An aluminum wing on a passenger jet is 38 m long when its temperature is 28°C. At what temperature would the wing be 9 cm (0.09 m) shorter?

Answer 1

To calculate the final temperature from the given quantities, we use the equation for linear thermal expansion:

ΔL = L₀ × α × ΔT, where :

ΔL is the change in length of the wing: -9 cm

L₀ is the initial length of the wing: 38 m

α is the coefficient of linear thermal expansion for aluminum: 2.3 × 10^-5 / °C

ΔT is the final temperature T_f - the initial temperature T_i (28° C)

To calculate the final temperature, this equation can be rewritten:

T_f = T_i + ΔL / (L₀ × α)

Putting the known values into this equation:

T_f = 28° C - 0.09 m /( 38 m × 2.3 × 10^-5 / °C) = 28° C - 103° C = -75° C