Change of state and latent heat
Melting, boiling and sublimation
Matter is usually found as a solid, a liquid or a gas. Going from one of these states to another is called a change of state.
Put some ice from the freezer in a beaker with a thermometer, and heat it steadily. Watch the thermometer as the ice warms up.
At 0 degrees, the ice starts melting, and the temperature stops rising, even though we are still heating. It stays at 0 degrees until all the ice has melted.
The change from solid to liquid is melting, or fusion, and the temperature at which it happens is the melting point. While it melts, solid and liquid exist together in thermal equilibrium.
Once all the ice has melted, the temperature rises steadily again, until the water reaches 100 degrees.
Now bubbles of vapour form all through the water. It boils, and again the temperature stays fixed at 100 degrees until all the water has turned to steam.
The change from liquid to vapour is vaporisation, and the temperature at which liquid and vapour exist together is the boiling point.
Some solids skip the liquid state altogether. Camphor, iodine and dry ice, which is solid carbon dioxide, turn straight into vapour. This is sublimation.
Plot temperature against the heat supplied. You get rising slopes while one state warms up, and flat plateaus wherever the state changes.
Latent heat
On the flat parts of the graph, heat goes in, but the temperature does not change. Where does that energy go?
It goes into pulling the molecules apart: breaking the bonds that hold the solid together, or freeing liquid molecules into a gas. It does not make them move faster, so the temperature stays put.
The heat per kilogram needed to change the state at constant temperature is called the latent heat, L. So Q equals m L.
For ice melting, the latent heat of fusion is about 3.33 × 10⁵ joules per kilogram. For water boiling, the latent heat of vaporisation is about 22.6 × 10⁵ joules per kilogram, nearly seven times larger.
Compare the plateaus on the graph. Boiling a kilogram of water takes far more heat than melting it, or even than warming it all the way from 0 to 100 degrees.
That is also why a steam burn is worse than a burn from boiling water. Each gram of steam that condenses on the skin gives out about 2260 joules more.
A worked example: how much heat turns 3 kilograms of ice at minus 12 degrees into steam at 100 degrees? We will use the values from the NCERT example, and take one step at a time.
Warm the ice: 3 times 2100 times 12, about 0.076 megajoules. Melt it: 3 times 3.35 × 10⁵, about 1.005 megajoules.
Warm the water: 3 times 4186 times 100, about 1.256 megajoules. Boil it: 3 times 2.256 × 10⁶, about 6.768 megajoules.
Add them up: about 9.1 × 10⁶ joules. Three quarters of it is spent just on boiling.
Pressure, regelation and pressure cookers
Melting and boiling points depend on pressure. The values we usually quote, 0 and 100 degrees Celsius, are at standard atmospheric pressure.
Pressing on ice lowers its melting point slightly. Watch a thin wire with heavy weights at both ends, hung over a block of ice.
Under the wire the pressure is high, so the ice melts below 0 degrees and the wire sinks through. Above the wire, the pressure is back to normal, and the water freezes again.
The wire passes right through the block, yet the block stays in one piece. Refreezing like this, once the pressure is removed, is called regelation.
Ice skating works partly this way. The thin blade presses hard on the ice, a thin layer of water forms underneath, and it acts as a lubricant.
Boiling points change the other way. More pressure means a higher boiling point; less pressure, a lower one.
High in the mountains, the air pressure is low, so water boils below 100 degrees. Rice and dal take much longer to cook, because the water simply cannot get as hot.
A pressure cooker does the opposite. The sealed lid traps the steam, the pressure inside rises, and the water boils at about 120 degrees. The food cooks much faster.
Water can even boil without heating. Seal a flask of hot water, turn it upside down and pour cold water over it. The vapour inside condenses, the pressure drops, and the water boils again.
Try it: from ice to steam
- Press Heat (or Space). The heater supplies heat at a steady rate.
- On the plateaus the temperature is fixed while the state changes.
- Compare the readouts mL_f and mL_v: boiling needs about 7 times more heat.
- Tick “Pressure cooker” to move the boiling plateau up to about 120 °C.
Steam burns
Why does steam at 100 °C cause a more severe burn than the same mass of water at 100 °C?
- Steam is at a higher temperature than boiling water
- Steam gives out its latent heat of vaporisation when it condenses on the skin
- Steam has a higher specific heat than water
- Steam moves faster, so it hits the skin harder
Answer
B. Both are at 100 °C. But steam must first condense, giving out Lv ≈ 2.26 × 10⁶ J kg⁻¹, about 2260 J per gram, before it even starts cooling like hot water. That extra latent heat is what makes steam burns so bad.
Finding the latent heat of fusion
0.15 kg of ice at 0 °C is mixed with 0.30 kg of water at 50 °C. The final temperature is 6.7 °C. Taking s_water = 4186 J kg⁻¹ K⁻¹, what is the latent heat of fusion of ice?
- 1.67 × 10⁵ J kg⁻¹
- 3.34 × 10⁵ J kg⁻¹
- 3.63 × 10⁵ J kg⁻¹
- 2.26 × 10⁶ J kg⁻¹
Answer
B. Heat lost by the warm water = 0.30 × 4186 × (50 − 6.7) ≈ 54 380 J. Heat gained by the ice = 0.15 L (to melt) + 0.15 × 4186 × 6.7 ≈ 0.15 L + 4210 J (melted ice warming to 6.7 °C). So 0.15 L ≈ 50 170 J and L ≈ 3.34 × 10⁵ J kg⁻¹. Forgetting the second step gives 3.63 × 10⁵.
Summary
- Latent heat:
Q = m L - Ice (fusion):
L_f ≈ 3.33 × 10⁵ J kg⁻¹ - Water (vaporisation):
L_v ≈ 22.6 × 10⁵ J kg⁻¹ - Warming within one state:
Q = m s ΔT
- During melting and boiling, the temperature stays constant until the change of state is complete: the plateaus on the T–Q graph.
- Latent heat goes into separating the molecules, not into making them move faster.
- Sublimation: solid straight to vapour (camphor, iodine, dry ice).
- More pressure lowers the melting point of ice (regelation, skating) and raises the boiling point of water (pressure cooker). Low pressure on mountains lowers it.