(i) If there is an increase in the area of a solid object due to heating, then the expansion is called superficial or areal expansion.
(ii) Superficial expansion is determined in terms of coefficient of superficial expansion. The ratio of increase in area of the body, per degree rise in temperature to its unit area is called coefficient of superficial expansion. Coefficient of superficial expansion is different for different materials. Its SI unit is also per Kelvin.
(iii) The equation relating to the change in area to the change in temperature is given below:

\(\frac { \triangle A }{ { A }_{ 0 } } \) =α_A ΔT
ΔA  - Change in area
A₀ - Original area
ΔT - Change in area
α_A - Coefficient of superficial expansion

(i) When heat energy is supplied to a body, there can be an increase in the dimension of the object. This change in the dimension due to rise in temperature is called thermal expansion of the object.
(ii) The expansion of liquids (eg. mercury) can be seen when a thermometer is placed in warm water. All forms of matter (solid, liquid and gas) undergo expansion on heating.
(iii) When a solid is heated, the atoms gain energy and vibrate more vigorously. This results in the expansion of the solid.
(iv) The different types of expansion of solid are
i) Linear expansion
ii) Superficial expansion
iii) Cubical expansion
(v) When heated, the atoms in a liquid or gas gain energy and are forced further apart. The extent of expansion varies from substance to substance. For a given rise in temperature, a liquid will have more expansion than a solid and a gaseous substance has the highest expansion when compared with the other two.

Change in volume \((\Delta V)=0.3-0.25 =0.05\mathrm{~m}^{3}\)
Original volume \(\left(V_{0}\right)=0.3 \mathrm{~m}^{3}\)
Change in Temperature \(\Delta \mathrm{T}=50 \mathrm{~K}\)
\(a_{\mathrm{V}} =?  \)
\(\frac{\Delta V}{V_{0}} =a_{\mathrm{V}} \Delta \mathrm{T}\)
\(a_{\mathrm{V}} =\frac{0.05}{0.3 \times 50}=\frac{0.05}{15}=0.0033 \mathrm{~K}^{-1}\)
Co-efficient of cubical expansion of Zinc bar 0.0033

Data:
Initial pressure (P₁)= P
Final Pressure (P₂) = 4P
Initial volume (V₁) = 20cc = 20cm³
Final volume (V₂) = ?
Using Boyle's Law, PV = constant
P₁V₁ = P₂V₂
\({ V }_{ 2 }=\frac { { P }_{ 1 } }{ { P }_{ 2 } } \times { v }_{ 1 }\)
\(=\frac { P }{ 4P } \times 20{ cm }^{ 3 }\)
V₂ = 5 cm³

If a liquid is heated directly without using any container, then the expansion that we observe is termed as "real expansion" of the liquid.

(i) Increase in length per unit of the length of the solid object per degree celsius rise in temperature is called 'coefficient of linear expansion'.
(ii) Its SI unit is per kelvin.
\(\frac { \triangle L }{ { L }_{ 0 } } ={ \alpha }_{ L }\triangle T\Rightarrow { \alpha }_{ L }\frac { \triangle L }{ \triangle T.L_{ 0 } } \)
ΔL - change in length
L₀ - original length
ΔT - change in Temperature
α_L - coefficient of Linear expansion

Thermal energy is a form of energy which is transferred between any two objects due to the difference in their temperatures.

Charles's law is otherwise called as the law of volume. It states that, when the pressure of gas is kept constant, the volume of the gas is directly proportional to the temperature of the gas.
\(\mathrm{V} \propto {T}\)

The coefficient of linear expansion,
α_L =24 K^-1
The coefficient of cubical expansion,
α_v =3α_L= 3 x 24
= 72 K^-1
The initial temperature, T₁ = 303 K
The initial volume, V₀ = 0.3 m³
The final volume, V₁ = 0.35 m³
Change in volume ΔV = 0.35 - 0.30
= 0.05 m³
To find: The final temperature T₂= ?
ΔV = α_v. V₀ (ΔT)
0.05 = 72 x 0.3 x (T₂ - 303)
0.05 = 21.6 (T₂ - 303)
= 21.6 T₂ - 6544.8
21.6 T₂ = 6544.8 - 0.05
T₂ =\(\frac { 6544.8 }{ 21.6 } \)
Final temperature, T₂ = 303K

Length of AI sheet, L = 30 m
Coefficient of linear expansion, Δl = 23 x 10^-6 K^-1
Change in temperature ΔT = 300 k
To find: Change in length ΔL =?
ΔL = L α_L ΔL
= 30 x 23 x 10^-6 x 300
= 2.07 x 10^-1
ΔL = 0.207 m

A substance that heats up quickly has a low specific heat capacity. Higher the specific heat capacity of a substance, lower is the increase in its temperature.