A steel aircraft carrier is 358 m long when moving through the icy North Atlantic at a temperature of 1.99 °C. By how much does the carrier lengthen when it is traveling in the warm Mediterranean Sea at a temperature of 22.0 °C?
a = 13*10^-6/deg.C = Temp. coeff.
358*a*(T2-T1) = 358*13*10^-6*(22-1.99) = 0.093 m. = 9.3 cm.
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To find out how much the carrier lengthens when it's traveling in the warm Mediterranean Sea, we need to calculate the change in length due to the temperature difference.
The change in length of an object due to temperature is given by the formula:
ΔL = α * L_initial * ΔT
Where:
ΔL is the change in length
α is the coefficient of linear expansion
L_initial is the initial length of the object
ΔT is the change in temperature
To solve this problem, we need to know the coefficient of linear expansion for steel.
The coefficient of linear expansion for steel is typically around 12 x 10^-6 per °C.
Given:
L_initial = 358 m
T_initial = 1.99 °C
T_final = 22.0 °C
To calculate the change in length, we can now substitute the values in the formula:
ΔL = (12 x 10^-6 / °C) * (358 m) * (22.0 °C - 1.99 °C)
Calculating this expression will give us the change in length of the carrier when traveling in the warm Mediterranean Sea.