is the height where the curve first flattens."
 }
]

{
 "keyExplanation": "Find the first flat plateau — its height is the melting temperature. The plateau sits at 44 °C, so lauric acid melts at 44 °C. The other plateau is the boiling temperature."
}

[
 {
  "value": 631.0,
  "misconception": "you read the first plateau — that is the melting temperature; boiling is the SECOND plateau, the higher one",
  "feedback": "This answer is wrong — you read the first plateau — that is the melting temperature; boiling is the SECOND plateau, the higher one."
 },
 {
  "value": 1700.0,
  "misconception": "you read the top of the curve instead of a plateau — the boiling temperature is the height where the curve flattens the second time",
  "feedback": "This answer is wrong — you read the top of the curve instead of a plateau — the boiling temperature is the height where the curve flattens the second time."
 }
]

{
 "keyExplanation": "Find the second flat plateau — its height is the boiling temperature. The plateau sits at 1587 °C, so antimony boils at 1587 °C. The other plateau is the melting temperature."
}