Ice and its surprises: [1] Never saturates [2] Expands when freezes

This post will attempt to answer these two points

Ice has a heat capacity at 0 degc

Any substance would have heat capacity until it is saturated with energy. A common example is that the saturated water at 100 degc gets saturated at 419 Kj/kg when it is full of energy before phase change. Saturated steam achieves full energy when it breaks all H bonds at 100 degc at [about] 2256 Kj/kg heat of vaporization.

Ice is an exception. Because of tightly packed water molecules, the vibrational kinetic energy stays in ice even at zero K [- 273.15 degc]. ?Therefore, ice is never saturated with energy. Unlike water, which changes phase at 100 degc/1 bar, ice can exist till 0 K. ?Therefore, ice has specific heat. Ice can exist even at 0 K. Water can exist as solid ice at 1 bar pressure from 273.15 degc to - 273.15 degc, please see the image below. You would notice, that at 1 bar pressure on y-axis there is a lot of space for the temperature to shift left below 0 degc.

Credit: Google

In your fridge, the ice exists at -20 degc

An interesting point about ice

When we say ice melts at 0 degc/1 bar pressure, we refer to ice-water equilibrium.

Ice-water equilibrium exists at 0 degc/1 bar. The ice coexists with water at 0 degc.

Water converts to ice at a much lower temperature spontaneously.

Explanation

Water’s phase change to ice:

Gibbs free energy equation

dG = dH – TdS

G is Gibbs free energy, H is enthalpy, T is kelvin and S is entropy.

When water changes to ice, it not only forms intermolecular bonds, but some amount of its energy is lost as entropy as freezing is an exothermic process.

Entropy generation is [Enthalpy of freezing /T].

Let us look at the water at equilibrium with ice at 0 degc

Entropy generation at 0 degc = - 6.1/273 [ Q/T]

?Gibbs free energy = dH - TdS

Free energy change at 0 degc = - 6.1 - 273 [ -6.1/273] = 0 [ 0 degc = 273K]

[Enthalpy of freezing = -6.1 KJ/mol]

This explains how and why water and ice reach equilibrium having reached the same energy level. This is why ice and water coexist at 0 degc. When the Gibbs free energy change is zero the icing cannot proceed further to freezing. The process is not spontaneous. Any process becomes forward-moving spontaneous when the Gibbs free energy change dG is negative.

This negative entropy of ice compels water to find options so that the entropy can increase. The 2nd law of thermodynamics does not allow a negative entropy.

Why water expands to ice

Water expands into ice to increase its entropy. Ice is less dense than water. This is how and why ice expands at 0 degc.

How ice-water equilibrium is broken?

Referring back to Gibbs equation, dG = dH - TdS, the equilibrium can only be broken when dG is negative. In other words, when TdS > dH.?To make icing of water a spontaneous TdS of the Gibbs equation must increase.

To reduce dG and make it negative, you need to cool water to - 10 degc

At - 10 degc

Gibbs equation: - 6.1 - [ 263[ - 6.1/273]] = [- 6.1 + 5.87] = ??- 0.23 KJ/mol

Water freezes spontaneously at > -10 degc into a single phase.