# Liquid Expansion Formula

Liquid Expansion Formula

Is the coefficient or number associated with the thermal expansion of a liquid due to an increase in temperature. It compares the space of the occupied when it is measured at different temperatures, keeping other physical quantities like pressure at a constant value. There are linear, surface and volumetric expansion, where the linear is the more commonly used. This is written as:

Linear expansion = (initial length) * (coefficient of linear expansion) * (change of the temperature)

The equation is

ΔL= L α ΔT

We have:

ΔL: Expansion of the liquid

L: Length of the liquid before the change o temperature

ΔT: Change of the temperature

α: Coefficient of expansion associated individually to each material

Liquid Expansion equation Questions:

1) A liquid with a coefficient of expansion of 180*10(-6) /°C is subject to a change of temperature of 10 °C. If the liquid occupied a length of 1 cm before increasing the temperature, what is the change in its length?

Answer: The expansion is given by the equation:

ΔL = L α ΔT

substituting the value of L, the change in temperature and α,

ΔL = (0.01 m)* (180*10(-6)/°C)*10°C = 18*10(-6) m

ΔL = 18*10(-8) cm

2) A liquid is subject to a change of temperature of 50 °C, it changes its length occupied from 10 cm to 9 cm, what is the coefficient of expansion of the liquid?

Answer: The expansion is given by the equation:

ΔL= L α ΔT

From which it can be obtained the α,

α = ΔL /L ΔT

Then, substituting the value of change of temperature, and calculating the change of length ΔL = (Lf - Li) = (10 cm -9cm) = 1 cm,

α = 1 cm / (50 °C * 10 cm) = 2*10(-3)/°C