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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