Thermal expansion of a glass bottle

In summary, a typical mercury thermometer consists of a thin cylindrical tube and a spherical bulb. To find the change in height of the mercury column for a temperature change of 30 degrees, the thermal volume expansions of mercury and glass must be considered. Using the correct units, the volume expansion of mercury can be calculated and subtracted from the expansion due to glass to determine the effective expansion of mercury into the tube. This can then be equated to the volume of a length L in the tube, where L is the desired change in height.
  • #1
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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:

[tex]\Delta[/tex] V = Vexpansion
(V0 + [tex]\Delta[/tex]A) * [tex]\Delta[/tex]h = V0 + V0 * volume expansion value * [tex]\Delta[/tex] Temperature
[tex]\Pi[/tex] *(0.0040 cm/2)2 + [tex]\Pi[/tex] *(0.0040 cm/2)2 * ( thermal expansion of "what material?" * (30 degree) * ([tex]\Delta[/tex] h =( ([tex]\frac{4}{3}[/tex] * [tex]\Pi[/tex] * (0.25cm/2)3 ) + ([tex]\frac{4}{3}[/tex] * [tex]\Pi[/tex] * (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 [tex]\Delta[/tex] h = 3.1cm...

I wonder where did I do wrong? Whcih volume of expansion should I choose?
 
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  • #2
Firstly I assume the volume expansion for glass and mercury are given in the correct units. [here using cm to be consistent with the other units in the question]

You are on the right track...
You start by calculating the volume expansion of the mercury and subtract from it the expansion due to the glass. This gives the effective expansion of the mercury into the tube.
The volume expansion is found by multiplying the original volume by the rise in temperature and the expansion coefficient.
Equate this volume expansion to the volume of a length L in the tube.
Volume in tube is A x L where L is what you want to calculate. A is the cross section area.
 

Related to Thermal expansion of a glass bottle

What is thermal expansion?

Thermal expansion is the tendency of matter to expand or contract in response to changes in temperature.

How does thermal expansion affect a glass bottle?

When a glass bottle is heated, it will expand slightly. This is because the molecules in the glass move faster and take up more space, causing the bottle to increase in size.

What happens if a glass bottle is heated too much?

If a glass bottle is heated too much, it can break due to thermal stress. This is because different parts of the bottle will expand at different rates, causing internal strain and potentially leading to cracks or breaks.

Can thermal expansion be controlled in glass bottles?

Yes, thermal expansion can be controlled in glass bottles by using specialized types of glass that have a lower coefficient of thermal expansion. These glasses are designed to resist changes in size when exposed to temperature changes.

What are some practical applications of understanding thermal expansion in glass bottles?

Understanding thermal expansion in glass bottles is important in industries such as food and beverage packaging, where temperature changes during storage and transportation can affect the integrity of the products. It is also important in the construction of buildings and structures made of glass, as temperature changes can cause stress and potential damage to the glass panels.

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