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 = L₀(1+α_L∆T)

We have:

L_f = Final length

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

L_f = L₀ (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 L₀ = 200m, ∆T = 330°C-18°C = 312°C and α_L = 54* 10^-6 °C^-1 for oak.

L_f = L₀ (1+α_L∆T)

L_f = 200m*(1+54* 10^-6 °C^-1*312°C)

L_f = 203.37m.