Help Solving a Volume Expansion Problem

[Miike012]

I have no idea how to solve this problem. I feel like I need more information.

For one the new height of the liquid should depends on the volume expansion of the glass tube. I am not given any dimensions of the glass tube other than it's height.

Therefore if I am to believe that only the height of the tube changes then the change in height of the liquid does not depend on the length of expansion of the tube, it would only depend on the expansion of the cross sectional surface area of the tube, But I am not given such information.

Therefore I believe (if only the vertical height of the tube changes) then I will need to compare the change in vertical height to the change in volume of the liquid.

Anyways, I am lost... someone help.

 

[janhaa]

Maybe you can use this as a manual...

https://www.physicsforums.com/showthread.php?t=369840

 

[Miike012]

Maybe you can use this as a manual...

https://www.physicsforums.com/showthread.php?t=369840

The equation in the thread does not give me the correct answer

(The change in height of liquid in the tube I don't believe equal to the change in volume of the liquid over the new area of the tube, which is what the equation is saying. The change in height of liquid should be equal to the change in volume of liquid over the change in area of tube)

 

[janhaa]

OK, then you can propably use this relation

$h=\frac{V}{A}=\frac{V_o}{A_o}\left(\frac{1+\beta_l \Delta T}{1+2\alpha_g\Delta T}\right)$

so you can try and see if it works out...

 

[paranormal]

Hello,

Thank you for reaching out for help with your volume expansion problem. It sounds like you are on the right track by considering the dimensions of the glass tube and the expansion of its cross-sectional surface area. However, as you mentioned, without more information it is difficult to provide a specific solution.

To accurately solve this problem, we would need to know the initial volume and height of the liquid in the tube, as well as the material and dimensions of the tube itself. This would allow us to calculate the change in volume and height after the tube expands.

In general, when dealing with volume expansion problems, it is important to consider the coefficient of thermal expansion, which is a measure of how much a material expands or contracts with a change in temperature. This coefficient can vary depending on the material, so it would be helpful to know the specific material of the glass tube in order to calculate the change in volume.

I hope this helps guide you in the right direction. If you have any further questions or need more information, please don't hesitate to ask. Best of luck with your problem-solving!