The supersonic aircraft Concorde has a length of 61.3 m when sitting on the grou

Question

The supersonic aircraft Concorde has a length of 61.3 m when sitting on the ground on a typical day when the temperature is 18.0 degree 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 times10^-5/degree C. What is the temperature T of the Concorde's skin in flight? T =

Explanation / Answer

We know that

change in Length = alpha(initial length)(change in temp)
0.25 m = 2.4 x 10-5/C(61.3 m)(Tf - 18 C)
(0.25 m/(2.4 x 10-5/C(61.3 m))) + 18 = Tf
Tf = 187.9293 C

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