The supersonic aircraft Concorde has a length of 63.0 m when sitting on the grou

Question

The supersonic aircraft Concorde has a length of 63.0 m when sitting on the ground on a typical day when the temperature is 14.0 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 30.0 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 times 10^-5/degree C. What is the temperature T of the Concorde's skin in flight?

Explanation / Answer

The coefficient of thermal expansion describes how the size of an object changes with a change in temperature. Specifically, it measures the fractional change in size per degree change in temperature at a constant pressure. Several types of coefficients have been developed: volumetric, area, and linear.

l = l t

0.3 = 63*2.4*10^-5*[T-14]

198.41 = [T-14]

T = 212.41 °C

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