# Thermal expansion of a glass bottle

A typical mercury thermometer is made up of a thin, cylindrical capillary tube with a diameter of 0.0040 cm, and the spherical bulb with a diameter of 0.25 cm. If we DON'T Neglect the expansion of the glasas, find the change in height of the mercury column for a temperature change of 30 degree.

In the solution, it was given that the thermal volume expansion of mercury = 18 * 10-5 and the thermal volume expansion of glass = 2 x 10-5

## The Attempt at a Solution

I have attempted to solve the problem, however, I don't really know which volume expansion value should I use in the problem.

I have setup:

$$\Delta$$ V = Vexpansion
(V0 + $$\Delta$$A) * $$\Delta$$h = V0 + V0 * volume expansion value * $$\Delta$$ Temperature
$$\Pi$$ *(0.0040 cm/2)2 + $$\Pi$$ *(0.0040 cm/2)2 * ( thermal expansion of "what material???" * (30 degree) * ($$\Delta$$ h =( ($$\frac{4}{3}$$ * $$\Pi$$ * (0.25cm/2)3 ) + ($$\frac{4}{3}$$ * $$\Pi$$ * (0.25cm/2)3 * (volume expansion of "which material" ) * (30 degree)

I have tried to solve with both thermal expansion number, however, I have got 650 cm and 631cm.

The solution of the problem is $$\Delta$$ h = 3.1cm...

I wonder where did I do wrong? Whcih volume of expansion should I choose?