Math practice · Unit #07 · 8th grade · States of matter & particle movement

Reading the Curve

A heating curve is a graph with secrets: flat spots where the temperature refuses to rise while the ice melts anyway. Learn to read the plateaus and you can see particles changing state — with numbers.

skills: piecewise graphs negative numbers rate of change ≈ 30 min
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Name Period Date
PART A

The heating curve of water

Ice at −10 °C, heated at a steady rate. Same energy in every minute — but the temperature does not climb steadily. The table is the data; your job is to explain it.

Steady heat into a block of ice
Time (min)Temp (°C)What's happening?
0−10
40
80
1225
1650
20100
26100

  1. Two stretches of time show zero temperature change. Which stretches — and what is the added energy doing instead of raising the temperature?

  2. From 12 → 16 min the temperature rose 25 °C. From 0 → 4 min it rose 10 °C. Which substance warmed faster per minute — ice or liquid water? Show both rates (°C/min).

  3. Sketch the curve on the grid: time on the x-axis, temperature on the y-axis. Mark the two plateaus. What is the slope of a plateau?

PART B

Below zero

Temperature goes negative — which makes it integer practice with a lab coat on.

  1. The ice starts at −10 °C and warms to 0 °C. Temperature change?

  2. From −5 °C to 25 °C: change?

  3. From 25 °C down to −10 °C: change? (Sign matters.)

  4. Kelvin is the scale that refuses negatives: 0 K is absolute zero, where particle motion stops. 0 °C = 273 K. What is 100 °C in K? What is −10 °C in K? Why can Celsius go negative but Kelvin can't?

PART C

The price of a phase change

Published values for water: melting 1 g of ice costs 334 J; boiling 1 g of water costs 2,260 J.

  1. Energy to melt 5 g of ice (already at 0 °C)?

  2. Energy to boil away those same 5 g (already at 100 °C)?

  3. Boiling costs how many times more than melting? (2,260 ÷ 334) Melting just loosens particles; boiling separates them completely. In one sentence: how does the price ratio support that story?

PART D

The mirror: a cooling curve

Steam at 110 °C cools all the way to ice at −10 °C. No new data needed — the cooling curve is the heating curve's mirror.

  1. At what two temperatures will the cooling curve have plateaus? Why the same temperatures as before?

  2. During the 100 °C plateau on the way down, is energy going in or coming out? Where does it go?

Answer key — teachers

Part A

Descriptions: ice warming → reaches melting point → melting (plateau) → water warming → water warming → reaches boiling point → boiling (plateau).

  1. 4–8 min (melting) and 20–26 min (boiling); the energy is breaking particles loose from their arrangement instead of speeding them up.
  2. Ice: 10 °C ÷ 4 min = 2.5 °C/min; water: 25 °C ÷ 4 min = 6.25 °C/min. Liquid water warmed faster per minute.
  3. Plateau slope = 0 — time passes, temperature holds.

Part B

  1. +10 °C
  2. +30 °C
  3. −35 °C
  4. 373 K; 263 K. Celsius zero is just water's freezing point (an arbitrary anchor) so colder than that = negative; Kelvin zero is the floor of all motion — nothing exists below it.

Part C

  1. 5 × 334 = 1,670 J
  2. 5 × 2,260 = 11,300 J
  3. ≈ 6.8× more. Full separation costs far more than loosening — the price ratio matches the particle story.

Part D

  1. 100 °C (condensing) and 0 °C (freezing) — phase changes happen at the same temperatures in both directions.
  2. Coming OUT — released to the surroundings as steam becomes liquid.