Answer to Question #104962 in Physics for Nyx

Question

A mercury thermometer is constructed as
shown. The capillary tube has a diameter
of 0.0037 cm, and the bulb has a diameter of
0.28 cm. Neglecting the expansion of the glass, find
the change in height of the mercury column
for a temperature change of 41 ◦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

$$∆V=β V∆T$$

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

$$∆h A= ∆V=β V∆T$$

$$\pi r^2∆h=\frac{4\pi R^3}{3}β ∆T$$

$$(0.00185)^2∆h=\frac{4 (0.14)^3}{3}(0.000182)(41)$$

$$∆h=7.98\ cm$$