How Does Mercury Completely Fill an Aluminum Container When Heated?

AI Thread Summary
To determine the final temperature at which mercury completely fills a 1-liter aluminum container when heated, the coefficients of thermal expansion for both aluminum and mercury must be applied. The volume expansion formula for aluminum (V = V[i] + 3α V[i] ΔT) and for mercury (V = V[i] + β V[i] ΔT) should be used to find the temperature at which the volume of mercury equals the volume of the container. The user is unsure how to combine these formulas effectively to solve for the final temperature. Clarification on integrating the thermal expansion calculations for both materials is needed to arrive at the solution.
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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

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