Physics · Molecular physics and thermodynamics · Grade 7

Melting, boiling and evaporation

How long does a kettle take to boil, and why does boiling water not get hotter than 100 °C?

The situation

In the morning you want to make tea for breakfast: you pour 1 litre of water into the electric kettle and press the button. After a little while the kettle begins to “roar”, then it boils and switches itself off. Energy is needed both to melt ice from the freezer and to evaporate boiling water — but how much? And why does the temperature of boiling water never rise above 100 °C, however long the kettle runs?

Topic

Melting, boiling and evaporation. Water in a kettle: quantity of heat and boiling point

Key ideas

Quantity of heat
Specific latent heat of fusion and vaporisation
Efficiency

Formulas

Q = c m Δ T

Heat needed for heating. Water: $c = 4186$ J/(kg·K), ice: $c = 2100$ J/(kg·K).

Q = λ m

Melting: $λ = 334$ kJ/kg. During melting the temperature stays at 0 °C.

Q = L m

Evaporation (boiling): $L = 2.26$ MJ/kg. During boiling the temperature does not change.

η = \frac{Q_{useful}}{P t} \Rightarrow t = \frac{c m Δ T}{η P}

The efficiency of the kettle and the heating time.

P_{loss} = k (T - T_{room})

Newton's law of cooling: a hot kettle gives heat to its surroundings ( $k$ is the heat transfer coefficient, W/K).

Theory

Quantity of heat

The energy needed to heat a substance depends on its mass, the change in temperature and the specific heat capacity $c$ . The $c$ of ice is almost 2 times smaller than that of water — so on the graph, ice heats twice as fast as water at the same power (the line is steeper).

Why does the graph have a “staircase”?

During melting and boiling, the heat supplied goes into breaking the bonds between molecules; their average kinetic energy — and therefore the temperature — does not change. This is latent heat: until the ice has melted completely the temperature stays at 0 °C, and until the water has evaporated it stays at the boiling point. On the mass graph you will see the change ice → water → steam at this time. The reverse process is freezing (crystallisation): when water freezes at 0 °C it releases the same heat $λ m$ , so the temperature also stays at 0 °C while it freezes. Crystalline solids melt at a definite temperature; amorphous solids (glass, wax, resin) have no definite melting point — they soften gradually (in the “Crystalline and amorphous solids” experiment).

The boiling point depends on pressure

Water boils when its saturated vapour pressure becomes equal to the external pressure. At sea level (101 kPa) this is 100 °C. In the mountains the pressure is low — water boils at a lower temperature: try changing the Altitude slider. In a pressure cooker, on the contrary, water boils above 100 °C and food cooks quickly.

The real kettle and the model

Not all the energy reaches the water: some of it heats the glass, steel and air — this is accounted for by the efficiency ( $η$ ); with the lid open the loss is greater. When the kettle boils, steam travels through a special channel to a bimetallic sensor and switches it off; with the lid open the steam escapes from the top and the kettle may not switch off. The model is simplified: the water temperature is the same throughout the volume, and evaporation before boiling and the dependence of $c$ and $L$ on temperature are not taken into account. Time is sped up 10 times.

Evaporation, condensation and saturated vapour

A liquid evaporates from its surface at any temperature: the fastest molecules fly out, and the average energy of the rest falls — an evaporating liquid cools (we blow on hot tea to cool it; the psychrometer in the “Humidity and dew” experiment is based on the same thing). The rate of evaporation depends on temperature, surface area, wind and air humidity. The reverse process is condensation: vapour touches a cold surface (a lid, a window) and turns into water, giving back the same heat $L m$ — which is why a burn from steam is more dangerous than a burn from boiling water. In a closed vessel evaporation and condensation become equal: the vapour is saturated, and its pressure $p_{s}$ depends only on temperature. Bubbles inside the water can grow and rise to the surface only when $p_{s}$ reaches the external pressure — this is boiling (compare $p_{s} (T)$ with the external pressure on the panel). Ice can also evaporate without melting — sublimation.

Lab work: latent heat of vaporisation

Electrical method. Switch off the auto switch-off and let the water boil for a few minutes. During boiling, the energy the heater gives to the water, $η W$ ( $W$ is the electrical energy taken from the mains), goes only into evaporation: $L = η W / Δ m$ , where $Δ m$ is the mass of water evaporated (in practice the kettle is weighed before and after). On the panel this calculation is made from measurements taken during boiling — compare it with $L = 2.26$ MJ/kg. If the loss to the surroundings is switched on, the result comes out larger: part of the energy has gone into the air. This error can be eliminated by measuring at two powers: $L = η (P_{1} - P_{2}) / (μ_{1} - μ_{2})$ , where $μ$ is the rate of evaporation, kg/s. In the classical calorimetric method steam is passed into a calorimeter of cold water: it condenses there, heats the water, and $L$ is found from the heat balance.

Did you know?

The energy needed to melt 1 kg of ice (334 kJ) could heat 1 kg of water by about 80 °C: $334 000 / 4186 \approx 80$ .
At about 3000 m above sea level water boils at ≈ 90 °C — which is why cooking in high mountains takes longer.

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.

More experiments in this section

Calorimeter: heat balance — Grade 7
Tandoor and sandal: heat — Grade 7
Gas under a piston — Grade 9
Humidity and dew — Grade 9
Heat engine: the Otto cycle — Grade 9
Entropy and the arrow of time — Grade 9
Brownian motion and diffusion — Grade 9
Surface tension and capillarity — Grade 9
Crystalline and amorphous solids — Grade 9
Phase transitions — Grade 10