# Solid Expansion Formula

Is the coefficient or number associated with the thermal expansion of a solid due to an increase in temperature. It compares the large of the solid 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 solid

L: Length of the solid before the change o temperature

ΔT: Change of the temperature

α: Coefficient of expansion associated individually to each material

Solid Expansion equation Questions:

1) A solid with a coefficient of expansion of 19*10^{(-6)} /°C is subject to a change of temperature of 10 °C. If the solid's length was 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)* (19*10^{(-6)}/°C)*10°C = 1.9*10^{(-6)} m

ΔL = 1.9*10^{(-8)} cm

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

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

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