Coefficient of volume expansion.?

Question

A Glass thermometer contains 1 cubic centimeter of mercury. If the column of Mercury is 0.5mm in diameter what will be the distance that the mercury rises up the tube for a temperature change of 20K? Neglect the expansion of the glass tube.

I know what process to use for this but just cannot do it. Finding it very hard, can anyone do it would be very much appreciated. Thanks :)

Answer 1

I already answered this! But i did notice an arithmetic mistake.

volume expansion of Hg is 0.181 x 10-3 cm³/cm³C

so 1cm³ x 0.181e-3 x 20 = 3.62e-3 cm³

A volume of 3.62e-3 cm³ is what height in the tube.

cylinder

V = πr²h

r = 0.25 mm = 0.025cm

3.62e-3 cm³ = π(0.025)²h

h = 1.843 cm

.

Answer 2

V = volume of bulb resevoir, 1000 mm^3

dH = hight of rise, mm

B = coefficient of expansion of mercury, 0.181 x 10^-3 per degree K

T1 = temperature K, 20

D = diameter of column

dT = change of temperature, C

dH = 4VBdT2/pi D^2

dH = 4(1000)(0.181 x 10^-3)(20)/(0.5^2 pi) =  18.4365 mm