# Thermal Expansion Formula

Thermal expansion is the increase in length suffered by a body due to an increase in temperature caused by an external medium.

Final length = initial length*(1+ coefficient of linear expansion * temperature difference)

The equation is written

L_{f} = L_{0}(1+α_{L}∆T)

We have:

L_{f} = Final length

L_{0} = Initial length

α_{L} = Coefficient of linear expansion

∆T = Temperature difference.

Thermal expansion Questions:

1) An 10m long aluminum rod initially, if you increase the temperature by 190°C from its initial temperature, how much longer will the rod be?

Answer: First calculate the thermal expansion using the formula above, where L_{0} = 10m, ∆T = 190°C and α_{L} = 23* 10^{-6} °C^{-1} for the aluminum.

L_{f} = L_{0} (1+α_{L}∆T)

L_{f} = 10m*(1+23* 10^{-6} °C^{-1}*190°C)

L_{f} = 10.0437m.

2) An 200m long oak bar at a temperature of 18°C initially, if the temperature is increased to 330°C, how much longer will the bar be?

Answer: First calculate the thermal expansion using the formula above, where L_{0} = 200m, ∆T = 330°C-18°C = 312°C and α_{L} = 54* 10^{-6} °C^{-1} for oak.

L_{f} = L_{0} (1+α_{L}∆T)

L_{f} = 200m*(1+54* 10^{-6} °C^{-1}*312°C)

L_{f} = 203.37m.

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