A mercury thermometer is constructed as
shown. The capillary tube has a diameter
of 0.0045 cm, and the bulb has a diameter of
0.24 cm. Neglecting the expansion of the glass, find
the change in height of the mercury column
for a temperature change of 36 ◦C. The
volume expansion coefficient for mercury is
0.000182 (◦C)^−1
Answer in units of cm.

The change in height of the mercury is approximately  2.981 cm

Explanation:

Recall that the formula for thermal expansion in volume is:

from which we solved for the change in volume due to a given change in temperature

We can estimate the initial volume of the mercury in the spherical bulb of diameter 0.24 cm ( radius R = 0.12 cm) using the formula for the volume of a sphere:

Therefore, the change in volume with a change in temperature of 36°C becomes:

Now, we can use this difference in volume, to estimate the height of the cylinder of mercury with diameter 0.0045 cm (radius r= 0.00225 cm):

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