Thermodynamics of phase change of water

Summary

Ice

Water changes to the ice at 0 degrees Celsius and 1-atmosphere pressure because its negative entropy of icing makes it unstable [ 2nd law of thermodynamics] and it has only one option, which is to expand into ice. Water expands in order to increase its entropy. At zero degrees Celsius, ice has a density of 0.917 g/cm3, whereas water has a density of 0.9998 g/cm3. Water is heavier than ice. As a substance becomes more dispersed in space, the thermal energy it carries is also spread over a larger volume, leading to an increase in its entropy.

Vapor

Because water reaches its maximum level of entropy at 100 degrees Celsius, it converts to vapor. Water exhausts all of its energy to raise its temperature any further. Entropy consumes an amount of water’s energy. To accommodate entropy, water expands and enters the vapor phase.

Water boiling

Water boils at 100 degc because at 100 degc water has no energy to exceed 100 degc at 1 atmospheric pressure. At 100 degc water generates vapor that holds the entropy load.

Water has a certain amount of stored potential energy in its bonds. The first thing to remember water has two types of enthalpies one is called [1] enthalpy of vaporization or enthalpy of fusion and [2] enthalpy of formation. In phase change, we do not break H-O-H bonds so we are not concerned with the enthalpy of the formation of water. In phase change, we are only concerned with intermolecular bonds

Enthalpy of phase change

The enthalpy of phase change, also known as the latent heat, is the amount of energy (enthalpy) that must be added or removed from the water to transform water into different phases. In the case of the evaporation of water, latent heat has two parts [1] sensible heat and [2] heat of vaporization. At 100 degc we are concerned with only heat of vaporization.

Enthalpy of vaporization of water at 100 degc = 2256 kJ/kg [ sensible heat at 100 degc is a fixed quantity of heat]

Enthalpy of fusion of ice at 0 degc = - 6.03 KJ/mol

Phase diagram of water

The red lines separating one phase from another are equilibrium lines.

What is equilibrium?

When two phases have the same available energy [ free energy] that we normally call Gibbs free energy, we call the phases in equilibrium. On the red lines in the image, since both phases have the same energy, they can travel from one phase to another freely. On the red dividing lines, two phases coexist. These are the equilibrium lines. 

Temperature-Entropy diagram of water

Entropy plays a major role in phase change. In this bell shape curve, on the left of the bell outline, there is a water region. On the right of the bell outline, there is a superheated steam region.

Inside the bell, there is the saturated region. Here water and vapor coexist and water and vapor have the same energy. Y-axis on the left is temperature. X -axis is entropy. Y axis on right is enthalpy. X-values written in violet color are the dryness fraction of water. The dryness fraction is a measure of intermolecular forces between water molecules. The topmost point of the bell is the critical point where two phases of water collapse into one phase.

The phase change of water

The first thing to remember is that at every temperature at 1 atmospheric pressure, the water has some fixed quantity of energy. The second thing is that when water breaks or makes intermolecular bonds like in the case of evaporation or freezing, a part of its energy gets spent to handle entropy. Only after discounting the energy lost by entropy, water has free energy available for phase change. Water’s energy is its internal energy. Within internal energy water’s energy is its potential energy stored in the intermolecular bonds [ we are concerned with intermolecular bonds]. The kinetic energy of water exists in water molecules’ vibrations.  

It is important to remember both phases at phase change have the same energy and therefore both phases coexist.

Water’s phase change to ice: Why does it happen at 0 degc?

The answer is water and ice are at equilibrium at 0 degc

How and why?

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

How to break ice-water equilibrium?

Referring back to Gibbs equation, dG = dH - TdS, the equilibrium can only be broken when dG is negative. In another word, 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.

Water phase change to vapor:

Why does it happen at 100 degc at 1 atmospheric pressure?

When water is heated, it reaches 100 degc by taking sensible heat. H- bonds begin breaking at 100 degc. As the intermolecular bonds break water begins expanding to accommodate entropy. In the process, entropy eats up a part of energy leaving some energy for water to evaporate which is the enthalpy of vaporization of water. This process continues until all H-bonds have broken at 100 degc and the dryness fraction of water has reached 1 and entropy has reached the maximum level. The dryness fraction is defined as the ratio of the mass of dry steam (vapor) to the combined mass of dry steam (vapor) & mass of liquid in the mixture. At this point, water has exhausted its all energy. Water transforms to vapor into a much larger volume to accommodate entropy loads.

Let us look at Gibbs equation

Enthalpy of vaporization [H] at 100 degc = 2256 KJ/kg

dG = dH – TdS = 2256 – 373 [ 2256/373] = 0

This explains how and why water and vapor reach equilibrium and coexist having finished all energy at 100 degc and 1 atmospheric pressure.

Why water boils at 100 degc

Water boils at 100 degc because at water has no energy to exceed 100 degc at 1 atmospheric pressure. At 100 degc water generates vapor that holds the entropy load. Having exhausted all energy water and vapor coexist at 100 degc and 1 atmospheric pressure known as saturated steam.