(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.

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

(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.

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.

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.