Statement of Boyle's law:
When the temperature of a gas is kept constant, the volume of a fixed mass of gas is inversely proportional to its pressure.
∴ P α 1/V

In other words, for an invariable mass of a perfect gas, at constant temperature, the product of pressure and volume is a constant.
Pressure x Volume = constant
PV = constant

Cubical expansion:
(i) If there is an increase in the volume of a solid body due to heating, then the expansion is called cubical or volumetric expansion.
(ii) As in the cases of linear and areal expansion, cubical expansion is also expressed in terms of coefficient of cubical expansion. The ratio of increase in volume of the body per degree rise in temperature to its unit volume is called coefficient of cubical expansion. This is also measured in K^-1.

(iii) The equation relating to the change in volume to the change in temperature is given below:
\(\frac { \triangle V }{ { V }_{ 0 } } \) = α_v ΔT
ΔV - Change in volume
V₀ - Original volume
ΔT - Change in temperature
α_v - Coefficient of cubical expansion.

(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

Linear expansion:
(i) When a body is heated or cooled, the length of the body changes due to change in its temperature. This expansion is said to be a linear or longitudinal expansion.
(ii) The ration of increase in length of a body per degree celsius rise in temperature to its unit length is called the coefficient of linear expansion. Its SI unit is per Kelvin. The value of coefficient of linear expansion is different for different materials.

(iii) The equation relating the change in length to the change in temperature of a body is given below:
\(\frac { \triangle L }{ { L }_{ 0 } } \) =α_L ΔT
ΔL  - Change in length
L₀ - Original length
ΔT - Change in temperature
α_L - Coefficient of linear 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.

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

Data:
Level of the liquid L₁ = 50 ml
Level of the liquid L₂ = 48.5 ml
Level of the liquid L₃ = 51.2 ml
Apparent expansion = L₃ − L₁
= 51.2 ml – 50 ml = 1.2ml
Real expansion = L₃ − L₂
= 51.2 ml – 48.5ml = 2.7ml
So, Real expansion > apparent expansion

Aim:
To measure real and apparent expansion of liquid.
Apparatus Required:
a) Round bottomed flask, a narrow glass tube with a scale, burner.
Procedure:
b) The liquid whose real and apparent expansion is to be determined is poured in a container up to a level.
c) Mark this level as L₁.
d) Now, heat the container and the liquid using a burner.
e) Initially, the container receives the thermal energy and it expands.
f) As a result, the volume of the liquid appears to have reduced.
g) Mark this reduced level of liquid as L₂.
h) On further heating, the thermal energy is supplied to the liquid through the container results in the expansion of the liquid.
i) Hence, the level of liquid rises to L₃
j) Now, the difference between the levels L₁ and L₃ is called apparent expansion. Apparent expansion = L₃ - L₁.
k) The difference between the levels L₂ and L₃ is called real expansion. Real expansion = L₃ - L₂.
Result:
The real expansion is always more than the apparent expansion.

(i) The ideal gas equation is an equation, which relates to all the properties of an ideal gas.
(ii) An ideal gas obeys Boyle's law and Charles's law and Avogadro's law.
(iii) According to Boyle's law,
PV = constant ... (1)
(iv) According to Charles's law,
V/T = constant ... (2)
(v) According to Avogadro's law,
V/n = constant ... (3)
(vi) After combining equations (1), (2), and (3), we can get the following equation.
PV/nT = constant ... (4)
The above relation is called the combined gas law
(vii) If you consider a gas which contains μ moles of the gas, the number of atoms contained will be equal to μ times the Avogadro number, N_A. i.e.,
\(n=\mu N_A\) ...... (5)
(viii) Using equation (5), equation (4) can be written as
\(PV/\mu N_AT\) = constant
(ix) The value of constant in the above equation is taken to be k_B, which is called as Boltzmann's constant. Its value is (1.381 x10^-23JK^-1). Hence, we have the following equation:
\(PV/\mu N_AT=K_B\)
\(PV=\mu N_AK_BT\)
(xi) Here, \(\mu N_AK_B=R\), which is termed as universal gas constant whose value is 8.31 J mol^-1 K^-1.
PV = RT ...... (6)
Ideal gas equation is also called as equation of state because it gives the relation between the state variables and it is used to describe the state of any gas.

(i) 0°C ice is colder than water.
(ii) This can be explained in terms of the latent heat of fusion (336 kJ) which is required to convert ice at 0°C to water at 0°C.
(iii) In simpler terms water at 0°C has higher heat content than ice at the same temperature.
(iv) Thus we conclude ice at 0°C is colder, from either of your hands.
(v) Then, you would felt more chillness on those hand, you kept ice at 0°C.