The supersonic aircraft Concorde has a length of 61.9 m when sitting on the grou

Question

The supersonic aircraft Concorde has a length of 61.9 m when sitting on the ground on a typical day when the temperature is 17.0 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 20.0 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 = 2.40×105 /C . What is the temperature T of the Concorde's skin in flight? Temp should be in celcius

Explanation / Answer

Here,

length , Lo = 61.9 m

T1 = 17 degree C

change in length , x = 20 cm = 0.20 m

= 2.40×105 1/C

for the final temperature T

x = Lo * * (T - T1)

0.20 = 61.9 * 2.40×10^5 * (T - 17)

solving for T

T = 151.6 degree C

the final temperature of the plane is flight is 151.6 degree C

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