Calculating Depth of Mercury Column at Higher Temperature

[Beva@371]

Homework Statement

Here is the question:

A glass tube of radius 0.8cm contains liquid mercury to a depth of 64.0cm at 120C. Find the depth of the mercury column at 1000C.Assume that the linear expansion coefficient of the glass is 10X10-6K-1 and the linear expansion coefficient of mercury is 0.61X10-4K-1


3. And here is the solution... But what I don't understand is how the area in bold below was achieved. Every time I do the calculation i arrive at 2.072263 and the answer tells me I should be getting 0.0207! where are the two extra decimal points coming from?

Radius r =0.8 cm
Area of cross section A = πr 2
= 2.0106 cm 2
Depth h = 64 cm
Initial volume V = Ah
= 128.679 cm 3
Initial temperature t = 12 o C
Final temepreature t ' = 100 o C
The linear expansion coefficient of the glass α = 10X10-6K-1
The linear expansion coefficient of mercury α ' = 0.61X10-4K-1
The volume expansion coefficient of the glass γ = 3α
= 30X10-6K-1
The volume expansion coefficient of mercury γ ' = 3α '
= 1.83X10-4K-1
Change in volume of glass dV = Vγ ( t ' - t )
= 0.33971256 cm 3
Change in volume of mercury dV ' = Vγ' ( t ' - t )
= 0.020722466 cm 3
Net change in volume dV" = dV - dV '
= 0.318990094 cm 3
So, Change in length of the column dL = dV" / A
= 0.1586 cm
The depth of the mercury column at 1000C , h ' = h -dL
= 63.84 cm

 

[Daniiel]

88K*1.83X10-4 K-1*128.679 cm 3

0.020722466 cm 3

the question you have written has T 120C and 1000C factor of 10 out from what the solution has

but not a factor of 100.. which is weird

 

[rickz02]

The answer 0.0207 cm^3 doesn't look right to me. Mercury has a higher linear of expansion thus its expansion should be greater than that of the glass. For me 2.07 cm^3 is a more convincing answer. Where did you get that solution anyway?

 

[Beva@371]

It's one of the even numbered questions in the back of my text with no solution so I found that one online. But try as I might (and I'm very new to math and physics so could easily be missing something here) I can't get 1.83 x 10(^-4)(88) 128.56 to equal 0.0207... I get 2.07 and like you said, find the answer really odd.

 

[Beva@371]

Thanks Rickz, I redid the question trusting the 2.07 and got the answer 64.862. I think this is more likely.