Why do the substances expand on heating? Explain using atomic theory.

i) In matter, interatomic/molecular forces bind the atoms or molecules. The interatomic separation between the atoms determines the potential energy due to binding force. 
The variation is shown in the figure below. 

ii) Consider two atoms A₁ and A₂ at O and P. At a point of minimum energy, the atoms are at a distance r₀ apart and temperature is minimum at this point.
iii) If we increase the temperature, the atoms absorb the energy and energy of each atom increases.
iv) Let at temperature T₁, the energy be U_1. There are two positions r₁(=OL) and r₂(=OK) corresponding to energy U₁.
v) Both the positions r₁ and r₂ are equally probable. Therefore the atom A₂ starts vibrating between positions L and K.
vi) At temperature T₁, the position of atom A₂ is taken at G (mean position of L and K).
vii) The potential energy curve is unsymmetrical and G is on the right side of P. Hence, at temperature T₁, the average distance between A₁ and A₂ is OG = r₀ +∆r > r₀.
viii) Thus with the increase in temperature, the distance between two atoms increases and hence substance expands on heating.