A steel aircraft carrier is 361 m long when moving through the icy North Atlantic at a temperature of 1.7° C. By how much does the carrier lengthen when it is traveling in the warm Mediterranean Sea at a temperature of 16° C?
To determine the change in length of the steel aircraft carrier when moving from the North Atlantic to the Mediterranean Sea, we can use the concept of thermal expansion. Thermal expansion is the tendency of a material to expand or contract in response to changes in temperature.
The formula for linear thermal expansion is given by:
ΔL = L0 * α * ΔT
ΔL represents the change in length, L0 is the initial length (361 m in this case), α is the coefficient of linear expansion, and ΔT is the change in temperature.
The coefficient of linear expansion for steel is approximately 12 x 10^-6 per degree Celsius.
Now, let's calculate the change in length:
ΔT = 16°C - 1.7°C = 14.3°C
ΔL = 361 m * (12 x 10^-6) * 14.3°C
ΔL ≈ 0.062 m
Therefore, the steel aircraft carrier would lengthen by approximately 0.062 meters when traveling from the North Atlantic to the Mediterranean Sea.
To find out how much the steel aircraft carrier lengthens when it is traveling in the warm Mediterranean Sea at a temperature of 16°C, we can use the concept of thermal expansion.
The equation for thermal expansion is given by:
ΔL = α * L0 * ΔT
Where:
- ΔL is the change in length
- α is the coefficient of linear expansion of the material (in this case, steel)
- L0 is the original length of the object
- ΔT is the change in temperature
First, we need to determine the coefficient of linear expansion (α) for steel. The coefficient of linear expansion for steel is approximately 12 × 10^(-6) per degree Celsius.
Now we can calculate the change in length (ΔL). Given that the original length (L0) is 361 m and the change in temperature (ΔT) is 16°C - 1.7°C = 14.3°C, we can substitute these values into the equation.
ΔL = (12 × 10^(-6) /°C) * 361 m * 14.3°C
Calculating this:
ΔL = 6.161 m
Therefore, the steel aircraft carrier lengthens by approximately 6.161 meters when traveling in the warm Mediterranean Sea at a temperature of 16°C.
deltaL = (361 m)*alpha*(16 - 1.7)
"alpha" is the coefficient of linear expansion for steel.
alpha = 13*10^-6 (deg C)^-1
deltaL = .0672 m = 6.7 cm