Change Of State

A change of state refers to the physical transformation of matter from one state to another—solid, liquid, or gas—without altering its chemical composition. This process is governed by the addition or removal of energy, typically in the form of heat. For example, when you heat ice (solid), it melts into water (liquid), and further heating turns it into vapour (gas). These transitions are common in everyday life. A hot cup of coffee cools down as the liquid evaporates, releasing steam into the air. Similarly, freezing water into ice for drinks is another simple illustration of a change of state. These transformations, while seemingly basic, are critical in numerous industrial processes, like refrigeration and distillation, which rely on the controlled manipulation of matter's physical states.

Change of State

A physical alteration in a matter is said to be a modification in the condition of the matter. These alterations are reversible in nature and do not entail any alterations to the chemical composition of the matter. Moreover, deposition, sublimation, melting, freezing, vaporization, etc. are some of examples of evolutions in the state of the matter.

What is Phase?

We know that there are three states of matter. So, the term phase is used to describe a specific state of matter, such as solid, liquid or gas. A transition from one phase to another is called a phase change. So we need to supply or extract heat from any substance to change its phase or state. For any given pressure a phase change takes place at a definite temperature. So the temperature will not change during phase change.
Water is a very common substance known to us. So at 0⁰C temperature ice and liquid water can change their phase and at 100⁰C the liquid water and steam can change their phase to each other at the atmospheric pressure.

Latent Heat

Latent heat is also called hidden heat. In this there is no change in the temperature of the body and because of that it is said to be hidden or latent as we are not feeling any change in the temperature of the body. The amount of heat required to change the state of the mass $m$ of the substance is written as $\square$ where $L$ is the latent heat. Its unit is $\mathrm{cal} / \mathrm{gm}$ or, $J / \mathrm{kg}$ and Dimension: $\left[L^2 T^{-2}\right]$

Basically, the latent heat is classified into two types
(i) Latent heat of fusion: The latent heat of fusion is the heat energy required to change one kilogram of the material in its solid state at its melting point to one kilogram of the material in its liquid state. The latent heat of fusion for water (or latent heat of ice) is $-L_F=L_{\text {ice }} \approx 80 \mathrm{cal} / \mathrm{gm} \approx 60 \mathrm{~kJ} / \mathrm{mol} \approx 336 \mathrm{kilo}-$ joule $/ \mathrm{kg}$
(ii) Latent heat of vaporisation: The latent heat of vaporisation is the heat energy required to change one kilogram of the material in its liquid state at its boiling point to one kilogram of the material in its gaseous state. The latent heat of vaporisation of water (the latent heat of steam) is $L_V=L_{\text {steam }} \approx 540 \mathrm{cal} / \mathrm{gm} \approx 40.8 \mathrm{~kJ} / \mathrm{mol} \approx 2260 \mathrm{kilojoule} / \mathrm{kg}$

The latent heat of vaporisation is more than the latent heat of fusion. This is because when a substance gets converted from liquid to vapour, so the increase in volume is large. Hence more amount of heat is required. But when a solid gets converted to a liquid, then there is a negligible increase in volume. Hence very small amount of heat is required.

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Solved Examples Based on Change of State

Example 1: The amount of heat required to raise the temperature of 1 g ice from 0 C to 10 C is $Q _ 1$ While $Q _ 2$ is required to heat 1 g water from 0 C to 10 C then

1) $Q_1=Q_2$
2) $Q_1>Q_2$
3) $Q_1<Q_2$
4) Nothing can be predicted

Solution:

Latent Heat

Amount of heat required to change the state of the mass m of the substance.

wherein

Temperature remains constant.

As ice required some heat for fusion as well i.e caused latent heat of fusion

Hence, the answer is the option (2).

Example 2: The amount of energy (in cal) required to raise the temperature of 5 g ice at $0^{\circ} \mathrm{C}$ to water at $20^{\circ} \mathrm{C}$ is (specific heat capacity of water $=1 \mathrm{cal} / \mathrm{g}^0 \mathrm{C}$, latent heat of fusion $=80 \mathrm{cal} / \mathrm{g}$ )

1)300

2)400

3) 500

4)600

Solution:

Latent Heat
$
\mathrm{Q}=\mathrm{mL}
$

wherein
$Q=$ heat supplied
$\mathrm{m}=$ mass of substance
$\mathrm{L}=$ latent heat

$
\begin{aligned}
& Q=m L+m s \Delta T \\
& =5 \times 80 \mathrm{cal}+5 \times 20 \times 1=500 \mathrm{cal}
\end{aligned}
$

Hence, the answer is the option (3).

Example 3: When a gram of ice at $-10^{\circ} \mathrm{C}$ ( specific heat $=0.5 \mathrm{cal} g^{-1{ }^{\circ}} \mathrm{C}^{-1}$ ) is added to $M_2$ gram of water at $50^{\circ} \mathrm{C}$, finally no ice is left and the water is at $0^{\circ} \mathrm{C}$. The value of latent heat of ice, in cal $g^{-1}$ is :

1) $\frac{5 M_1}{M_2}-50$
2) $\frac{50 M_2}{M_1}$
3) $\frac{5 M_2}{M_1}-5$
4) $\frac{50 M_2}{M_1}-5$

Solution:

Latent Heat

$
\begin{aligned}
& Q=m L \\
& \text { wherein } \\
& Q=\text { heat supplied } \\
& m=\text { mass of substance } \\
& L=\text { latent heat }
\end{aligned}
$
As we know that

$
\begin{aligned}
& \text { heat taken by ice }=\text { heat given by water } \\
& M_1 S_{i c e}(10)+M_1 L g=M_2 S_{\text {water }}(50) \\
& \Rightarrow \frac{M_1}{2} \times 10+M_1 L g=M_2 \times 50 \\
& \Rightarrow 5+L g=50 \frac{M_2}{M_1} \\
& \Rightarrow L g=\frac{50 M_2}{M_1}-5
\end{aligned}
$

Hence, the answer is the option (4).

Example 4: The amount of heat (in cal) required to convert 2gm of water which is at 80^o C to 2 gm of vapour at 100^o C is

1) 1012

2) 912

3) 1112

4)1212

Solution:

The latent heat of vaporisation is 536 cal/gm.

$\begin{aligned} & Q=m s \Delta T+m L \\ & =2 \times 1 \times 20 \mathrm{cal}+2 \times 536 \mathrm{cal}=1112 \mathrm{cal}\end{aligned}$

Hence, the answer is the option (3).

Example 5: Latent heat of fusion (in cal/gm) of ice is

1) 1

2) 20

3) 60

4) 80

Solution:
$
L_F=L_{\mathrm{ice}} \approx 80 \mathrm{cal} / \mathrm{gm} \approx 60 \mathrm{~kJ} / \mathrm{mol} \approx 336 \text { kilo }- \text { joule } / \mathrm{kg}
$
The latent heat of the fusion of ice is $80 \mathrm{cal} / \mathrm{gm}$.

Hence, the answer is the option (4).

Summary

A change of state involves the transformation of matter between solid, liquid, and gas without altering its chemical structure, typically through the addition or removal of heat. Key processes include melting, freezing, vaporization, sublimation, and deposition. The latent heat required for these transitions is either for fusion (solid to liquid) or vaporization (liquid to gas), with no temperature change during the process. Real-life examples like melting ice and boiling water illustrate these concepts, which are essential for understanding physical changes in matter.