States of Matter

Theory — States of Matter

Phase Diagrams

A phase diagram maps the state of a substance (solid, liquid, or gas) against pressure and temperature. Three lines separate the regions: the solid–liquid (melting) line, the liquid–gas (vaporization) line, and the solid–gas (sublimation) line.

The triple point is where all three lines meet — solid, liquid, and gas coexist.
The critical point is the end of the liquid–gas line; beyond its temperature (the critical temperature) and pressure, the substance is a supercritical fluid and liquid and gas are no longer distinct.

The Slope of the Solid–Liquid Line

The slope of the solid–liquid line reveals which phase is denser. For almost all substances the solid is denser than the liquid, so increasing pressure favours the solid and the line tilts to the right (positive slope) — this is the case for carbon dioxide and benzene.

Water is the famous exception. Ice is less dense than liquid water (it floats), so increasing pressure favours the liquid and the solid–liquid line tilts to the left (negative slope). This is why ice melts under pressure and why water expands when it freezes.

Reading the solid–liquid line Line leans LEFT (negative slope) → solid is LESS dense than liquid (water)
Line leans RIGHT (positive slope) → solid is DENSER than liquid (CO₂, benzene)

Thermal (Linear) Expansion

When a solid is heated, it expands. For a rod or wire of original length L, the change in length is proportional to the original length and the temperature change, scaled by the material's coefficient of linear expansion α.

Linear Expansion ΔL = α L ΔT

ΔL = change in length · α = coefficient (per °C) · L = original length · ΔT = temperature change

Phase Changes and Their Names

Every change of state has a name. Adding heat drives a substance toward gas; removing heat drives it toward solid. During a change of state the temperature stays constant on a plateau while heat is added or removed, because the energy goes into rearranging the particles rather than changing the temperature.

Change of state	Name(s)	Heat
Solid → liquid	melting (fusion)	absorbed
Liquid → gas	vaporization (boiling, evaporation)	absorbed
Solid → gas	sublimation	absorbed
Gas → liquid	condensation	released
Liquid → solid	freezing (solidification, crystallization)	released
Gas → solid	deposition	released

Sloped sections

Temperature changes while a single phase (solid, liquid, or gas) warms or cools.

Plateaus

Temperature holds steady during a change of state while heat is added or removed.

Direction

Heating: solid→liquid→gas. Cooling: gas→liquid→solid. Sublimation and deposition skip the liquid.

Substance	Triple point	Critical temp.	Solid vs liquid density
Water	0.0061 atm, 0.01 °C	374 °C	Solid less dense (line leans left)
Carbon dioxide	5.11 atm, −56.6 °C	31 °C	Solid denser (line leans right)
Benzene	0.048 atm, 5.5 °C	289 °C	Solid denser (line leans right)

Apparatus

The equipment a real states-of-matter experiment uses to change temperature and pressure and to measure the response. In the simulation these are modelled for you, but the readings correspond to what each instrument would measure.

Thermometer

Tracks the temperature through every stage of a heating or cooling curve.

Hot plate

Adds heat at a steady rate to drive melting, boiling, and sublimation.

Metal rods

Aluminium, copper, iron, and steel samples that expand measurably when heated.

Electronic balance

Measures sample mass, used with density to compare solid and liquid phases.

Pressure gauge

Reads the pressure on a sample — the second axis of every phase diagram.

Sealed sample cell

Holds the substance so temperature and pressure can be changed to map its phases.

Instructions — Running the Virtual Experiment

The simulation has three sections. Work through them in order. In the expansion section, calculate the answer yourself first, then check it. In the phase-diagram and cooling-curve sections, make your prediction first, then reveal the answer to test your understanding.

Part 1 — Phase Diagrams

Open Simulation → Phase Diagrams. Choose a substance (water, CO₂, or benzene). Locate the triple point and critical point, and look at the slope of the solid–liquid line. Predict whether the solid is denser or less dense than the liquid, then reveal the answer and compare the three substances.

Part 2 — Linear Expansion

Open Linear Expansion. Choose a fixed trial (metal, original length, temperature change). Calculate ΔL yourself with ΔL = αLΔT, type it in, then run the experiment and compare. Repeat for at least two metals.

Part 3 — Phase-Change Curves

Open Phase-Change Curves. Choose a process — heating curve, cooling curve, sublimation, or deposition. Run it to watch the temperature change, then name the transition at each plateau from the options (melting/fusion, vaporization/boiling, condensation, freezing/solidification/crystallization, sublimation, deposition) and check. Try all four processes.

Simulation — States of Matter

Step 1 — choose a substance

Key points

Triple point—

Critical temp.—

Step 2 — predict, then check

From the slope of the solid–liquid line, is the solid denser or less dense than the liquid?

Study the solid–liquid line, make your choice, then check.

Step 1 — choose a fixed trial

Given

Coefficient α—

Original length L—

Temp change ΔT—

Step 2 — calculate, then check

Your ΔL (mm)

Your ΔL—

Correct ΔL—

Heat the rod, work out ΔL, type it, then check.

Step 1 — choose a process

Pick a process, run it, then name the transition at each plateau.

Step 2 — name the transition(s)

First plateau — which state change is this?

Second plateau — which state change is this?

Team Questions

Question 1. On a phase diagram, what is the name of the single point where solid, liquid, and gas all coexist? (One phrase)

Question 2. Water's solid–liquid line leans to the left (negative slope). What does this tell you about the density of ice compared with liquid water? (One phrase)

Question 3. An aluminium rod (α = 23×10⁻⁶ /°C) is 2.0 m long and heated by 100 °C. Find ΔL in mm. (ΔL = αLΔT; type to 2 decimals)

Question 4. Beyond the critical point, liquid and gas are no longer distinct. What is the temperature at this point called? (One phrase)

Question 5. On a cooling curve, what is happening to the substance during a flat plateau? (One phrase)

Question 6. CO₂'s solid–liquid line leans to the right. Is solid CO₂ (dry ice) denser or less dense than liquid CO₂? (One word)

Question 7 — Challenge. A copper rod (α = 17×10⁻⁶ /°C) is 1.5 m long and heated by 80 °C. Find ΔL in mm. (Type to 2 decimals)

Example Lab Report

Sample report demonstrating the expected format. Include your phase-diagram observations for the three substances, your expansion calculations for at least two metals, and your cooling-curve prediction.

States of Matter

Physics | Section: [Your Section] | Date: [Date]

Lab Members: [Names of all members present]

Objective

To interpret phase diagrams, determine relative solid and liquid densities from the solid–liquid line, calculate linear thermal expansion, and predict cooling curves with their state changes.

Phase Diagrams

For water, the solid–liquid line leans left (negative slope), showing ice is less dense than liquid water. For carbon dioxide and benzene, the line leans right, showing the solid is denser than the liquid. The triple point and critical temperature were recorded for each substance.

Linear Expansion — Worked Example

Metal	α (10⁻⁶/°C)	L (m)	ΔT (°C)	ΔL (mm)
Aluminium	23	2.0	100	4.60
Copper	17	1.5	80	2.04

ΔL = αLΔT = (23×10⁻⁶)(2.0)(100) = 0.0046 m = 4.60 mm

Cooling Curve

The curve has two plateaus: the upper plateau is condensation (gas → liquid) and the lower plateau is freezing (liquid → solid). Between and after the plateaus the temperature falls steadily as a single phase cools.

Conclusion

Phase diagrams reveal both the conditions for each state and the relative densities of solid and liquid. Metals expand predictably with temperature according to ΔL = αLΔT, and cooling curves show constant-temperature plateaus during condensation and freezing.

Practice Questions

Use ΔL = αLΔT for expansion. α values (10⁻⁶/°C): aluminium 23, copper 17, iron 12, steel 13.

Question 1

An iron beam (α = 12×10⁻⁶ /°C) is 3.0 m long and is heated by 50 °C. Find ΔL in mm.

Hint: ΔL = (12×10⁻⁶)(3.0)(50) = 0.0018 m = 1.80 mm.

Question 2

Sketch the phase diagram of water and explain why its solid–liquid line slopes up to the left, unlike most substances.

Hint: ice is less dense than liquid water, so higher pressure favours the liquid.

Question 3

A steel rail (α = 13×10⁻⁶ /°C) is 1.0 m long and heated by 120 °C. Find ΔL in mm, and explain why expansion gaps are left in railway tracks.

Hint: ΔL = (13×10⁻⁶)(1.0)(120) = 0.00156 m = 1.56 mm.

Question 4

On a cooling curve for water vapour cooling to ice, identify the temperature of each plateau and the state change occurring there.

Hint: 100 °C condensation (gas→liquid); 0 °C freezing (liquid→solid).

Question 5

Compare the phase diagrams of CO₂ and water. Which way does each solid–liquid line lean, and what does that say about the solid's density in each case?

Hint: CO₂ leans right (solid denser); water leans left (solid less dense).

Question 6 — Challenge

Dry ice (solid CO₂) sublimes at ordinary pressure instead of melting. Using the CO₂ phase diagram, explain why, referring to the triple-point pressure.

Hint: CO₂'s triple point is at 5.11 atm; at 1 atm the liquid phase cannot exist, so solid goes straight to gas.

States of Matter

Theory — States of Matter

Phase Diagrams

The Slope of the Solid–Liquid Line

Thermal (Linear) Expansion

Phase Changes and Their Names

Sloped sections

Plateaus

Direction

Apparatus

Instructions — Running the Virtual Experiment

Simulation — States of Matter

Step 1 — choose a substance

Step 2 — predict, then check

Step 1 — choose a fixed trial

Step 2 — calculate, then check

Step 1 — choose a process

Step 2 — name the transition(s)

Team Questions

Example Lab Report

States of Matter

Objective

Phase Diagrams

Linear Expansion — Worked Example

Cooling Curve

Conclusion

Practice Questions

Welcome — one quick step before you start