How Does Mercury Completely Fill an Aluminum Container When Heated?

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SUMMARY

The discussion centers on determining the final temperature at which mercury completely fills a 1-liter aluminum container when both substances are heated. The coefficients of thermal expansion are given as αAl = 24 × 10-6 (°C)-1 for aluminum and βHg = 1.82 × 10-4 (°C)-1 for mercury. The user seeks guidance on how to combine the volume expansion formulas for both materials to find the final temperature. The relevant formulas are V = V[i] + 3α V[i] ΔT for aluminum and V = V[i] + β V[i] ΔT for mercury.

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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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