Question

An aluminum wing on a passenger jet is
40 m
long when its temperature is
19°C.
At what temperature would the wing be 6 cm (0.06 m) shorter?

Answer 1

T₁ is the initial temperature and T is the final temperature. B is a linear temperature expansion coefficient. dt - the change of the temperature. l -- length of aluminum wing.

$$B=\frac{1}{l}\times\frac{dl}{dt}$$

$$dt=\frac{1}{l}\times\frac{dl}{B}$$

$$\frac{1}{l}=0.025\ \ [\frac{1}{m}]$$ $$dl=-0.06\ \ [m]$$

$$dt=0.025\times\frac{0.06}{22.2\times10^{-6}}=\frac{6.7\times10^{-5}}{10^{-6}}=-67\ ^{o}C$$

$$T=T_1+dt=(19-67)\ ^{o}C=-48\ ^{o}C$$