Thermal Expansion in Liquids
Liquids do not have linear and superficial expansion but these only have volume expansion. Since liquids are always to be heated along with the vessel that contains them so initially on heating the system, the level of liquid in vessel falls but later on, it starts rising due to faster expansion of the liquid.
The actual increase in the volume of the liquid = The apparent increase in the volume of liquid + The increase in the volume of the vessel.
Liquids have two coefficients of volume expansion.
1. Coefficientof Apparent Expansion (γApparent): It is due to the apparent increase in the volume of liquid if expansion of vessel containing the liquid is not takeninto account.
\({{\gamma }_{apparent}}=\frac{Apparent\,\,\exp ansion\,\,in\,\,volume}{Initial\,\,Volume\times \Delta T}=\frac{{{\left( \Delta V \right)}_{Apparnet}}}{{{V}_{0}}\times \Delta T}\).
2. Coefficient of Real Expansion (γReal): It is due to the actual increase in volume of liquid due to heating.
\(\left( {{\gamma }_{\operatorname{Re}al}} \right)=\frac{\operatorname{Re}al\,\,increase\,\,in\,\,volume}{Initial\,\,volume\times \Delta T}=\frac{{{\left( \Delta V \right)}_{\operatorname{Re}al}}}{{{V}_{0}}\times \Delta T}\).
The coefficient of expansion of flask, \({{\gamma }_{Vessel}}=\frac{{{\left( \Delta V\right)}_{Vessel}}}{{{V}_{0}}\times \Delta T}\).
Hence, γReal = γApparent + γVessel
The change in volume in liquid relative to vessel is:
ΔVApparent = V₀ γApparent ΔT
ΔVApparent = V₀ (γReal – γVessel) ΔT = V₀ (γReal – 3α) ΔT
ΔVApparent = V₀ (γReal – 3α) ΔT
Where,
α = Coefficient of linear expansion of the vessel.