Q.During summers in India, one of the common practice to keep cool is to make ice balls of crushed ice, dip it in flavoured sugar syrup and sip it. For this a stick is inserted into crushed ice and is squeezed in the palm to make it into the ball. Equivalently in winter, in those areas where it snows, people make snow balls and throw around. Explain the formation of ball out of crushed ice or snow in the light of P–T diagram of water.

Concept: Phase Equilibrium and Pressure-Induced Melting

The formation of ice or snow balls relies on the unusual slope of water's solid–liquid equilibrium line in the pressure–temperature ($P$–$T$) diagram.

Step 1 (Anomalous slope): Water's $P$–$T$ diagram shows that the fusion curve (boundary between ice and liquid) has a negative slope. This means increasing pressure at constant temperature lowers the melting point of ice, or equivalently, ice can melt under pressure even below $0\,°\mathrm{C}$.

Step 2 (Pressure application): When you squeeze crushed ice or snow in your palm, you apply significant local pressure at the contact points between ice crystals. This pressure shifts the equilibrium: solid ice partially melts into liquid water at the interfaces. …

Why pressure makes ice melt (and then refreeze)

Water is unusual. For almost every substance, the solid phase is denser than the liquid, so increasing pressure favors the solid. Water is the opposite: ice is less dense than liquid water. This single fact has profound consequences.

On a pressure–temperature (P–T) phase diagram, the boundary between two phases shows the conditions where both coexist in equilibrium. For most substances, the solid–liquid line slopes upward to the right (higher pressure stabilizes the denser solid). For water, the ice–liquid boundary slopes backward—upward to the left. This negative slope means that increasing pressure on ice at 0 °C shifts the equilibrium toward liquid water.

When you squeeze crushed ice in your palm, you are doing exactly that: raising the pressure locally. Ice at the contact points between crystals melts, even though the temperature is below 0 °C at atmospheric pressure. The thin film of liquid water wets the surfaces, filling gaps. The moment you release the pressure, the equilibrium shifts back—water refreezes, welding the ice fragments into a coherent ball. This cycle of pressure-induced melting and refreezing is called regelation.

Step-by-step: from crushed ice to a solid ball

1. Initial state: loose ice crystals

   Crushed ice or snow consists of many small ice particles with air gaps between them. At atmospheric pressure and a temperature near 0 °C (or slightly below in winter), the ice is stable.

2. Apply pressure by squeezing

   When you press the ice in your palm, the force is concentrated at the contact points between crystals. The local pressure $P$ rises significantly above atmospheric pressure $P_0$.

3. Consult the P–T diagram

   On water's phase diagram, the ice–water coexistence curve has the equation (approximately, near the triple point):

where $\alpha \approx 0.0075\,^\circ\text{C/atm}$ is positive. The melting temperature decreases with increasing pressure. So at pressure $P > P_0$, ice melts at a temperature below 0 °C.

4. Melting at the contact points

   Even if the bulk temperature is, say, $-2\,^\circ\text{C}$, the elevated pressure at grain boundaries can push the local melting point below $-2\,^\circ\text{C}$, causing ice to melt. A thin layer of liquid water forms between the crystals.

5. Water acts as a binder

   Liquid water has high surface tension and wets ice readily. It flows into the voids, coating surfaces and drawing the fragments together by capillary forces.

6. Release the pressure

   When you stop squeezing, the pressure drops back to $P_0$. Now the melting point returns to 0 °C. Since the ambient temperature is at or below 0 °C, the liquid water is thermodynamically unstable—it refreezes almost instantly.

7. Regelation: the ice crystals fuse

   The refrozen water forms ice bridges between the original fragments, locking them into a single rigid mass. You are left with a solid ice ball that holds its shape.

The one-line physical argument: Le Chatelier's principle says a system under increased pressure shifts toward whichever phase occupies less volume — for water that's the liquid phase, since ice is less dense. So squeezing ice pushes the ice–water equilibrium toward melting even below $0°C$, without needing to invoke the full Clausius–Clapeyron slope, $\frac{dP}{dT}=\frac{L}{T\Delta V}$, though that equation is the formal reason the fusion curve tilts backward: $\Delta V=V_{liquid}-V_{ice}<0$ forces $\frac{dP}{dT}<0$, a sign reversal unique among common substances. Squeeze → local melt at contact …