Final answer:
Using the thermal expansion equation and the coefficient of linear expansion for aluminum, the estimated temperature of the Concorde's skin in flight is approximately 195.81^oC. This temperature is obtained by accounting for the expansion of the airplane due to the heat generated by friction at high speeds.
Step-by-step explanation:
To determine the temperature of the Concorde's skin in flight, we need to use the concept of thermal expansion of materials, specifically aluminum.
Thermal expansion can be described with the equation ΔL = L_0αΔT, where ΔL is the change in length, L_0 is the original length, α is the coefficient of linear expansion, and ΔT is the change in temperature.
We were provided that the Concorde expands by 25 cm (0.25 m) during flight, and its original length is 62.1 m.
The thermal expansion coefficient for aluminum is approximately 22x10^-6 1/^oC.
The original temperature on a typical day is given as 15^oC.
To find the final temperature, we solve for ΔT using the equation above:
ΔT = ΔL / (L_0α). Plugging in the numbers, we have ΔT = 0.25 m / (62.1 m * 22x10^-6 1/^oC) = ΔT = 0.25 m / (62.1 m * 22x10^-6 1/^oC) = 180.81^oC.
Adding this to the original temperature gives us the temperature of the skin in flight: 15^oC + 180.81^oC = 195.81^oC.