<p>The supersonic aircraft Concorde has a length of 61.4 when sitting on the gro

Question

<p>The supersonic aircraft Concorde has a length of 61.4 when sitting on the ground on a typical day when the temperature is 17.0. 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 . (The passenger cabin is on rollers, so the airplane expands around the passenger cabin.)<br /><br />Take the coefficient of linear expansion for aluminum to be = 2.40&#215;10&#8722;5.What is the temperature of the Concorde's skin in flight?<br /><br /></p>

Explanation / Answer

The equation of linear expansion is:

L = L0 T

Rearranging to solve for T1

L = L0 T

L/( L0) = T

T = T1 - T0 = L /( L0)

T1 = L/( L0) + T0

Plugging in our given values:

T1 = (30.0 m)/((22.2 * 10-6 (Co)-1) 61.4 m) + 17o

T1 = 22230 Co

Note: I'm assuming that units are in standard SI (Celsius for temperature, meters for length). I couldn't make out the coefficient of linear expansion you gave so I looked up the value online. The formula:

T1 = L/( L0) + T0

Should give you the correct answer in case any of my values were incorrect.

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