Answer:
The aluminum vat will be approximately 0.0176 meters (or 17.6 millimeters) longer when it contains boiling water at 1 atm pressure.
Step-by-step explanation:
To calculate the change in length of the aluminum vat when it contains boiling water at 1 atm pressure, we can use the coefficient of linear expansion for aluminum. The coefficient of linear expansion (α) represents how much a material's length changes per degree Celsius of temperature change.
For aluminum, the coefficient of linear expansion is approximately 0.000022 per °C (at around room temperature).
The formula to calculate the change in length (ΔL) is given by:
ΔL = α * L * ΔT
where:
ΔL = change in length
α = coefficient of linear expansion
L = original length
ΔT = change in temperature
Given:
L = 11 m (original length)
ΔT = change in temperature = boiling point of water (100°C) - room temperature (20°C) = 80°C
Now, let's plug the values into the formula:
ΔL = 0.000022 * 11 m * 80°C
ΔL ≈ 0.0176 m
Therefore,the aluminum vat will be approximately 0.0176 meters (or 17.6 millimeters) longer when it contains boiling water at 1 atm pressure.