What is the In-Flight Temperature of Concorde's Skin?

[azn_enigma]

~~~Now I'm Really Stuck~~~

The supersonic aircraft Concorde has a length of 61.2 m when sitting on the ground on a typical day when the temperature is 16.0 °C. The Concorde is primarily made of aluminum. In flight at twice the speed of sound, friction with the air warms the Concorde's skin and causes the aircraft to lengthen by 25.0 cm. (The passenger cabin is on rollers, so the airplane expands around the passenger cabin.)

Take the coefficient of linear expansion for aluminum to be alpha = 2.40×10−5 /°C

What is the temperature T of the Concorde's skin in flight?


i got 186.2


not sure though :s

 

[radou]

If you followed the expression $$l = l_{0}(1+ k \Delta t)$$, where $$\Delta t = t - t_{0}$$, and k is your coefficient of linear expansion, then it should be correct.

 

[ravenprp]

weat_smile:

Hi there,

It looks like you have made a good attempt at solving the problem. However, I believe your answer may be incorrect.

To solve this problem, we can use the formula for linear expansion:

ΔL = L0 * α * ΔT

Where:
ΔL = change in length
L0 = initial length
α = coefficient of linear expansion
ΔT = change in temperature

In this case, we know that the change in length (ΔL) is 25.0 cm, the initial length (L0) is 61.2 m, and the coefficient of linear expansion (α) is 2.40×10−5 /°C. We are trying to find the change in temperature (ΔT).

Plugging in the values, we get:

25.0 cm = 61.2 m * 2.40×10−5 /°C * ΔT

Solving for ΔT, we get:

ΔT = 25.0 cm / (61.2 m * 2.40×10−5 /°C) = 173.6 °C

Therefore, the temperature of the Concorde's skin in flight would be 16.0 °C + 173.6 °C = 189.6 °C.

I hope this helps! Keep up the good work and don't get discouraged. Math can be tricky sometimes, but with practice, you'll get the hang of it. :)