# Thermal Expansion Formula

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

Lf = L0(1+αL∆T)

We have:

Lf = Final length

L0 = Initial length

αL = 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 L0 = 10m, ∆T = 190°C and αL = 23* 10-6 °C-1 for the aluminum.

Lf = L0 (1+αL∆T)

Lf = 10m*(1+23* 10-6 °C-1*190°C)

Lf = 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 L0 = 200m, ∆T = 330°C-18°C = 312°C and αL = 54* 10-6 °C-1 for oak.

Lf = L0 (1+αL∆T)

Lf = 200m*(1+54* 10-6 °C-1*312°C)

Lf = 203.37m.