- #1
Beva@371
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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