Change of State

The figure plots temperature (in °C, up to 100) on the vertical axis against time on the horizontal axis. It is a heating curve for a fixed mass of ice taken initially below 0 °C. The curve is not drawn to scale — the durations of different segments are schematic, not proportional to actual times.

Starting from the left, the temperature rises steadily as the ice warms up. When it reaches 0 °C, the curve flattens into a long, low horizontal segment. This is the melting plateau: the temperature stays constant at 0 °C while the ice absorbs heat and changes phase to liquid water. The length of this flat segment corresponds to the latent heat of fusion — the energy needed to melt the ice completely without raising its temperature.

Once all the ice has melted, the temperature begins to rise again, climbing steeply from 0 °C to 100 °C. This sloping segment represents the heating of liquid water. At 100 °C, the curve flattens again into a boiling plateau. Here the temperature remains constant while the water absorbs heat and vaporises into steam. After the boiling plateau, the curve continues upward as a dashed rising segment, indicating that once all water has turned to steam, the temperature of the steam can rise further (above 100 °C).

The key physical idea is that during a phase change, the energy supplied goes into breaking intermolecular bonds rather than increasing kinetic energy, so the temperature stays constant. The heat absorbed during a phase change is given by

where $Q$ is the heat absorbed, $m$ is the mass of the substance, and $L$ is the specific latent heat. For melting, $L$ is the specific latent heat of fusion ($L_f$); for boiling, it is the specific latent heat of vaporisation ($L_v$).

The figure shows a block of ice supported at its ends, with a thin wire resting across its top. From each end of the wire hangs a 5 kg mass. The wire, under the combined weight of the two masses, slowly cuts its way down through the ice block. Yet — and this is the striking part — the ice above the wire refreezes behind it, so the wire passes completely through the solid block without the block being cut in two. The ice remains a single, intact slab.

This demonstration is the classic illustration of regelation: the phenomenon in which ice melts under pressure and refreezes when the pressure is released. The wire exerts a large pressure on the ice directly beneath it (because the contact area is tiny). That pressure lowers the melting point of ice below $0\,^{\circ}\mathrm{C}$, so the ice under the wire melts. The wire sinks into the resulting film of water. Once the wire has passed, the water above it is no longer under high pressure, so its melting point returns to $0\,^{\circ}\mathrm{C}$. Since the surrounding ice is at $0\,^{\circ}\mathrm{C}$, the water refreezes, sealing the cut.

The key physics is the Clausius–Clapeyron relation for the solid–liquid phase boundary. For a substance like water, which expands on freezing (ice is less dense than liquid water), the melting point decreases with increasing pressure. The textbook gives the formula that governs this shift:

Here:

• $\Delta T$ is the change in melting temperature (in kelvin or °C — the numerical change is the same).
• $\Delta P$ is the change in pressure applied to the solid.
• $T$ is the equilibrium melting temperature at the given pressure (in kelvin).
• $V_2$ is the volume per unit mass (or per mole) of the liquid phase.
• $V_1$ is the volume per unit mass (or per mole) of the solid phase.
• $L$ is the latent heat of fusion per unit mass (or per mole).

For ice and water at $0\,^{\circ}\mathrm{C}$ ($273\ \mathrm{K}$), $V_2 - V_1$ is negative (water is denser than ice, so liquid water occupies less volume than the same mass of ice). That minus sign makes $\Delta T / \Delta P$ negative: an increase in pressure lowers the melting point. The textbook uses this relation to explain why the wire can melt its way through the ice, and why the water refreezes once the pressure is removed.

Fig. 10.11 is a simple but powerful experimental setup. A round-bottom flask, half-filled with water, sits on a wire gauze over a burner, clamped to a retort stand. A thermometer passes through a cork in the flask’s neck to measure the temperature of the water (or steam). A bent glass tube also passes through the cork; its open end acts as a steam outlet, allowing the vapour to escape into the air.

The figure is not a graph — it is a diagram of the apparatus used to study the boiling process. The key physical idea it teaches is that during boiling, the temperature of the liquid does not rise even though heat is continuously supplied. The thermometer reading stays constant at the boiling point (100 °C at standard atmospheric pressure) until all the liquid has turned into vapour. The steam outlet tube shows that the vapour is being released; if you were to collect the steam and condense it, you would find that the amount of heat absorbed per unit mass is a fixed value — the latent heat of vaporisation.

The textbook uses this figure to introduce the concept of latent heat. The heat $Q$ required to convert a mass $m$ of liquid at its boiling point into vapour at the same temperature is given by

where $L_v$ is the latent heat of vaporisation (in J kg$^{-1}$). For water at 1 atm, $L_v \approx 2.26 \times 10^6$ J kg$^{-1}$. The figure makes clear that this heat does not raise the temperature — it goes entirely into overcoming the intermolecular forces that hold the liquid together, allowing the molecules to escape into the gas phase.

This boxed figure in the NCERT text (placed immediately after the discussion of the triple point, and left unnumbered in the original) shows two separate pressure–temperature (P-T) phase diagrams side by side, one for water and one for carbon dioxide (CO2), each not drawn to scale.

Panel (a) — Water. The horizontal axis is temperature in °C, the vertical axis is pressure. Three curves divide the plane into three regions labelled Solid, Liquid, and Vapour:

• Curve BO — the sublimation curve, along which solid ice and water vapour coexist in equilibrium, running from a point B at low temperature/low pressure up to the point O.
• Curve AO — the fusion (melting) curve, along which solid ice and liquid water coexist in equilibrium, running from a point A at higher pressure down to O. This curve leans slightly backward (a small negative slope) as pressure increases — a feature unique to water among common substances, reflecting the fact that ice is less dense than liquid water.
• Curve OC — the vaporisation curve, along which liquid water and water vapour coexist in equilibrium, running from O up toward a point C.

The point O, where all three curves meet, is the triple point of water: $T = 0.01^\circ\text{C}$, $P \approx 0.006\ \text{atm}$ ($611.73\ \text{Pa}$). The vaporisation curve OC continues up to the critical point, beyond which liquid and vapour become indistinguishable, near $374^\circ\text{C}$. The temperature axis spans roughly from about $-220^\circ\text{C}$ (deep in the solid/sublimation region), through the fixed points at $0.01^\circ\text{C}$ and $100^\circ\text{C}$ (the normal boiling point, where the vaporisation curve crosses 1 atm), up to the critical temperature near $374^\circ\text{C}$; the pressure axis spans from well below $0.006\ \text{atm}$ past 1 atm up to the higher pressures near the critical point.

Panel (b) — Carbon dioxide (CO2). The same three regions and three curves (sublimation, fusion, vaporisation) appear, but CO2's triple point O is at $T = -56.6^\circ\text{C}$, $P = 5.11\ \text{atm}$ — a much higher pressure than water's triple point. The axis values marked are approximately $-78.5^\circ\text{C}$ (the sublimation temperature at 1 atm — this is why solid CO2, "dry ice," sublimes directly to gas at ordinary atmospheric pressure without ever forming a liquid), $-56.6^\circ\text{C}$ (the triple-point temperature), and $20^\circ\text{C}$, up to the critical temperature near $31.1^\circ\text{C}$; pressures marked are approximately $1.0\ \text{atm}$, $5.11\ \text{atm}$ (the triple-point pressure), $56.0\ \text{atm}$ (the pressure at which CO2 is liquid at room temperature), and the critical pressure near $73.0\ \text{atm}$. Unlike water, CO2's fusion curve AO has the normal (positive) slope — melting point rises with pressure — because solid CO2 is denser than liquid CO2, the behaviour of most substances.