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An aluminum vat is 11 m long at room temperature (20°C). How much longer is it when it contains boiling water at 1 atm pressure?

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User Bery
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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.

User Shubham Mittal
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