How Does Mercury Completely Fill an Aluminum Container When Heated?

In summary, the problem is to find the final temperature at which a 1-liter aluminum container, filled with 0.975 liters of mercury, will completely fill the container when both are heated. The coefficients of thermal expansion for aluminum and mercury are given. The formulas for calculating the final temperature for each substance are provided, but it is unclear how to combine them for this specific problem. An attachment may provide further clarification.
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apaxapax
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Homework Statement



A 1-liter aluminum container at 20oC is filled with 0.975 liters of mercury at
20oC. If both the container and the mercury are heated, at what final temperature
will the mercury completely fill the container?
αAl = 24 × 10-6 (Cº)-1; βHg = 1.82×10-4 (°C)-1

Any help on this would be great. I am not sure how to get the final temperature here. I calculated the final temp for Hg only for 1L. Not sure how to include the AL container into the problem. Am I supposed to combine the formulas somehow?

V= V + 3α V Δ T Used for AL container..not sure how to use here

V= V + β V Δ T Used for Hg to figure final temp need to expand to 1 liter.

The Attempt at a Solution



thanks for the help

See attached
 
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heres attachment
 

Attachments

  • TE.jpg
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Related to How Does Mercury Completely Fill an Aluminum Container When Heated?

1. What is thermal expansion and why does it occur?

Thermal expansion is the tendency of matter to expand when heated and contract when cooled. It occurs because as the temperature increases, the particles in a substance gain energy and move apart, causing the substance to expand.

2. How does thermal expansion affect everyday objects?

Thermal expansion can cause everyday objects, such as bridges and roads, to expand and contract with changes in temperature, leading to potential structural damage. It can also cause issues with the accuracy of measurement tools, such as rulers and thermometers.

3. What factors can affect the degree of thermal expansion?

The degree of thermal expansion can be affected by the material properties, temperature change, and the dimension and shape of the object. Different materials have different coefficients of thermal expansion, meaning they will expand and contract at different rates.

4. How is thermal expansion measured and calculated?

Thermal expansion is typically measured by the change in length, area, or volume of a substance with a change in temperature. The coefficient of thermal expansion is calculated by dividing the change in dimension by the original dimension and the change in temperature.

5. How can thermal expansion be controlled or minimized?

Thermal expansion can be controlled or minimized by using materials with low coefficients of thermal expansion, incorporating joints and gaps to allow for expansion and contraction, and using insulation to reduce temperature changes. It is also important to consider the effects of thermal expansion during the design and construction of structures and objects.

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