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

$$∆hA=∆V=βV∆T$$

$$πr ^ 2 ∆h=\frac{4\pi R^3}{3}β∆T$$

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

$$∆h=2.58\ cm$$