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Mercury is often used as an expansion medium in a thermometer. The mercury sits in a bulb on the bottom of the thermometer and rises up a thin...

Let's first obtain the volume at both temperatures using the relationship Volume = Mass/Density. 


At 0 degrees C (`V_1`e have:


`V_1` = `(3.250 g)/(13.596 g/(cm^3))` = .2390 `cm^3` ` `


At 25 degrees C (`V_2`e have:


`V_2`  = `(3.250 g)/(13.534 g/(cm^3))` = .2401 `cm^3` 


We will think of the column of mercury inside the capillary as a cylinder. The height of the cylinder is given by the formula


`h = V/(pi * r^2)`


The radius, r, in centimeters is `(0.180 mm) / 2 * (1 cm)/(10 mm)` or .009 cm. Therefore, at 0 degrees, the height is:


`h_1` =`(.2390 cm^3)/(pi*(.009 cm)^2)`  = 939.2 `cm`


` `


At 25 degrees C, the height is:


`h_2 =``(.2401 cm^3)/(pi*(.009 cm)^2) = 943.5 cm`


Subtracting these two, 943.5 cm - 939.2 cm, we obtain a rise in mercury height of 4.3 cm, the final answer. 


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