**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 (**γ_{Apparent}**):** 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 (**γ_{Real}**):** 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, γ_{Real} = γ_{Apparent}
+ γ_{Vessel}

The change in volume in liquid relative to vessel is:

ΔV_{Apparent} = V₀ γ_{Apparent}
ΔT

ΔV_{Apparent} = V₀ (γ_{Real}
– γ_{Vessel}) ΔT = V₀ (γ_{Real} – 3α) ΔT

ΔVApparent = V₀ (γ_{Real} – 3α)
ΔT

Where,

α = Coefficient of linear expansion of the vessel.