a steel aircraft carrier is 370 meter long when moving through the icy north atlantic at a temperature of 2.0 degrees celsius. by how much the carrier lengthen when it is travelling in the warm mediterranean sea at a temperature of 21 degrees celsius?
Pharmacy
To determine how much the steel aircraft carrier lengthens when it is traveling in the warm Mediterranean Sea at a temperature of 21 degrees Celsius, we can use the thermal expansion coefficient of steel.
The thermal expansion coefficient (α) of steel is approximately 12 x 10^-6 per degree Celsius.
We can use the formula for thermal expansion to calculate the change in length (ΔL):
ΔL = α * L * ΔT
Where:
ΔL = Change in length
α = Thermal expansion coefficient
L = Original length
ΔT = Change in temperature
Given:
Original length (L) = 370 meters
Temperature change (ΔT) = 21°C - 2°C = 19°C
Thermal expansion coefficient (α) = 12 x 10^-6 per °C
Substituting the given values into the formula:
ΔL = (12 x 10^-6) * 370 * 19
Calculating this:
ΔL = (12 * 10^-6) * 370 * 19
ΔL = 0.0834 meters
Therefore, the steel aircraft carrier would lengthen by approximately 0.0834 meters when it is traveling in the warm Mediterranean Sea at a temperature of 21 degrees Celsius.
To calculate the change in length of the steel aircraft carrier, we need to apply the principle of thermal expansion. The equation that represents the change in length due to temperature is given by:
ΔL = α * L * ΔT
Where:
ΔL is the change in length
α is the coefficient of linear expansion for the material (steel in this case)
L is the original length
ΔT is the change in temperature
First, we need to find the coefficient of linear expansion for steel. For most common steels, the coefficient of linear expansion is approximately 12 x 10^-6 (1/°C). However, it can vary depending on the specific type of steel. For this explanation, let's assume it to be 12 x 10^-6 (1/°C).
Given:
Original length of the carrier (L) = 370 meters
Change in temperature (ΔT) = 21°C - 2°C = 19°C
Coefficient of linear expansion for steel (α) = 12 x 10^-6 (1/°C)
Now, substituting these values into the equation, we can calculate the change in length (ΔL):
ΔL = (12 x 10^-6) * 370 * 19
Using the values in the equation, we can simplify the calculation:
ΔL = 8.508 meters
Therefore, the steel aircraft carrier would elongate by approximately 8.508 meters when traveling in the warm Mediterranean Sea at a temperature of 21 degrees Celsius.