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

(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:
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

(i) Co-efficient of apparent expansion is defined as the ratio of the apparent rise in the volume of the liquid per degree rise in temperature to its unit volume.
(ii) Its SI unit is K^-1.

When the temperature of a gas is kept constant, the volume of a fixed mass of  gas is inversely proportional to its pressure. \(\mathrm{P} \alpha \frac{1}{\mathrm{~V}}\)

One calorie is defined as the amount of heat energy required to raise the temperature of 1 gram of water through 1^o C.

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.

Ideal gas

8.31 J mol^-1 K^-1

Arial expansion