At what temperature would the wing

Question

An aluminum wing on a passenger jet is 26 m

 long when its temperature is 21°C.

 At what temperature would the wing be 6 cm (0.06 m) shorter?

Answer 1

You need to know the metal's thermal expansion coefficient to solve this. Generally, you'll find this in a textbook or a handout. I looked it up online for plain aluminum and found 22.5 µm/(m ºC). I'll rewrite that as 22.5x10^-6 m/(m ºC) to do the unit conversion right away and have everything in meters..

Thermal expansion or contraction is always a proportion of the original length, so

ΔL = αL₀ΔT

Let's solve for ΔT to get

ΔT = ΔL/(αL₀)

Now put in our given values. ΔL is negative since the wing shrank and a Δ is always final value - initial value

T-21°C = -0.06m/(22.5x10^-6 m/(m ºC)×26m)

On the right, the meters all cancel leaving 1/(1/°C) which is just °C. That's a good sign! Having the right unit should give you confidence that the number along with it is also right.

T-21°C = -103°C

Solving for T gives us -82°C