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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

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# Homework Help: Trouble with a decimal point

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