Problem involving mercury thermometer

AI Thread Summary
To determine the spacing between the °C marks on a mercury thermometer, the volume expansion of mercury must be calculated using the formula ΔV = βV0ΔT, where ΔT is set to 1°C. After converting 7.5 mL of mercury to mm³, a volume change of approximately 4.0725 mm³ is found. To find the change in height, the cross-sectional area of the thermometer tube (1.2 mm²) must be used to relate the volume change to height. The height change can be calculated by dividing the volume change by the cross-sectional area. This approach will yield the necessary spacing between the °C marks.
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Homework Statement


A mercury thermometer contains 7.5 mL of mercury. If the tube of the thermometer has a cross-sectional area of 1.2 mm2, what should the spacing between the °C marks be? (The volume expansion coefficient for mercury is 1.81 x 10-4 °C−1.)



Homework Equations


ΔV=βV0ΔT

The Attempt at a Solution


I set ΔT = 1, converted the mL into mm3.

I got ΔV = [5.43*(10-4)](7500)(1) = 4.0725 mm3.
However, I don't know what to do with the area!
 
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What do you get if multiply the cross sectional area by the change in height?
 

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