Why Does Turpentine Not Overflow When Heated in an Aluminum Cylinder?

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Homework Help Overview

The problem involves a hollow aluminum cylinder filled with turpentine, examining the effects of heating and cooling on the liquid's volume and potential overflow. The subject area includes thermal expansion and fluid dynamics.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of thermal expansion formulas, questioning the use of linear versus volumetric coefficients for the materials involved. There is confusion regarding the correct approach to calculating the volume changes of both the aluminum cylinder and the turpentine.

Discussion Status

Some participants have clarified the distinction between linear and volumetric expansion coefficients, noting that the solutions manual appears to use different approaches for the aluminum and turpentine. There is ongoing exploration of the implications of these choices on the calculations.

Contextual Notes

Participants are navigating the specifics of thermal expansion coefficients and their application in this context, with some uncertainty about the formulas used in the solutions manual.

Feodalherren
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Homework Statement


A hollow aluminum cylinder 2cm deep has an internal capacity of 2L at 20C. It is completely filled with turpentine and then slowly warmed to 80C.
a) How much turpentine overflows?
b)If the cylinder is then cooled back to 20 C how far below the cylinder's rim does the turpentine recede?


Homework Equations


Vnew=Vold(1+αΔT)^3


The Attempt at a Solution


I'm so confused. I just plugged and chugged into the formula.

It seems that the solutions manual uses the formula for the Al container, getting 2.0087L, which I follow. Then for the turpentine, they just do
2L(1+αΔT)=2.108L
So they do NOT cube it. What am I missing here? Why aren't they cubing the turpentine?
 
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Did they use the volume or the linear expansion coefficient?
 
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Ahh they used linear for the Al and volume for the turpentine. Thanks a bunch!
 
Feodalherren said:
Ahh they used linear for the Al and volume for the turpentine. Thanks a bunch!
They should have cubed for both, unless the used the volumetric coefficient of expansion for aluminum.

Chet
 

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