Question

A mercury thermometer is constructed as
shown. The capillary tube has a diameter
of 0.0029 cm, and the bulb has a diameter of
0.12 cm.
∆h
A
T T+∆T
Neglecting the expansion of the glass, find
the change in height of the mercury column
for a temperature change of 33 ◦C. The
volume expansion coefficient for mercury is
0.000182 (◦C)−1
.
Answer in units of cm.

Answer 1

The volume change of the mercury is

$$∆V=βV∆T$$

and it should be equal to the mercury volume in the tube, since we ignore the expansion of the glass

$$∆hA=∆V=βV∆T$$

$$πr ^ 2 ∆h=\frac{4\pi R^3}{3}β∆T$$

$$(0.00145)^ 2 ∆h=\frac{4\pi (0.06)^3}{3}(0.000182)(33)$$

$$∆h=2.58\ cm$$