Another thermal expansion problem

[1MileCrash]

Homework Statement

A vertical glass tube of length L = 1.2800000 is half-filled with a liquid at 20.0000* C. How much will the height of the liquid column change when the tube is heated to 30.0000*C?

Glass linear expansion co = 1e-5/K
Liquid volume expansion co = 4e-5/K

Homework Equations

The Attempt at a Solution

I don't understand why the length of the tube matters other than as giving me the initial height of the liquid. Shouldn't I be given the radius of the tube instead? How far the length of the tube grows has absolutely no effect on how much the height of the liquid changes, but the space within the tube does..

 

[technician]

The circumference of the tube will change. Hope this helps

 

[RTW69]

The length of the tube doesn't matter nor does its radius (cancels out). It looks like you will need to calculate the Δ length the tube and liquid by ΔV/ΔA for each independently. Remember that γ=2α and β=3α. I am guessing that ΔV/ΔA for liquid will be greater than ΔV/ΔA for the tube.

 

[technician]

I got ΔL = 0.14mm. Do you have an answer?

 

[asteriatic]

I would approach this problem by first calculating the initial height of the liquid column using the given length of the tube. Then, I would use the coefficients of linear and volume expansion for glass and the liquid to calculate the change in height of the liquid column. The change in temperature from 20.0000*C to 30.0000*C would also need to be taken into account in the calculations. The length of the tube does play a role in this problem as it determines the initial height of the liquid column, but the radius of the tube would also need to be known in order to calculate the exact change in height. Overall, the problem can be solved by using the relevant equations and taking all necessary factors into consideration.