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Phase Change


One can use the term phase to describe a specific state of matter, such as solid state, liquid state or gaseous  state. The compound $H_{2}O$ exists in the solid phase as ice, in the liquid phase as water, and in the gaseous phase as steam. A transition from one state to another is called a phase change or phase transition. During phase transition the temperature remains constant regardless of the amount of heat added. For any given pressure a phase change takes place at a definite temperature, usually accompanied by emission or absorption of heat and a change of volume and density. 

Focusing on the three common states of matter, six different phase changes are possible. Which is given in the following table 
Phase Change Table
The most familiar phase change occurs between the solid and liquid states and the liquid and gaseous state. In this section we will learn more about phase change. 

Phase Changes of Water

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This diagram illustrates the heating curve for water and depicts how temperature changes as heat is added to a substance.
Phase Change Diagram

Solid to Liquid phase change
Initially the ice is below its freezing point (A to B region). When we add heat to ice at $0^{0}C$ and normal atmospheric pressure it reaches its melting point, the temperature of the ice dose not increase. Instead, some of it melts to form liquid water. At this stage both solid and liquid exists. If we add the heat slowly, to maintain the system very close to thermal equilibrium, the temperature remains at $0^{0}C$ until all the ice is melted. The effect of adding heat to this system is not to raise its temperature but to change its phase from solid to liquid (B to C region).
The heat necessary to melt the ice is termed the heat of fusion for water. And it is a measure of how much energy is required to convert a solid into a liquid.
To change 1kg of ice at $0^{0}C$ to 1kg of liquid water at $0^{0}C$ and normal atmospheric pressure requires $3.34 \times 10^{5}J$ of heat.

Region C to D
Once the ice has melted, the energy added to the liquid water can now go to increase the kinetic energy of the water molecules, and the temperature begin to rise again. The rate at which the temperature rises is governed by the specific heat of liquid water. The heat curve reaches the second plateau at D (waters boiling point of $100^{0}C$).

Liquid to Gas phase change
Liquid to gas phase change at the region of D to E is shown in the above diagram. T this temperature, any heat added to the water goes breaking the hydrogen bonds between the water molecules as liquid water is converted to steam. Just as with the first plateau at the melting point, the temperature remains constant as long as the liquid and and gas phases coexist. The wide region indicates that much more energy is required for the vaporization process as opposed to the melting process.
The heat need to convert liquid water to steam is called the heat of vaporization of water. Vaporization takes significantly more energy than melting because to convert liquid water to steam requires completely breaking the hydrogen bonds and separating the water molecules. The last section of heating curve represents the situation when all the liquid water has been converted to steam.

Phase Change Diagram

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Phase changes occur when heat is added or subtracted from a substance, pressure can also bring about phase changes. An increase in pressure compresses a substance and favors the solid state, while a decrease in pressure allows a substance to expand and favors the gaseous state. The relation between temperature, pressure and phase can be displayed using a phase diagram.
Water Phase Diagram
In a phase diagram, temperature is plotted on the horizontal axis and pressure along the vertical axis. The region for solid, liquid and gas are defined for various combinations of temperature and pressure.

Phase Change Equation

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The amount of energy per unit mass that must be transferred as thermal energy when a sample completely undergoes a phase change is known as the heat of transformation $L$.
Thus, when a sample of mass $m$ completely undergoes a phase change, the total energy transferred is
$Q$ = $Lm$
$Q$ = The total heat energy transferred
$L$ = Heat of transformation
$m$ = Mass of the sample

The heat of transformation have different value depends on the phase transition, if the phase changes is from liquid to solid or from solid to liquid then the heat of transformation is known as
the heat of fusion ($L_{f}$). If the phase changes is from gas to liquid or from liquid to gas, the thermal energy required for this transformation is known as the heat of Vaporization ($L_{v}$).

Phase Change Problems

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The following are the phase change problems:

Solved Examples

Question 1: How much heat energy is needed to melt 6 grams of ice at its melting point?
The heat of fusion of water is given by $L_{f}$ = $\frac{333 J}{1 g}$

Heat required is 

$Q$ = $Lm$

= $\frac{333 J}{1 g}$$\times 6g$

=$2 \times 10^{3}J$


Question 2: How much is the energy required to convert $1$ grams of water at $100 ^{0}C$ to steam at $100 ^{0}C$?
We know that the heat of Vaporization  $L_{v}$ = $2.26 \times 10^{6}$J/kg

Heat required is 

$Q$ = $Lm$

= $(2.26 \times 10^{6})\times (1 \times 10^{-3})$

=$2.26 \times 10^{3}J$